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Author: 


Wellington,  Arthur  Mellen 


Title: 


The  economic  theory  of 
the  location  of  railways 

Place: 

New  York 

Date: 

1888 


Q}LniZ6-5 


COLUMBIA  UNIVERSITY  LIBRARIES 
PRESERVATION  DIVISION 

BIBLIOGRAPHIC  MICROFORM  TARGET 


MASTER   NEGATIVE  * 


ORIGINAL  MATERIAL  AS  FILMED  -    EXISTING  BIBLIOGRAPHIC  RECORD 


BUSINESS 

530 .65 
W461 


Wellington,  Arthur  Mellen,  1847-1895. 

The  economic  theory  of  the  location  of  railways;  an  analysis 
of  the  conditions  controlling  the  laying  out  of  railways  to 
effect  the  most  judicious  expenditure  of  capital,  by  Arthur 
Mellen  Wellington  ..3i  Rev.  and  enl.  ed.  New  York,  J.  Wilev 
&  sons:  ,otc.,  etc.,^fW.1888* 

XX,  980  p.  Incl.  lllus.,  tables,     fold.  maps,  diagrs.  (part  fold.)    21i« 
1.  Railroads— Location.     2.  Ilallroads— Economics  of  construction. 


Library  of  Congress 

Copy  2. 

Copyright     1887:  11001 


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MAIN  ENTRY:    Wellington.  Arthur  Meilen 


The  economic  theory  of  the  location  of. 


■  ■ 


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THE  LIBRARIES 


School  of  Business 


THE 


Economic  Theory 


OK  THE 


Location  of  Railways. 


IN    PREPARATION 

By  thb  Samb  Author 
la  one  thio  rolumc  of  ordinary  pocket-book  form  and  size 

THE 

FIELD   WORK 

OF 

RAILWAY     LOCATION 

AND 

Laying  Out  of  Works 

ACCORDING  TO  THB 

MOST  RECENT  AND  APPROVED  PRACTICE 
ON  AMERICAN   RAILWAYS. 


In  this  volume  will  be  included  various  formula  and  methods 
never  heretofore  published  for  the  expeditious  and  correct  con- 
duct of  the  mechanical  work  of  location.  It  is  hoped  to  give 
everything  which  is  essential  and  noihinfr  which  is  unessential 
to  a  thorough  understanding  of  the  principles  and  methods  of 
instrumental  field-work,  when  conducted  to  insure  final  excel- 
lence in  the  simplest  way  and  with  due  subordination  to  eco- 
nomic considerations.  The  tables,  while  strictly  limited  to  the 
requirements  of  good  practice,  will  be  an  especial  feature, 
modelled  typographically  on  the  best  German  models. 


THE 


ECONOMIC    THEORY 


OF  THE 


Location  of  Railways 


AN  ANALYSIS  OF  THE  CONDITIONS  CONTROLLING  THE 

LAYING     OUT    OF     RAILWAYS     TO     EFFECT 

THE  MOST  JUDICIOUS  EXPENDI- 

TURE    OF    CAPITAL 


BY 

ARTHUR  MELLEN  WELLINGTON 

M.  Am.  Soc.  C.E. 

I^TE     PRINCIPAL    ASSISTANT    ENGINEER    FOR    LOCATION    AND    SURVEVS    MEXICAN    NATIONAL    RAIL- 

WAV,     ASSISTANT     GENERAL     MANAGER     IN    CHARGE    OF    LOCATION     MEXICAN   CEN- 

TRAL    RAILWAY    AND    CHIEF    ENGINEER    OF    THE   AMERICAN    LINE 

FROM     VERA     CRUZ     TO     THB     CITY    OF     MEXICO 


•For  K  i.  clear  that  in  whatever  it  is  our  duty  to  act.  those  matters  also  it  is  our  duty  to  study." 

•*•'*•    I      \    \  ••/*  '*S  •  -*^R-  Thomas  Arnoli> 

•  *     ••       ,    «•,♦•••••' 

•  .•     ••       ,     ,*•♦•    •••«« 
•  »•  •••    •••••     •     ••••••      » 

•  • :••:•••*'.:•:••.• 

THIRD  revised;  ^'pipiEjiltA^Gfij^  ClilTION  ''* 


•  •        t      •       , 

•  •   ••      *   • 


*    • 


«    •• 


•  • 


NEW  YORK 


/  'ii 


John  Wiley  &  Sons 
15  AsTOR  Place 

London 


Engineering  News 
Tribune  Building 
)N 


WAL 


(fsL^A.Q^*^.^^''*-*^ 


J)5'30,66 


y   Ti 


'\\ 


Copyright, 

1887, 
0v  A.  M.  WELLINGTON. 


•   •     • . 


• «    • 


'  • 


«  « 

•    *      ! 
•       »      • 


i        «       .         •       • 

(     *       «  t    «       «  • 


Electrotypera, 
New  York. 


r* 

Ci 


TO  THE 
GREAT  MEN  OF 
A  FORMER  GENERATION, 
WHO  ORIGINATED  THE  AMERICAN 
RAILWAY  SYSTEM,  THIS  ATTEMPT  TO  IM- 
PROVE   UPON    THEIR    PRACTICE   IS   ADMIRINGLY 
INSCRIBED,    IN    TOKEN    OF    RESPECT 
FOR    THEIR    FAR-SIGHTED 
SAGACITY  AND  STILL 
UNEQUALLED 
SKILL. 


PREFACE. 


Only  in  a  very  figurative  sense  can  this  book  be  said  to  be  a  "  revised 
edition"  of  the  little  volume  under  the  same  title  which  the  writer  pub- 
lished ten  years  ago.  The  substance  of  the  old  book  remains  unchanged, 
so  far  as  it  went,  but  every  page  and  sentence  has  been  rewritten,  except 
the  dedication.  The  most  important  change  in  the  nature  of  an  addition 
is  the  much  greater  attention  given  to  traffic  and  revenue  questions, 
which  are  particularly  likely  to  be  underrated  or  forgotten.  The  mechan- 
ics of  curve  resistance  have  been  discussed,  it  is  hoped,  more  adequately 
than  heretofore,  and  on  a  more  solid  basis  of  experimental  fact,  with  some 
important  practical  questions  which  depend  thereon.  The  theory  of  the 
-effect  of  variations  in  velocity  on  the  motion  of  trains  is  an  entirely  new 
addition,  supplying  one  of  the  most  important  omissions  of  the  former 
■edition  and  of  other  engineering  text-books.  The  theory  of  various  de- 
tails of  the  locomotive,  which  did  not  seem  to  have  been  elsewhere  ade- 
•quately  discussed  for  the  purposes  of  this  volume,  has  been  given,  it  is 
hoped,  more  fully  and  correctly  than  heretofore.  Parts  IV.  and  V.  are 
entirely  new. 

On  the  other  hand,  the  new  edition  has  been  abbreviated  by  omitting 
the  discussions,  some  thirty  in  all,  where  reasons  why  the  writer  felt  com- 
pelled to  differ  from  some  previously  published  conclusions  or  estimates 
were  given  in  deta.:!.  This  seemed  necessary  ten  years  ago,  but  at 
present  it  appeared  as  if  the  space  might  be  better  used. 

The  number  of  engravings  has  been  increased  from  half  a  dozen  to 
313,  the  number  of  pages  from  216  to  950,  and  the  number  of  tables  from 
44  to  204.  All  of  the  tables,  with  a  few  exceptions  noted  in  connection 
with  each,  are  original  computations  of  the  writer  or  compilations  from 
original  sources  of  information.  As  practically  all  the  work  of  prepar- 
ing them,  and  of  rewriting  the  text,  has  been  done  outside  of  those  hours 
which  are  ordinarily  and  more  rationally  regarded  as  working  hours,  a 
long  delay  in  republication  has  been  unavoidable  ;  but  if  there  be  truth 


Vlll 


PREFACE, 


enough  in  the  old  antithesis  of  "easy  writing"  and  "curst  hard  reading 
to  hold  good  when  twisted  wrong  end  to.  there  should  be  some  com- 
pensation in  store  for  any  reader  who  may  have  chanced  to  be  annoyed 

^^  In^rdeTto  adapt  the  volume  to  the  more  convenient  use  of  all  classes 
of  readers,  three  sizes  of  type  have  been  used  : 

Long  Primer  type  is  used  for  those  parts  of  the  volume 
which  were  deemed  most  likely  to  be  such  as  every  interested 
reader  would  wish  to  read,  including  those  who  desire  only  to 
ascertain  the  more  important  conclusions,  free  from  technicali> 

ties. 

Bourgeois  type  is  used  for  discussions  which  relate  more  to  the  details 
of  the  subject  than  to  principles,  and  hence  may  be  passed  over  by  those 
who  are  not  engineers,  or  who  are  ready  to  take  the  reasons  for  what  ,s 
Printed  in  larger  type  for  granted.  Nevertheless,  much  of  the  matter 
E  is  printfd  in' his  smaller  type,  as  for  instance  the  long  chapter  on- 
The  locomotive  engine  and  the  whole  of  Part  V..  is  among  the  most  im- 
portant in  the  book  for  the  professional  engmeer. 

BREV1E1  type  is  used  for  minor  notes  and  comments  which  it  seemed  essen- 
dal  or  dcsimbk  to  give,  as  of  much  possible  importance  to  those  w.shmg  to  look 
t:i^:::Z^orso;..  ,.n^cu^.r  branch  thereof,  with  still  greater  care,  but 
which  might  otherwise  be  passed  over. 

The  mathematical  form  of  discussion  has  been  intentionally  avoided 
first  because  the  boolc  has  been  written  for  practical  men  as  well  as  for 

rre«r.c^^^^^^^^^^^^ 

^rta^fixtd  premises,  mathematical  methods  furnish  i-aluable  w.ng* 
for  flyingover  tntermediate  obstructions ;  but  whenever  the  ch.ef  d,ffi- 

lu  ty  o"  a  problem  lies  in  the  multiplicity  and  ^f -»"^;  "'/"^  P^^™; 
cuiLy  v^i      F  r#»rnncilinff  them  with   each    other,   there   is 

the  writer  will  not  attempt.  ,.orr^rt 

To  fullv  set  forth  in  any  one  volume  these  premises  for  the  correct 

Uyilg  ou"^f  railways,  which''  ^'^^^^^^^^Z:^'^:^ 
their  construction,  operation,  and  finances,  ana  vary  m  cac 


PREFACE. 


IX 


l>e  impossible.  The  purpose  in  view  has  been  merely  to  give  between 
the  covers  of  one  book  whatever  was  necessary  for  some  approach  to  a 
correct  solution  of  every  probable  problem,  which  could  not  be  found 
in  other  publications.  This  necessarily  led  to  a  large  book,  since  this 
work  still  remains  the  only  one  on  its  subject  in  the  language.  Sev- 
eral of  a  somewhat  similar  nature  have  appeared  in  French  and  German 
since  the  first  edition  of  this  work  was  published,  but  from  difference  of 
•operating  conditions,  and  their  profuse  use  of  mathematics,  the  resem- 
blance is  not  close. 

The  word  "ton"  in  this  volume  means  2000  lbs.,  unless  otherwise  ex- 
plicitly stated. 

.  The  term  "  velocity-head "  has  been  borrowed  from  hydraulics  to 
•designate  a  somewhat  different  thing,  which  heretofore  has  had  no  name 
at  all.  The  "  velocity- head  "  of  hydraulics  and  of  this  volume  are  closely 
related  but  not  identical,  and  should  not  be  confused. 

Grades  have  been  designated  for  the  most  part  by  their  rate  per  cent 
and  not  by  their  rate  per  mile,  in  accordance  with  an  increasing  custom 
which  may  well  become  universal,  as  the  more  rational.     The  approxi- 
mate rate  per* mile  is  given  at  once  by  multiplying  the  per  cent  by  50 
(52.8). 

Owing  to  the  great  number  of  tables,  and  the  probability  that  others 
might  be  added  in  future  editions,  it  was  impossible  to  even  attempt  to 
refer  in  the  text  to  all  those  which  contained  a  given  class  of  information. 
To  insure  doing  this  reference  must  be  had  to  the  Index,  which  it  has 
been  endeavored  to  make  very  complete. 

Most  of  the  computations  of  percentages,  costs  per  mile,  and  the  like. 
in  this  volume,  were  made  with  a  slide-rule— an  instrument  too  little 
known  and  used  by  engineers.  Hence  many  errors  of  i  or  2  in  the 
third  digit,  or  of  one  or  two  tenths  of  one  per  cent,  probably  exist,  but. 
it  is  hoped,  few  of  a  more  serious  nature.  The  admirable  computing 
instrument  of  Mr.  Edwin  Thacher.  which  would  have  insured  greater 
accuracy  with  but  little  more  trouble,  was  secured  by  the  writer  too  late 
to  be  of  much  service. 

The  author  will  be  at  all  times  pleased  to  receive  corrections  of  typo-* 
graphical  or  other  errors,  or  supposed  errors,  extensions  of  any  of  the 

tables,  or  other  similar  matter. 

A.M.  W. 

Tribune  Building,  New  York.  May,  1887. 


mmmM-^-tpr- 


PREFACE  TO  THE  FIRST  EDITION. 


The  investigation  of  which  this  volume  is  the  fruit  had  its  origin  in 
the  preparation  of  a  few  notes  for  an  anticipated  location,  and  has  since 
gradually  expanded  into  a  single  magazine  article,  a  short  series  of 
papers,  and  at  last  into  a  volume.  Even  the  latter  has  been  expanded 
far  beyond  the  writer's  original  intention  by  the  close  and,  it  is  to  be 
feared,  tedious  attention  to  detail  which  he  found  continually  more 
needful ;  and  it  is  kept  within  its  present  dimensions  only  by  excluding 
considerable  matter  and  superficially  considering  or  neglecting  altogether 
a  number  of  subjects  which  the  writer  deems  of  real  importance  for  the 
correct  conduct  of  location.  In  the  improbable  event  that  the  sale  of 
this  volume  should  justify  a  thorough  revision  at  some  future  day,  he 
hopes  to  produce  one  more  in  keeping  with  the  professional  interest  and 
importance  of  the  subject,  by  rectifying  the  faults  of  omission  and  com- 
mission which  he  clearly  perceives. 

The  writer  does  not  intend  to  imply,  however,  that  he  has  fallen  into 
unacknowledged  errors  of  fact  or  theory.  All  known  errors  have  been 
frankly  corrected  as  soon  as  discovered.  For  such  others  as  may  prob- 
ably exist  the  writer  can  only  hope  that  they  will  be  regarded  with 
that  leniency  which  an  exploration  of  a  neglected  field  of  labor  may 
fairly  ask.  For  such  the  present  volume  is,  with  all  its  imperfections. 
A  recognition  of  the  value  of  previous  discussions  of  the  same  subjects 
would  be  a  more  welcome  duty;  but  the  writer  deems  it  but  simple 
justice  to  himself  and  his  readers  to  declare  frankly  that,  so  far  as  his 
knowledge  extends  and  he  is  competent  to  judge,  all  of  the  few  existing 
discussions  of  the  various  leading  topics  of  this  volume  are  so  superficial 
or  so  imperfect  in  method  as  to  have  little  or  no  value  as  a  guide  for 
location.  Some  of  them  express  correct  views,  and  some  of  them  will 
sometimes  give  correct  results ;  but  none  of  them  are  trustworthy,  and 
several  of  those  which  are  given  under  distinguished  names  are  incredi- 
bly defective.     The  various  problems  of  location,  in  fact,  have  been  dis- 


ill 


.'^V\ 


I 


XII 


PREFACE    TO    THE  FIRST  EDITION. 


cussed  or  neglected  by  technical  writers  with  an  airy  lightness  wh.ch 
would  convince  a,,  unskilful  reader  that  they  were  either  too  simple  or 
too  unimportant,  or  too  well  understood,  for  any  careful  analysis.  And 
vet  there  is  no  field  of  professional  labor  in  which  a  limited  amount  of 
modest  incompetency,  at  $150  per  month,  can  set  so  many  picks  and 
shovels  and  locomotives  at  work  to  no  purpose  whatever. 

As  a  natural  consequence  of  this  general  negligence,  all  our  railways 
are  uneconomically  located,  most  of  them  in  respect  to  their  genera! 
route  and  system  of  gradients,  and  all  of  them  in  respect  to  the  minor 
details  of  alignment,  and  in  many  cases  these  errors  are  shockingly 
evident    ...  In  the  care  taken  in  this  respect  we  are  not  advancing 
beyond,  but  rather  falling  below,  the  standard  set  up  forty  years  ago 
when  the  art  of  designing  railways  started  out  in  this  ^°""i;;y  «'''>  ="^^ 
brilliant  promise.     The  works  of  Latrobe  and  Jervis  and  Thomson  and 
Whistler  show  a  truly  remarkable  ability,  considering  their  early  day. 
and  bear  the  clearest  marks  of  original  and  self-reliant  thought :  but  the 
ereat  men  of  that  earlier  day  have  no  successors;  for  we  have  done 
nothing  but  copy  them  ill  ever  since,  and  a  copyist  is  not  a  successor. 
We  copy  their  errors,  but  we  do  not  copy  that  admirable  habit  of  per- 
sonal investigation  and  far-sighted  intellectual  courage  which  created 
precedents,  and  has  made  the  work  of  their  hands-in  despite  of  many 
faults— the  high-water  mark  of  American  locating  skill. 


/ 


.4- 


^onalS^ 


CONTENTS. 


Introduction, 


PAGE 
I 


PART  I. 

ECONOMIC   PREMISES. 

^^'1.  The  Inception  of  Railway  Projects  and  Conditions 

governing  it '^ 

II.  The  Modern  Railway  Corporation 28 

III  The  Nature  and  Causes  connected  with   Location 

which  modify  the  Volume  of  Railway  Revenue,    .    48 
IV.  The  Probable  Volume  of  Traffic  and  Law  of  Growth 

therein '^ 

V.  Operating  Expenses ^^ 

[Maintenance  of  Way.  118;  Fuel,  132;  Repairs  of  Engines, 
139;  Repairs  of  Cars,  160;  Train-wages,  etc.,  168;  Summary, 
180] 

PART  II. 

THE  MINOR. DETAILS  OF  ALIGNMENT 

VI.  The  Nature  and  Relative  Importance  of  the  Minor 

Details  of  Alignment '^5 

VII.  Distance •    •    •  ^95 

[Effect  on  Operating  Expenses,  198;  Effect  on  Receipts,  211; 
Law  as  to  Connections,  219;  Moral  Effect  of  Short  Line,  239.] 

VIII.  Curvature ;    *  '^^'^ 

[Danger  of  Accident.  245:  Statistics  of  Curvature,  259;   Diffi- 
culty in  Making  Time,  26S;  Effect  on  Smooth  Riding  of  Cars,  275 ; 


fr,:nT-r--'mt 


m 


m 


xiv  CONTENTS. 

PAG* 
CHAP. 

Moral  Effect  to  deter  Travel,  276;  Effect  to  obstruct  the  use 
of  Heavy  Engines,  278;  Mechanics  of  Curve  Resistance,  281; 
Rail-sections,  307;  Effect  on  Operating  Expenses,  313;  Long 
Tangents,  324.] 

IX.  Rise  and  Fall 327 

[Classes  of.  330;  Laws  of  Accelerated  and  Retarded  Motion, 
331;  Virtual  Profiles,  346;  Safe  Limits  of  Undulations  of  Grades, 
356;  Limits  of  Classes.  366;  Effect  on  Operating  Expenses,  375; 
Estimating  Amount  of,  384;  Vertical  Curves,  385.] 

PART  III. 
LIMITING  GRADIENTS  AND   CURVATURE. 

X.  The  Relative  Importance  of  Gradients 39? 

XL  The  Locomotive  Engine 399" 

[Tables  of  Standard  Dimensions,  407;  Running-Gear,  421; 
Tractive  Power,  434;  The  Locomotive  Boiler,  449;  The  Cylin- 
der Power,  457;  Theoretical  Gain  by  Expansion,  467;  Causes 
of  Loss  of  Efficiency,  470.J 

XII.  Rolling-Stock 485 

XIII.  Train  Resistance 49^ 

[Freight-Train  Resistance,  496;  Starting  Resistances,  511; 
Effect  of  Size  of  Wheel  and  Axle,  513;  Velocity  Resistances, 
517;  Train  Resistance  Table,  524;   Engine  Friction,  530.] 

XIV.  The  Effect  of  Grades  on  Train-Load 53^ 

[Table  of  Capacity  of  all  Engines  on  all  Grades,  544;  Percent- 
age of  Change  in  Net  Load  from  a  Change  in  any  Grade,  554  ] 

XV.  The  Effect  of  Train-Load  on  Operating  Expenses,    560 

[Cost  of  Increasing  Weight  of  Engines,  560;  Cost  of  Increas- 
ing Number  of  Engines,  568;  Proportion  of  Traffic  affected  by 
Rate  of  Ruling  Grade.  576;  Effect  of  a  Difference  in  Ruling 
Grade,  on  the  Cost  of  Distance,  Curvature,  and  Rise  and  Fall, 
581.]  ' 

XVI.  Assistant  Engines, •    •  5^5 

[Power  of  Assistant  Engines,  591;  Duty  of  Assistant  Engines, 
598;  Cost  of  Assistant   Engines,  601;   Comparison  of  Pusher 
Grades  with  Uniform  Gradients,  604.] 
XVII.  The  Balance  of  Grades  for  Unequal  Traffic,     .    .  608: 
XVIII.  Limiting  Curvature  and  Compensation  therefor,    .  620 


CONTENTS. 


XV 


PAGE 
CHAP.  r 

XIX.  The  Limit  of  Maximum  Curvature, o35 

[The    Inherent   Costliness  of   Sharp    Curvature,  638;   The 
Limiting  Effect  of  Curvature,  645.] 

XX.  The  Choice  of  Gradients,  and   Devices   for  Re- 

ducing Them, "59 

[How  to  Project  Low  Grades.  660;  How  to  Project  Pusher 
Grades;— Easy  Gradients,  666;  Heavy  Gradients,  669;  Expe- 
dients for  reducing  the  Rate  and  Cost  of  High  Grades,  675; 
Great  Inclines  of  the  World,  699.] 

PART   IV. 

LARGER  ECONOMIC  PROBLEMS. 

XXI.  Trunk  Lines  and  Branch  Lines, ^    -  707 

[Law  of  Geometric  Increment  of  Traffic,  708;  Trunk  Lines, 
Non-Competitive,  718;  Competitive  Trunk  Lines,  723; 
Branch  Lines,  73I-] 

XXII.  Light  Rails  and  Light  Railways, 737 

[Rails,  737;  Expedient  Economies,  748;  Rails  and  Track 
Labor,  758.] 

XXIII.  The  Economy  of  Construction 762 

[Least  harmful  Economies,  764;  Most  harmful  Economies, 
768;  Cross-ties,  775;  Storms  and  Structures,  781.] 

XXIV.  The  Improvement  of  Old  Lines, 78s 

[Usual    Defects,    787;    Constructing  Virtual  Profile,  798; 
Remedying  Defects,  799.] 

XXV.  Grade  Crossings  and  Interlocking 809 

•    XXVI.  Terminals, ^^^ 

PART  V. 
THE  CONDUCT  OF  LOCATION, 

XXVII.  The  Art  of  Reconnaissance 831 

XXVIII.  Ocular  Illusions 843 

XXIX.  When  to  make  Surveys 856 

XXX.  The  Field-work  of  Surveys 860 

XXXI.  Topography:  its  Uses  and  Abuse, 874 

'  XXXII.  Mapping  and  Projecting  Location 886 

XXXIII.  The  Estimation  of  Quantities, 895 


iliii 


XVI 


CONTENTS. 


-CHAP. 


APPENDICES. 

PAGB 

A.  Experiments  on  the  Resistances  of  Rolling-Stock,    .    .  909 

B.  Experiments  with  New  Apparatus  on  Journal  Friction 

AT  Low  Velocities, 9»3 

C.  The   American   Line  from   Vera  Cruz  to   the  City  of 

Mexico  via  Jalapa.  with  Notes  on  the  Best  Methods 
OF  surmounting  High  Elevations  by  Rail 925 

[The  usual  List  of  Tables  is  omitted,  as  too  voluminous.  The 
tables  and  engravings  are  separately  indexed  at  the  back  of  the 
book.] 


9! 


INDEX 


TO  THE  MORE  IMPORTANT 

RULES,   TABLES,  FORMULA,   AND   FINAL    CONCLUSIONS. 

WHICH   MAY   BE   NEEDED 

FOR  IMMEDIATE  APPLICATION. 


<•  It  may  be  ^marked  that  it  was  no  part  of  the  purpose  of  thisvolume  to 
fumi  h  a  collection  of  mere  rules,  professing  to  require  only  an  ab.Uty  to 
rd  tor  their  successful  application.     Rules  can  seldom  be  sa^eyappUed 
wTthou.  a  clear  understanding  of  the  principles  on  wh.ch  ^ey  rest_ 

_J.  B.  Henck,  Preface  to     Field-Book. 


r  This  MX  has  purposely  b»n  ,nade  and  kept  as  brief  as  possible  It  HAS  no 
CROsfREFERENCES  NOR  DOO«LE  REFERENCES.  For  anything  not  found,  see  Gen- 
Z^nZuZ  the  subjoined  references  are  repeated,  and  for  the  n,ost  part  .n 
SMALL  capitals.] 


Assistant  Engines- 
Advantages 

Balance  of  grades  for 

Cost  of  service 

vs.  Uniform  grades 

Projecting  .  • 

Branch  Lines- 
Rules  for  laying  out 

Cable  Railways 

Choice  between  close  lines 

Construction- 
Order  of  expedient  economies 

Worst  errors  in 

Curvature- 
Compensation  for 


PAGE 

593 
602- 

604 
,     666 

733-6 
.     686 

.     583 

.     764 
.     76S 

.     632 


xviu 


INDEX   TO   CONCLUSIONS 


FOR  IMMEDIATE  APPLICATION 


XIX 


%  i: 


ii 


if 


Curvature- 
Effect  on  accidents 

"        expenses 

"        use  of  heavy  engines 

"         making  time 

"        smooth  riding  of  cars 
Maximum  limit  of 
Moral  effect  of 

Curve  Resistance- 
Conclusions  as  to  *  • 

Dead  Weight- 
Passenger,  why  tends  to  increase 

Distance— 

Effect  on  competitive  receipts 

••        non-competitive  receipts 
••        expenses 
Increasing,  to  secure  more  traflBc 
Law  as  to  connections      .  • 

Moral  effect  of  short  line 
Freight-Train  Speed  . 

Grade-Crossings- 

And  interlocking  .  .  • 

Crades-  ^        ,, 

Balance  of,  for  unequal  traffic,  table 

Effect  on  passenger  traffic 

'*        train-load,  law  as  to 
General  law  for  choosing 
How  to  reduce  in  easy  country 
Pusher  grades,  pros  and  cons 
Relative  importance  of  gradients 
Train-load  on  all  grades,  table 
Trains  affected  by  grades 
Value  of  reducing  grades 

Crowth  of  Traffic- 
Geometric  law  as  to 
Proper  allowance  for 

Inclined  Planes 

Light  Railways- 
Proper  direction  for  economy 

Location— 

A  priori  basis  for 
General  law  for  good 


for 
example 


PACK 

.     258 

.     321 
.     281 

.  274 

.  275 

.  653 

.  277 

.     304 

.     567 

.     228 

234-6 
.  209 
.  238 
.  219 
.     240 

.  371 
.    811 

.  185 
.     580 

554-6 
,  660 
.  665 
.    669 

.  396 

.  546 

.  576 

.  572 

.    715 
80-86 

.    686 
.    761 

.      18 
.     660 


and  Rise  and 


Locomotives- 
Adhesive  traction  limits  . 

Dimensions,  etc.   . 

Train-load  on  all  grades  . 

Long  Tangents- 
Value  of     .  .  • 

Mapping  Surveys 

Minor  Details-(Distance,  Curvature 
Comparative  importance 

Narrow  Gauge 

Old  Lines- 
Best  manner  of  improving 

Usual  defects  to  be  corrected 

Operating  Expenses- 
Percentages  .  . 

Rails- 
Proper  form  of     .  • 

**      weight  of  • 

Reconnaissance- 
Choice  of  lines  to  survey 

Fundamental  rule  for 

Revenue— 

Per  head  of  population     . 

Rise  and  Fall- 
Effect  on  operating  expenses 

Estimating  amount  of 

Limits  of  classes  . 

Safe  limits  for 

In  grade-lines,  to  what  extent  admissible 

Superelevation- 
Proper  rule  for     .  •  •  • 

Surveys- 
Choice  of  lines  to  run       .  •  • 

Switchbacks— 

For  thin  traffic  and  great  inclines 

Termini- 
Location  of  .  •  •  • 

Topography-  .  , 

(Physical  geography).  Harmonizing  Ime  wiin 

(Mapping),  Its  uses  and  abuse     . 

Towns- 
Loss  from  not  going  to    . 


Fall.) 


PAGE 

•     437 
407-10 

.     544 

.     324 

.     888 

.     186 
.     751 

.     808 

.     788 

.     179 

.     308 
747.  761 

.     857 
.     835 

.     104 

.     381 

.     384 

.     374 

363-8 

.     368 

.     301 

.     860 

.     950 
.       67 

.     655 

.     880 

.  63-4 


XX 


INDEX   TO   CONCLUSIONS. 


Traffic- 
How  to  estimate  the  probable  volume  o 

Train-mile— 

Cost  by  items        .  ,  , 

Train  Resistance- 
Freight,  amount    . 

Passenger,  amount 

Trunk  Lines- 
Competitive,  conditions  of  success 

Non-competitive,  rule  for  laying  out 

Valley  Lines— 

And  inundations  .  .  , 

Merits  of,  for  railway  lines 

Valleys- 
Descending  into    .  •  • 

Vertical  Curves- 
Laying  out  .  •  • 

Length  of  .  .  •  , 

Virtual  Profile- 
Nature  and  use  of  .  • 


PACE 

86,  95-102 

.     179 

.     502 
.     518 

.     731 
.     720 

.     783 
.     850- 

.     682 

.     387 
.     36s 

346,  351.  354 


{ 


\ 


f  i 


/i' 


-S' 


llOWh^^ 


^^^ 


THE  ECONOMIC  THEORY  OF  THE 
LOCATION  OF  RAILWAYS. 


INTRODUCTION. 

As  the  correct  solution  of  any  problem  depends  primarily  on 
a  true  understanding  of  what  the  problem  really  is,  and  wherein 
lies  its  difficulty,  we  may  profitably  pause  upon  the  threshold  of 
our  subject  to  consider  first,  in  a  more  general  way  its  real 
nature;  the  causes  which  impede  sound  practice  ;  the  condi- 
tions on  which  success  or  failure  depends  ;  the  directions  in 
which  error  is  most  to  be  feared.  Thus  we  shall  more  fully  at- 
tain that  great  prerequisite  for  success  in  any  work-a  clear 
mental  perspective,  saving  us  from  confusing  the  obvious  with 
the  important,  and  the  obscure  and  remote  with  the  un.m- 
portant. 

It  would  be  well  if  engineering  were  less  generally  thought 
of,  and  even  defined,  as  the  art  of  constructing.  In  a  certain  im- 
portant sense  it  is  rather  the  art  of  not  constructing  ;  or,  to  de- 
fine  it  rudelv  but  not'inaptly,  it  is  the  art  of  doing  that  well 
with   one   dollar,  which   any  bungler  can   do  with    two  after  a 

fashion.  ,         ^  •         • 

There  are,  indeed,  certain  great  triumphs  of  engineering 
genius-the  locomotive,  the  truss  bridge,  the  steel  rail-which  so 
rude  a  definition  does  not  cover,  for  the  bungler  cannot  attempt 
them  at  all ;  but  such  are  rather  invention  than  engineering 
proper.     There  is  also  in  some  branches  of  engineering,  as  w 


mrRODUCTION. 


INTRODUCTION, 


bridge-building,  a  certain  other  sic^e  to 'it,  not  covered  by  such  a 
definition,  which  consists  in  doing  that  safely,  at  some  cost  or 
other,  which  the  bungler  is  likely  to  try  to  do  and  fail.  He 
therefore,  in  such  branches,  who  is  simply  able  to  design  a  struc- 
ture which  will  not  fall  down,  may  doubtless  in  some  measure 
be  called  an  engineer,  although  certainly  not  one  of  a  very  high 

tvpe. 

But  to  such  engineering  as  is  needed  for  laying  out  railways, 

at  least,  the  definition  given  is  literally  applicable,  for  the  eco- 
nomic problem  is  all  there  is  to  it.    The  ill-designed  bridge  breaks 
down  ;  the  ill-designed  dam  gives  way  ;  the  ill-designed  boiler 
explodes;    the   badly  built   tunnel  caves   in,  and  the   bungler's 
bungling'is  betrayed.     But  a  little  practice  and  a  little  study  of 
field    geometry  will    enable   any   one  of   ordinary    intelligence, 
without   any   engineering   knowledge    whatever   in    the   larger 
sense,  to  lay  out  a  railway  from  almost  anywhere  to  anywhere, 
which  will  carry  the  locomotive  with  perfect  safety,  and  perhaps 
show  no  obtrusive  defects  under  what  is  too  often  the  only  test- 
inspection   after  construction  from  the  rear  end  of  a  palace-car. 
Thus,    for   such    work,  the    healthful    checks  which    reveal   the 
bungler's  errors  to  the  world  and   to  himself  do  not  exist.     Na- 
lure,  unhappily,  has  provided   no  way  for  the  locomotive— like 
Mr.   Jingle's  intelligent  pointer— to  refuse  to  pass  over  an   ill- 
designed  railway  as  it  refuses  to  pass  over  an  ill-designed  bridge. 
Therefore,  since  there  is  no  natural  line  between  safety  and 
danger  to  mark  even  so  rude  a  distinction  as  that  between  the 
utterly  bad  and  the  barely  tolerable,  in  the  kind  of  engineering 
work  we  are  to  study,  one  may   fairly  say  that  the  locating  en- 
gineer has  but  the  one  end  before  him  to  justify  his  existence  as 
such— to  get  the  most  value  for  a  dollar  which  nature  permits  ; 
and  but  one  failure  to  fear— that  he  will  not  do  so.     Except  as 
his  work  necessarily  involves  the  preliminary  design  of  construc- 
tive details,  he  has  no  lives  to  save  or  imperil ;  and  the  young  en- 
gineer cannot  too  early  nor  too  forcibly  iiave  it  impressed  upon 
his  mind  that  it  takes  no  skill  worth  speaking  of  to  do  such  work 
after  a  fashion,  unless  in  the  comparatively  few  localities  (rare  in- 


<leed  in  the  United  States)  where  to  get  a  reasonable  line  of  any 
kind  is  something  of  a  fe^i  His  true  function  and  excuse  for 
being  as  an  engineer,  as  distinguished  from  a  skilled  workman, 
begins  and  ends  in  comprehending  and  striking  a  just  balance 
beuveen  topographical  possibilities,  first  cost,  and  future  reve- 
nue and  operating  expenses.  . 

While  this,  in  a  certain  sense,  is  peculiar  to  the  branch  of  en- 
gineering we  are  to  study,  yet  a  curiously  close  analogy  may  be 
drawn,  tending  to  show  tliat  it  is  as  essentially  true  of  all  other 
branches  of  engineering  as  of  this.     For  example,  it  is  beyond 
doubt  that  the  true  reason  for  the  striking  progress  in  bridge- 
building  in  recent  vears  has  been,  not  that  men  have  been  driven 
into  excellence  by  "the  responsibility  of  human  life"  resting  on 
them  —for  after  the  types  have  once  been  invented,  a  relatively 
low  oider  of  engineering  skill  suffices   to  reduce  that  risk  alone 
to  a  minimum.     But  the  impelling  force  has  been  the  keen  com- 
petitive struggle  to  bring  the  first  cost  of  every  bridge  as  low  as 
possible  and  yet  do  nothing  which  shall  injure  its  permanent 
^fficiencv  and  compel  it  to  be  speedily  rebuilt ;  nothing,  in  other 
words   which  shall    increase  the  future  "  maintenance  and  oper- 
ating expenses."     But  whereas  the  "  operating  expenses"  of  bad 
bridge-engineering  come    in  a  series  of  startling  catastrophes 
which  shock  the  community  and  dismay  the  moneyed  interests 
concerned,  causing  good  work  to  be  appreciated  and  insisted  on, 
and   scaring  off   the  amateurs  and   'prentice  hands  from  -med- 
dling and  muddling,"  after  the  manner  of  their  kind,  the  operat- 
ing expenses  from  bad  railway  location  come  by  a  gentle   but 
unceasing   ooze   from    every  pore  which    attracts   no   attention, 
albeit    resulting  in  a  loss  vastly  larger  than  any  possible   loss 
from  bad  construction  ;  for  it  requires  some  training  and  experi- 
ence even  to  appreciate   the  loss  as  existing,  and  still  more  of 
both  to  appreciate  it  as  remediable.     In  fact  no  one  can  do  so, 
except  in  the  most  general  way,  without  special  investigation  of 
each   special  case.     Errors  which,  even   if  committed,  are    not 
likely  to  be  discovered,  are  rarely  much  feared,  and  at  last  the 
-consciousness  that  there  is  danger  of  error  becomes  dulled. 


ill 


INTRODUCTION. 


IN  TROD  UCTION. 


il 


In  these  facts  we  have  plain  reasons  why  average  practice  in 
laving  out  railways  should  inevitably  tend,  as  it  does  tend,  to  be 
and  remain  of  a  low  grade.  It  is  not  difficult,  in  fact,  to  see 
reasons  why  it  can  never  well  be  otherwise,  except  m  degree, 
unless  the  progress  of  science  should  wholly  change  the  nature 
of  the  work  ;  and  a  correct  appreciation  of  how  great  is  this 
danger,  and  why  it  exists,  will  greatly  help  to  save  the  student 

from  it.  «... 

The  permanent  difficulty  lies  in  this  :  High  efficiency  in  any 

art  or  calling  in  which  many  minds  of  no  phenomenal  gifts  are 

engaeed  requires  that  every  man's  work  should  be  readily  com- 

parable  either  with  a  certain  uniform  standard  or  with  the  work 

of    his    fellows.      In   constructive    engineering    this    is    possible. 

Broadly   speaking,   a   hundred-foot    bridge    is   a   hundred-foot 

bridge,  tlie  world   over.     It  has   everywhere    to    fulfil  but   twa 

primary  conditions  :  It  must  carry  a  certain  nearly  uniform  load 

per  foot,  and  it  must  not  fall  down.     The  same  is  in  substance 

irue  of   every  form   of  constructive   engineering.     Every  man  s 

practice  therein,  therefore,  is  comparable,  and  is  compared   wMtb 

the  highest  level  of  practice,  the  world  over.     Those  most  highly 

skilled  are  discovered  and  recognized.     The  moderately  ski   ed 

perceive  and  correct  their  deficiencies.     The  hopelessly  unskilled 

retire  to  other  pursuits.  .      ,     .  ,. 

In  laying  out  railway  lines,  and  less  strikingly  in  some  other 
analogous  kinds  of  engineering  work,  this  is  forever  impossible. 
We  cannot  reduce  the  laws  of  topography,  nor  even  of  finance,  to 
equations  and  formula.     Every  line  is  a  problem  by  itself,  with 
its  own  peculiar  phvsical  and  commercial  conditions,  so  that  the 
engineer  is  deprived   of  the  aid  to  be  had  by  comparing  with, 
and  copving  the  details  of,  the  practice  of  others.     Under  these 
circumstances,  the  difference  of  conditions  will  be  apt  to  be  hon- 
estly accepted  by  the  reader  who  may  have  sinned  against  good 
practice   and   by  all  others   concerned,  as  the  reasons  why   an- 
other line,  one  hundred  or  one  thousand  miles  off,  should  have 
cost  so  much  less  and  yet  be  so  much  better  worth  owning  than 
his  own.     He  who  has  done  well,  therefore,  is  cut  off  from  any 


absolute  knowledge  and  general  recognition  of  that  fact,  and 
the  guilty  reader,  who  has  done  ill,  is  cut  off  from  the  still 
greater  gain  which  would  come  to  him  from  a  revelation  of 
where  and  wherein  he  has  done  ill.  In  most  such  cases  each 
will  have  in  some  detail  shown  better  judgment  than  the  other ; 
but  from  the  lack  of  unquestionable  evidence  of  this,  each  is 
denied  the  instruction  which  he  might  otherwise  receive  from 
that  fact,  and  so  is  in  great  danger  of  falling  into  the  most  natu- 
ral  and  most  human  error,  believing  that  all  that  he  has  done 
is  good,  which  has  not  been  proven  to  be  bad,  and  so  ceasing  to 
make  effort  to  improve  upon  what  is  good  enough  to  pass,  and 
merely  multiplying  errors  with  advancing  experience,  without 
really  advancing  in  knowledge. 

For  these  reasons  the  student  should  begin  with  the  conscious- 
ness that  the  level  of  average  practice  in  railway  location;  his 
own  included,  is  by  its  nature  restricted,  not  to  the  sum  of  the 
united  abilities  of  all  those  who  are  or  have  been  engaged  in  it, 
as  in  constructive  engineering,  but  to  the  average  individual  level 
of  capacity  and  knowledge.  No  more  is  needed  than  this  un- 
doubted fact  to  prove  to  demonstration  that  average  practice  is 
and  must  be,  both  comparatively  and  absolutely,  of  a  pretty  low 
grade  ;  and  hence  it  becomes  every  one  who  may  be  entrusted 
with  such  work  to  have  constantly  before  him  the  fact  that  he 
stands  thus  alone,  and  to  scrutinize  with  the  sternest  skepti- 
cism, the  conclusions  which  he  may  reach,  remembering  that  his 
danger  of  grave  errors  of  judgment  is  thereby  multiplied  many- 
fold.  As  he  measures  only  by  his  own  knowledge,  all  the  work 
he  does  will  naturally  seem  good  even  if  really  bad. 

To  the  preceding,  which  may  be  called  the  subjective  ob- 
stacles to  good  practice,  must  be  added  another  and  perhaps  a 
greater  one.  Inasmuch  as  no  one  can  even  know  for  himself 
the  absolute  quality  of  his  own  skill  in  this  particular  branch  of 
engineering,  it  is  almost  a  natural  corollary  that  corporations 
should  very  uniformly  decline  to  take  it  for  granted,  by  assum- 
ing that  there  are  any  measurable  differences  in  qualifications  for 
such  work  amon^  those  who  have  proved  their   competency  in 


; 


INTRODUCTION. 


IN  TROD  UCTION, 


II 
III 


other  branches  of  engineering.     Hence  it  happens  that  railway 
location  tends  more  and  more  to  be  entrusted  to  those  to  whom 
it  is  a  mere  temporary  incident  in  their  professional  career,  and 
who  consider  the    work    mainly    from    the    constructive    stand- 
point, without  much  attention  to  those  larger  economic  ques- 
tions which  it  is  the  purpose  of  this  volume  to  discuss,  and   to 
which,  in  well-conducted   work,    the   mere    constructive  details 
should  be  wholly  subordinate.     But  as  the  inexperienced  young- 
man  can  only  gauge  the  inportance  of  various  work  by  the  at- 
tention which  he  sees  paid  to  it    by  his  superiors,  he  is,  as  it 
were,  pushed  by  others  into  an  error  which  it  is  difficult  for  him 
to  avoid  at  best  ;  for  he  will  soon  note  that  the  assumption  and 
practice  of  the  world  is,  that  whoever  is  fit  to  design  the  struc- 
tures of  a  railway  is  thereby  fitted,  without  further  study  or 
preparation,  to  design    the  railway  as  a    whole.     In   fact,    this 
vicious  principle   is  in  very  many  instances  pushed   to   the   ab- 
surd extreme  of   entrusting  engineers  of  inferior  capacity  with 
the  location  of  railways,  and   only  seeking  for  a  higher  grade 
of  skill  when  the  design  of  the  cheaper  man  is  to  be  embodied 
in  construction.     The  error  in   so  doing   is   the   same  in   kind 
and  in  degree  as  if  it  were  assumed  that  whoever  was  fitted  to 
build  a  house  was  fitted   to  design  one.     The  mental  qualities 
and  special  training  needed  are  much  the  same  in  each  case,  but 
the  two  kinds  of  work  are  distinct,  and  skill   in   one  does  not 

argue  skill  in  the  other. 

Nevertheless,  railways  must  be  built,  and  fortunately  there  is 
a  bright  side  as  well  as  a  dark  side  to  the  picture.  There  is 
indeed  a  pitiable  waste  resulting  from  the  conditions  outlined  : 
such,  to  mention  a  simple  and  readily  comprehended  example,  as 
has  resulted  from  the  location  of  the  entire  railway  system  of 
the  prairie  States  of  the  West,— taking  it  as  a  whole  and  neglect- 
ing the  many  individual  exceptions,— where  the  fatal  ease  with 
which  an  air-line  may  be  run  from  almost  anywhere  to  any- 
where, by  using  heavy  enough  grades,  has  brought  the  average 
train-load  lower  than  in  the  rugged  regions  of  the  East,  and 
caused  perhaps  a  greater  percentage  of  utterly  needless  waste. 


and  a  more  discreditable  aggregate  of  thoroughly  bad  location, 
than  in  any  other  considerable  region  of  the  world  ;  and  in  view 
of   such  facts,  tlie  distorted  pre-eminence  given    by  engineers, 
and  by  those  who  teach  them  and  employ  them,  to  the  pettiest 
details  of  how  to  build  the  separate  works  which  make  a  railway, 
to  the  neglect  of  the  larger   questions  of  where  to    build    and 
when  to  build,  and  whether  to  build  them  at  all,  has  in  it  some- 
thing at  once  astounding  and  discouraging.     But  in  a  larger 
view  this  is  in  no  way  surprising.     It  is  but  the  common  result 
of  man's  attempts  at  solving  every  serious  problem  which  does 
not  admit  of  exact   and   positive   solution,   like   a   problem    in 
geometry,  but    contains    such    indeterminate    elements    that    to 
solve    it  perfectly  is   given  only  to    Omniscience.     In    all    such 
cases  mankind  in  general  shirks  the  issue,  or  jumps  at  a  solu- 
tion in  the  rudest  way,  as  is  seen  not  only  in  the  work  of  engi- 
neers, but    in  that  of  farmers  and    legislators    and    merchants, 
physicians  and    builders.     Compared    with    the    dismal    failure 
which  so  many  men    make  in  every  one  of  these  callings,  the 
work  of  engineers  in  laying  out  railways  shines  by  comparison. 
For  after  all,  the  fact,  if  it  be  a  fact,— as  in  a  rude  way  it  is,— 
that  between  waste  in  construction  and  waste  in  operation  and 
waste    from  inaccessibility  to    possible    patrons,   it  takes    about 
twice  as  great   expenditure  of  capital  and  labor  as   it  need   to 
afford   existing    transportation    facilities — this   really    means    no 
more  than  that,  instead  of  realizing  ninety  per  cent  of  the  ad- 
vantages which  might  be  gotten  from  George  Stephenson's  inven- 
tion, as  is  reasonably  possible,  only  some  seventy-five  or  eighty 
per  cent  is  actually  realized.     The  great  world  declines  to  take 
much  interest  in  such  a  trifling  waste  as  this,  being  accustomed 
to  much  greater  vi^aste  in  many  things,  and  having  something  of 
that  large  indifference  to  waste  which  pervades  all  nature.     Nor 
would  it  be  worth  while  here  to  insist  on  it  for  the  mere  sake  of 
pointing  out  that  it  exists,  but  solely  to  point  out  that,  as  the 
location  of  railways  is  the  one  department  of   engineering  in 
which  waste  on  a  gigantic  scale  is  possible  from  probable  errors 
of  judgment,  and  as  it  is  likewise  the  one  department  of  engi- 


8 


INTRODUCTIOiW 


IN  TROD  UCTION. 


neering  in  which  no  natural  check  exists  against  such  errors,  it 
is  fitting  that  engineers  should  prepare  themselves  for  it  with 
especial  care,  at  least  to  the  extent  of  acquiring  an  adequate 
conception  of  the  number  and  magnitude  of  the  errors  into 
which  they  may  fall. . 

Much  of  the  success  of  any  one  in  any  kind  of  work,  and  especially 
in  work  subject  to  the  peculiar  difficulties  of  that  we  are  considering, 
depends  upon  the  spirit  in  which  it  is  undertaken.     If  it  be  true,  as  it 
unquestionably  is.  that  no  one  ever  attained  great  success  in  any  walk  of 
life-or  certainly  in   no  intellectual  calling-who  found  no  other  nor 
higher  pleasure  in  doing  that  well  which  was  given  him  to  do  than  m 
the  money  or  the  glory  which  he  might  get  from  doing  it,  it  is  certain- 
ly  much  more  true  in  a  calling  where  those  ordinary  stimuli  work  very 
imperfectly  or  not  at  all.  and  in  which  one  is  often  called  upon  to  do  the 
direct  contrary  of  what  will  win  him  credit  from  the  thoughtless  and 
superficial.    The  desire  to  do  good  work  for  its  own  sake  is  then  the 
onlv  real  guarantee  that  good  work  will  be  done ;  for  although  a  kindly 
Providence  has  given  the  latent  power  to  do  bad  work  of  this  kmd  to 
every  human   being   with   a  tolerably   observant  eye   and   intelhgence 
enou-h  to  lay  up  bricks,  most  assuredly  the  power  to  do  good  work  will 
not  come  by  nature.     The  author,  therefore,  feels  that  he  need  make  no 
apolo-v  to  those  voung  men   who   may   honor   him  by   studymg  this 
volum^'e.  for  offering  them  one  page  at  least  of  true  wisdom,  in  the  state- 
ly  periods  of  one  of  the  greatest  thinkers  of  our  or  any  age;  which  he 
does  in  the  belief  that  they  will  find  its  study  more  profitable  than  that 
of  many  pages  in  this  or  any  other  text-book,  since,  if  they  have  studied 
it  to  some  purpose,  they  are  at  least  assured  the  most  permanently  grati- 
fymcr  of  all  success— the  consciousness  of  having  done  one  s  best : 

"l  look  on  that  man  as  happy,  who.  when  there  is  question  of  suc- 
cess, looks  into  his  work  for  a  reply-not  into  the  market,  not  into 
opinion,  not  into  patronage.  In  every  variety  of  human  employment, 
in  the  mechanical  and  in  the  fine  arts,  in  navigation,  in  farming,  in  legis- 
lating., there  are  among  the  numbers  who  do  their  work  perfunctorily, 
as  we%av.  or  just  to  pass,  and  as  badly  as  they  dare.-there  are  the  work- 
inc^men.'  on  whom  the  burden  of  the  business  falls.-those  who  love 
work,  and  love  to  see  it  rightly  done,  who  finish  their  task  for  its  own 
sake;  and  the  state  and  the  world  is  happy  that  has  the  most  of  such 
finishers.  The  world  will  always  do  justice  at  last  to  such  finishers  :  it 
cannot  otherwise.     He  who  has  acquired  the  ability  may  wait  securely 


the  occasion  of  making  it  felt  and  appreciated,  and  know  that  it  will  not 
loiter.  Men  talk  as  if  victory  were  something  fortunate.  Work  is  vic- 
tory. Wherever  work  is  done,  victory  is  obtained.  There  is  no  chance, 
and  no  blanks.  You  want  but  one  verdict :  if  you  have  your  own,  you 
are  secure  of  the  rest.  And  yet,  if  witnesses  are  wanted,  witnesses  are 
near.  There  was  never  a  man  born  so  wise  or  good,  but  one  or  more 
companions  came  into  the  world  with  him.  who  delight  in  his  faculty 
and  report  it.  I  cannot  see  without  awe.  that  no  man  thinks  alone,  and 
no  man  acts  alone;  but  the  divine  assessors  who  come  up  with  him  into 
life,  now  under  one  disguise,  now  under  another,  like  a  police  in  citi- 
zens' clothes,  walk  with  him,  step  for  step,  through  the  kingdom  of 

time. 

••  What  is  vulgar,  and  the  essence  of  all  vulgarity,  but  the  avarice  of 
reward  ?  'Tis  the  difference  of  artisan  and  artist,  of  talent  and  genius, 
of  sinner  and  saint.  The  man  whose  eyes  are  nailed,  not  on  the  nature 
of  his  act,  but  on  the  wages,— whether  it  be  money,  or  office,  or  fame- 
is  almost  equally  low."  * 

The  true  moral  to  be  drawn  from  such  glittering  generalities  is  not 
that  if  a  man  does  not  succeed  the  world  is  not  doing  justice  to  him  ; 
for  the  chances  are  a  hundred  to  one  that  it  is  meting  him  out  exact 
and  equal  justice,  and  that  unless  he  wipes  out  that  delusion  from  his 
mind  and  sets  about  correcting  his  deficiencies,  it  will  continue  to  do  so 
in  the  same  way :  nor  is  it  that  a  man  should  neglect  that  reasonable  care 
for  his  own  welfare  which  is  every  man's  duty,  nor  that  he  should  submit 
to  imposition,  nor  continue  very  often,  for  very  long,  to  render  something 
for  nothing :  In  this  utilitarian  age  there  is  little  danger  that  it  will  be 
so  interpreted.  But  the  author  has  seen— or  thinks  he  has  seen— so 
many  young  men  doing  permanent  injury  to  their  own  future  by  letting 
$150  a  month  fill  up  the  whole  arc  of  their  horizon,  that  he  has  seized 
his  chance,  while  he  has  them  foul,  to  inflict  a  little  advice.  He  grants 
it  is  against  the  laws  of  the  game,  and  stops. 

We  will  now  proceed  with  our  legitimate  subject,  and  endeavor  not 

to  depart  from  it. 

*  Ralph  Waldo  Emerson  :  "  Essay  on  Worship." 


■I  ii 


II 


PART  I. 


ECONOMIC    PREMISES. 


'*  The  location  of  a  railroad  is  giving  it  its  constitution.  It  may  be 
sick,  almost  unto  death,  with  accidents  of  construction  and  maneige- 
ment,  but  with  a  good  constitution  it  will  ultimately  recover." 

— D.  H.  AiNSWORTH.. 


1'^ 


A 


PART  I. 

ECONOMIC  PREMISES. 


CHAPTER  I. 

THE   INCEPTION   OF   RAILWAY    PROJECTS,  AND   CONDITIONS   GOVERN- 

ING    IT. 

1.  When  a  railway  is  projected,  and  while  its  construction 
is  still  in  doubt,  the  most  important  and  most  doubtful  ques- 
tion of  all  is  one  which  does  not  admit  of  any  general  discussion 
or  analysis  :  Whether  or  not  to  build  the  line  at  all.  The 
decision  of  this  question  is  not  within  the  legitimate  sphere  of 
an  engineer's  duties,  acting  as  such  ;  and  hence  it  should  not  be 
permitted  to  confuse  or  affect  his  mind  during  the  subsequent 
process  of  preparing  the  line  for  construction.  For  the  general 
question  of  whether  or  not  to  build  the  line  at  all  is  one  of 
finance  and  business  judgment  alone,  to  be  settled  by  a  more  or 
les's  exact  or  visionary  estimate  of  the  available  capital  for  con- 
struction, the  probable  gross  and  net  receipts,  and  the  resulting 
direct  and  indirect  advantages  to  the  projectors,  with  the  final 

conclusion  that — 

(i)  There  is  (or  is  not)  sufficient  need  of  a  railway  to  give  a 
fair  return  on  the  expenditure  of  a  certain  gross  amount  in  con- 
structing it;  and 

(2)  That  this  gross  amount  can  (or  cannot)  be  raised. 

This  conclusion  is  not  necessarily  expressed  by  a  definite  sum 
in  advance— in  fact  it  is  very  rarely  so  expressed  ;  but  such  a 


14  CHAP,   I.-INCEPTION  OF  RAILWAY  PROJECTS. 


CHAP.   I.— INCEPTION  OF  RAILWAY  PROJECTS. 


15 


conclusion  is  in  effect  reached,  although  often  in  a  very  vague 
form,  whenever  it  is  decided  to  proceed  with  construction 

2.  Neither  does  it  follow  that  the  deciding  motive  is  direct 
pecuniary  profit  ;  for  the  line  m^ay  be  of  great  value  to  the  in- 
ventors  and  the  public,  and  yet  never  pay  such  profit.     In   fact 
the  railway  system  of  the  world,  taken  as  a  whole,  and  especially 
that  of  the  United  States,  has  been  only  very  moderately  profit- 
able  in  any  direct  form  ;  owing  not  so  much  to  mistakes  of  judg- 
ment pure  and  simple,  as  to  tlie  very  large  proportion  of  lines 
which  have  been  built  simply  to   increase  the  value  of  land    to 
afford  local  transportation  facilities,  to  bring  traffic  to  the  main 
line,  and  similar  purposes.     Yet  the  resulting  gain  to  the  com- 
mun.ty,  from  these  indirect  advantages  alone,  has  been  vast  be- 
yond  computation  ;  so  much  so  that,  although  the  lines  on  which 
projectors  have  lost  money  have   been   many,  there  have   been 
few  or  none  which  have  involved  a  positive  loss  to  the  commu- 
nity as  a  whole,  excepting  some  of  those  which  have  merely 
paralleled  other  lines. 

,         3.  A  certain  number  of  lines,  also,  are  built  for  more  or  less 
Illegitimate  and  irregular  purposes:  to  sell  out  to,  or  sometimes 
one  may  fairly  say,  to  black-mail  other  lines  ;  to  make  profit  on 
the  construction  ;  as  means  of  warfare  against  other  lines  •  etc 
etc.     Nevertheless,  even  with  such  irregular  enterprises,  as  cer-' 
tainly  in  all  other  cases,  the  same  general  law  holds  :  It  is  the 
plain  interest  of  the  constructors,  in  all  cases,  to  obtain  as  good  a 
road  as  they  can  for  the  money,  and  to  build  it  on  business  prin- 
ciples  ;  to  spend  what  they  have  to  spend  to  the  very  best  ad  van- 
tage  and  to  spend  no  more  than  they  are  obliged  to  spend   to 
build  the  line  at  all  in  safe  operating  condition,  unless  the  addi- 
tional  expenditure,  and  not  simply  the  expenditure  as  a  whole  is 
clearly  a  good  investment.  * 

4.  From  the  point  of  view  of  this  volume,  therefore  all  rail- 
ways are  legitimate  enterprises,  and  their  construction  is  gov- 
erned  by  the  same  general  economic  laws.  These  laws,  vital  to 
the  successful  conduct  and  outcome  of  such  enterprises,  seem- 
mgly  very  plain  and  simple,  but  frequently  neglected  or  forgot- 


ten,  may,  as  respects  the  question  of  whether  to  build  the  line  or 
not,  be  summarized  as  follows  : 

5.  (i)  Railways  are  not  undertaken  Cinless  they  are  expected 
to  be  profitable,  not  to  the  general  public,  nor  to  other  parlies 
in  the  near  or  distant  future,  nor  to  those  who  lend  money  on 
them,  but  to  those  who  at  Jirst  control  the  enterprise.  If  the  means 
in  hand  be  not  sufficient  for  the  projectors  to  complete  the  road 
for  operation  and  to  control  its  operation  afterwards,  the  result 
to  them  is  usually  complete  loss.  Remembrance  of  this  fact 
becomes  the  more  important  because  the  available  means  (the 
great  bulk  of  which  is  borrowed  money)  are  almost  always  over- 
rated, and  the  demand  upon  them  underrated. 

The  logical  ^^rder  of  procedure  in  the  case  of  any  new  enter- 
prise— which  is,  first,  to  determine  whether  or  not  the  project  is 
a  sound  one,  and  to  be  carried  out  ;  and,  secondly,  to  make  the 
necessary  studies  as  to  trhe  manner  of  carrying  it  out — is  not 
necessarily  followed  in  order  of  time  :  often  it  cannot  be,  for  the 
final  decision  as  to  the  former  often  depends  on  the  results  of 
the  latter,  or  on  unknown  future  events.  Nevertheless,  although 
subsequent  events  may  cause  a  revision  of  such  assumptions, 
the  mere  initiation  of  the  study  of  details  implies  a  pro-Jornia 
conclusion,  that  the  project  as  a  whole  is  a  wise  one  if  wisely 
carried  out,  and  can  only  fail  by  bad  judgment  in  details.  This 
premise  must  be  from  the  beginning,  therefore,  under  all  circum- 
stances, the  basis  of  the  engineer's  action.     From  this  it  follows  : 

6.  (2)  No  increase  of  expenditure  over  the  unavoidable  mini- 
mum is  expedient  or  justifiable,  however  great  the  probable 
profits  and  value  of  an  enterprise  as  a  whole,  unless  the  increase 
can  with  reasonable  certainty  be  counted  on  to  be,  in  itself,  a 
profitable  investment.     Conversely, 

(3)  No  saving  of  expenditure  is  expedient  or  justifiable,  how- 
ever doubtful  the  future  of  the  enterprise  as  a  whole,  when  it  can 
with  certainty  be  counted  on  that  the  additional  expenditure  at 
least  will,  at  the  cost  for  the  capital  to  make  it,  be  in  itself  a 
paying  investment. 

For  if  the  project  as  a  whole  be  an  unwise  one,  the   projec- 


l6  CHAP.   I.— INCEPTION  OF  RAILWAY  PROJECTS. 


CHAP.    I.— INCEPTION  OF  RAILWAY  PROJECTS. 


17 


1  KJlLXii     il 


tors  will  lose  their  money  in  any  case  ;  but  an  additional  expendi- 
ture which  adds  more  value  to  the  property  than  it  costs  will,  at 
the  worst,  decrease  their  loss,  and  may  turn  the  scale  by  prevent- 
ing any  loss.  Doubtful  projects  least  of  all  can  afford  to  have 
their  future  imperilled  by  reckless  economies.  Nevertheless 
the  following  should  be  remembered  : 

7.  (4)  No  expenditure  is  wise,  however  otherwise  profitable, 
which  endangers  the  successful  completion  of  the  enterprise 
with  the  funds  on  hand  or  known  to  be  available. 

For  the  property  then  becomes  worthless  to  the  projectors,, 
however  valuable  it  may  become  to  others.  Successful  comple- 
tion, moreover,  includes  much  more  than  the  laying  of  the  track. 
It  includes  the  equipment,  the  terminal  facilities,  the  endurance 
of  thin  traffic  and  of  imperfect  exchange-traffic  facilities  until 
the  normal  business  of  the  line  has  been  fully  attained— always 
a  matter  of  time.  Therefore,  as  few  roads  are  even  sure  of  ob- 
taining the  capital  which  they  think  is  necessary  for  the  above 
purpose,  we  have  the  following  : 

8.  (5)  Expenditures  of  any  kind  on  new  projects  are  rarely 
wise,  however  otherwise  profitable,  which  can  be  postponed 
without  any  very  serious  loss,  however  sure  to  involve  some  loss 
if  all  goes  as  well  as  is  expected  ;— such  as  costly  works  which 
can  be  avoided  by  temporary  lines,  or  by  less  durable  but  cheaper 
structures,  complete  provisions  for  traffic  which  is  yet  in  the 
future,  and  elaborate  shops  and  buildings. 

On  the  other  hand,  economies  which  permanently  handicap 
the  line  with  inferior  works  or  alignment,  or  which  place  it  un- 
der a  permanent  disadvantage  in  seeking  for  business,  such  as 
using  over-light  rails,  keeping  away  from  towns  to  save  right-of- 
way  expenses,  heavy  grades,  etc.,  are  the  first  which  should  be 
avoided,  but  are  often  the  first  which  are  resorted  to,  for  rea- 
sons more  fully  discussed  in  Chapters  XXII.  and  XXIII. 

9.  The  profit  on  a  railway  property  depends, /rj/,  on  the 
judgment  shown  in  selecting  the  region  through  which  it  is  to 
be  built ;  and,  secondly,  on  the  skill  with  which  the  line  laid  down 
in  it  is  adapted  to  be  of  the  greatest  use  to  the  greatest  number 


of  people  (giving  large  gross  revenue)  at  the  smallest  cost  for 
the  service  rendered  (giving  small  operating  expenses).  The 
first  is  distinctively  the  province  of  the  projectors  ;  the  last  is 
distinctively  the  province  of  tiie  engineer.  Which  is  most  im- 
portant it  would  be  needless  to  inquire,  but  certainly  the  last,  in 
this  sense  at  least,  that,  if  it  be  well  done,  any  errors  in  respect 
to  the  assumed  need  for  a  railway,  although  they  may  be  un- 
fortunate, can  rarely  be  ruinous  ;  while  it  has  again  and  again 
been  proven  that  if  good  judgment  be  not  shown  in  the  details 
of  the  route  and  expenditure,  no  merely  constructive  skill  of  the 
engineer,  nor  excellence  of  judgment  in  selecting  a  locality,  can 
save  the  project  from  disaster. 

10.  All  the  preliminary  questions  of  probable  profit  and  loss 
involved  in  the  decision  to  build  a  line  of  some  kind  over  some 
given  general  route  being  supposed  to  be  finally  settled  and  dis- 
posed of,  and  the  construction  of  the  road  definitely  determined 
on  (if  the  expectations  as  to  cost  of  construction  and  available 
means  are  realized),  the  province  of  the  locating  engineer  and 
the  proper  subject-matter  of  this  volume  begins. 

We  are  now  done  altogether  with  all  considerations  as  to 
whether  the  future  of  the  company  as  a  whole  will  be  prosperous 
or  otherwise,  and  as  to  whether  the  probable  aggregate  profits 
or  cost  of  the  road,  either  per  mile  or  in  gross,  will  be  large  or 
small,  and  it  is  the  duty  of  the  engineer  to  neglect  them  abso- 
llutelv  in  laving  out  his  work,  considering  only  the  effect  of  his 
ecisions  upon  these  three  items  : 

1.  The  difference  in  gross  receipts  which  will  or  may  result 
rom  choosing  one  or  another  line. 

2.  The  difference  in  operating  expenses  which  will  or  may 
result  from  choosing  one  or  another  line,  one  or  another  gra- 

ient,  one  or  another  limit  of  curvature,  etc. 

3.  The  difference  in  annual  interest  charge  which  will  or 
ay  result  from  the  differences  in  cost  of  construction  caused 

y  differences  in  the  above  details. 
The  latter  should  be  computed,  of  course,  at  the  rate  or  rates 
7. 


i8 


CHAP.    I.— INCEPTION'  OF  PAIL IV AY  PROJECTS. 


CHAP.    I.— INCEPTION  OF  RAILWAY  PROJECTS. 


19 


of  interest  which  money  actually  costs  or  will  cost  his  company. 
This  is  supposed  to  be  known  to,  and  remembered  bv,  the 
engineer  ;  and  is  the  only  fact  connected  with  the  present  condi- 
tion or  future  prospects  of  the  finances  of  his  company  which 
should  legitimately  influence  his  decisions. 

11.  Not  unfrequently  this  rate  of  interest  cannot  be  consid- 
ered uniform,  but  must  be  assumed  to  increase  very  rapidly 
with  the  amount  invested  ;  and  not  unfrequently  the  rate  of 
interest  which  should  properly  be  assumed  will  verge  upon  the 
infinite.  It  is  always  more  likely  to  be  underrated  than  over- 
rated ;  whereas  prudence  requires  that  the  reverse  should  be 
the  case. 

But  however  great  or  small  the  amount  and  cost  of  the  avail- 
able capital,  although  our  decisions  themselves  will  vary,  yet  the 
methods  by  which  these  decisions  are  reached  will  not  vary  ;  for 
even  in  such  an  extreme  case  as  when  the  cost  of  more  capital 
than  is  absolutely  essential  is  infinitely  great,  we  are  simply 
permanently  reduced  to,  and  compelled  never  to  vary  from,  what 
should  be  the  ^priori  basis  for  construction  with  which  the  con- 
struction of  every  line  is  entered  upon, — however  prosperous  the 
company,  however  large  the  probable  traffic  and  profits, — because 
no  more  than  this  is  implied  in  the  mere  decision  to  build  the 
road,  which  is  : 

That  excepting  when  and  as  specijic  reasons  to  the  contrary  appear^ 
the  cheapest  line  is  to  be  built  over  which  it  is  physically  possible  to  carry 
the  probable  traffic  with  proper  safety  and  speed,  using  to  this  end  any 
grades  and  curves  and  length  of  line  which  may  be  most  conducive  to  this 
end  only — and  never  abandoning  it  by  increasing  the  expenditure,  unless 
the  investment — not  the  investment  as  a  whole,  for  the  line  as  a 
whole,  but  each  particular  investment  for  each  particular  purpose  at 
each  particular  point — will  be  in  one  7vay  or  another  profitable  in  itself. 
12.  In  other  words,  reduction  of  first  cost  to  the  lowest  pos- 
sible point  is,  in  logical  or  economic  order,  the  first  considera- 
tion ;  although  therefore  not  by  any  means  either  the  most 
important  or  the  governing  consideration.  That  this  is  so  is 
easily  seen,  however  often  forgotten.     It  is  not  only  business-like 


f^ 


»> 


m 


u  '}>}. 


common-sense  for  the  investors  and  their  servants,  but  it  is 
sound  political  economy  for  the  community  as  a  whole.  It  does 
not  mean  nor  imply  cheap  and  shabby  construction.  It  simply 
means  an  avoidance  of  waste,  either  in  saving  money  or 
spending  it.  It  simply  means  a  recognition  of  the  fact  that 
every  dollar  and  every  day's  work  which  goes  into  the  ground 
and  does  not  bring  something  out  of  it,  makes  not  only  the  indi- 
vidual but  the  whole  community  the  poorer.  The  welfare  of  all 
mankind,  as  well  as  of  investors  in  the  enterprises  which  employ 
engineers,  depends  upon  the  skill  with  which  the  investment  in 
its  constructive  or  manufacturing  enterprises  (destruction  of 
existing  capital)  is  kept  small,  and  the  productive  or  earning 
power  (creation  of  new  capital)  is  made  large.  The  difference 
between  the  two  is  the  so-called  "profit"  (net  addition  to  exist- 
ing capital),  which  goes  indeed  into  the  control  of  those  who 
created  it  by  perceiving  the  (supposed)  opportunity  or  necessity 
and  using  their  own  means  at  their  own  risk  to  supply  it ;  but  it 
is  not,  therefore,  for  the  true  interest  of  any  person  or  class  to 
make  it  less  by  increasing  the  investment,  for  otherwise  there  is 
a  waste  which,  as  it  benefits  no  one,  indirectly  injures  all.  Not 
€ven  the  laborer  who  uses  up  a  portion  of  the  wasted  capital  is 
really  the  gainer;  for  if,  on  the  one  hand,  the  capital  spent  (i.e., 
destroyed)  for  construction  or  plant  be  needlessly  large,  although 
the  poor  man  gains,  for  the  time  being,  wages  which  he  would 
tiot  otherwise  receive  from  that  particular  enterprise,  yet  it  is  as 
if  he  were  paid  wages  to  turn  a  crank  which  ground  no  grist — 
his  time  and  his  work  go  for  naught.  If  he  spend  half  his  time 
in  this  way  he  must,  in  the  long-run,  do  two  days'  work  for  the 
wages  of  one — a  condition  which  is  nearer  to  existing  in  railway 
-enterprises  than  is  always  realized  or  admitted. 

Comparison  of  the  condition  of  laborers  in  countries  and  ages  where  human 
labor  is  economized  (reduced  to  a  minimum  for  each  separate  service)  and 
where  it  is  not,  fully  establishes  this  important  economic  truth,  as  to  which 
many  false  notions  prevail. 

13.  On   the  other   hand,  if    the    proper  margin  of  profit  has 
been  reduced  by  reckless   and   costly  economies,  no  one  gains 


"^^V- — — ^<> 


20  CHAP.    L— INCEPTION  OF  RAILWAY  PROJECTS. 


even  the  semblance  of  benefit,  while  both  the  projectors  and  the 
patrons  of  the  enterprise  are  heavy  losers— the  projectors  in 
money,  the  patrons  in  convenient  service. 

These  two  vital  truths,  therefore,  which  directly  result  from 
what  has  preceded,  should  never  be  forgotten  :  that  because  a 
line  will  have  or  is  expected  to  have  a  prosperous  future— because,, 
perhaps,  it  is  to  be  built  by  the  State  for  great  reasons  of  state,, 
or  for  any  other  reason  will  have  plenty  of  money  in  the  treasury,, 
there  is  therefore  no  justification  in  that  fact  alone  for  making 
it  a  costly  road  as  well. 

On  the  other  hand,  no  road  is  so  poor  that  it  can  afford  to 
economize  when  certain  additional  expenditure  will  be  clearly 
very  profitable.  If  it  is  clearly  understood,  or  believed  for  good- 
reason,  that  a  given  additional  investment  will  certainly  pay  lo 
or  15  or  25  or  50  per  cent,  as  the  case  may  be,  it  may  almost  be 
said  that  the  poorest  company  can  find  ways  and  means  for 
obtaining  the  capital,  if  the  facts  be  properly  and  clearly  pre- 
sented. 

14.  The  temptation  to  err  by  neglecting  these  axiomatic 
laws— which  is  alwavs  present  with  every  one  in  laying  out  a 
railway— becomes  especially  difficult  to  guard  against  under  two. 
circumstances  of  frequent  occunence  : 

First,  when  a  line  of  light  traffic  is  to  be  carried  through  an- 
inherently  difficult  country,  so  that  the  cost  of  construction  must 
in  any  case  be  large.  The  tendency  to  look  on  a  slight  per- 
centage of  increase  in  cost  as  a  trifling  matter,  although  it  may,, 
nevertheless,  involve  an  expenditure  out  of  all  proportion  to  the 
real  advantage  secured,  is  very  strong,  very  difficult  to  avoids 
rarely  or  never  avoided  altogether.     Per  contra  : 

15.  Secondly,  when  a  line  of  comparatively  heavy  traffic  is  to. 
be  carried  through  a  region  offering  small  natural  difficulties,  a 
dangerous  tendency  arises  of  an  opposite  character;— a  tendency 
to  unduly  exaggerate  the  importance  of  a  large  percentage,  and- 
yet  small  aggregate  of  increased  cost.     This  tendency  is  especi- 

"    ally  probable  and  dangerous  when  means  for  construction  are 
limited,  or  when   the  margin  of  profit  on  the   enterprise  as   a 


CHAP.   I.— INCEPTION  OF  RAILWAY 


whole  is  liable  to  be  small  :  a  fact  which  should  not  be  per- 
mitted to  exercise  any  influence  whatever,  except  through  its 
reflex  effect  on  the  rate  of  interest  on  capital.  The  most  usual 
and  most  unfortunate  form  which  an  error  of  this  kind  can  take 
is  the  adoption  of  unduly  high  gradients  to  effect  a  really  trifling 
economy.  The  railways  of  the  Western  United  States,  as  al- 
ready noted,  have  suffered  greatly  from  this  cause. 

The  most  experienced  and  cautious  man  cannot  free  himself 
wholly  from  these  too  grave  errors  ;  the  inexperienced  engineer 
or  projector  should  therefore  be  continually  on  his  guard  against 
xhem. 

16.  It  has  seemed  essential  thus  to  lay  down  certain  prelimi- 
nary generalities  as  to  what  should  be  the  attitude  of  mind  of 
a  locating  engineer,  because  he  is  often  unconsciously  and  im- 
properly guided  in  his  actions  by  the  mere  bald  feeling  (whether 
justified  or  not  does  not  matter)  that  his  company  is  very  rich  or 
very  poor,  and  that  he  can  spend  or  must  save  accordingly. 
Supposing  him  to  enter  upon  the  work,  therefore,  with  that 
most  important  of  all  preliminaries,  a  correct  appreciation  of 
the  proper  basis  for  decisions,  the  problem  for  which  he  is  prop- 
erly responsible,  when  selecting  a  route  for  a  railway  whose 
construction  has  been  determined  on,  may  be  again  subdivided 
thus  : 

Firsts  and  by  very  much  the  most  important,  is  the  selection 
of  the  general  route  between  the  two  established  termini,  or,  as 
very  often  happens,  the  selection  of  one  or  both  termini  as  well. 

Secondly  comes  the  adaptation  of  the  line  in  detail  to  the 
topographical  conditions  which  exist  along  the  route  selected. 

17,  The  question  of  general  route  is  commonly  settled  by  the 
RECONNAISSANCE,  whicli  for  this  reason  must  be  classed  as  by 
far  the  most  important  duty  of  the  engineer  in  charge,  and  the 
one  for  which  it  is  most  essential  that  he  should  qualify  himself 
properly,  which  he  can  only  do  by  learning  to  estimate  and  give 
•due  relative  weight  to  all  those  circumstances  which  have  or 
may  have  a  bearing  upon  the  future  of  the  property,  as  well  as 


CHAP.   L^INCEPTJON  OF  RAILWAY  PROJECTS. 


CHAP.    I.— INCEPTION   OF  RAILWAY  PROJECTS. 


23 


D 


22         

"^Z^TuI'physical  possibilities  of  the    route  in  question 

Oth^l  se- fhe  I  qualLd  merely  in  the  latter  respect-h.s 

?.lTer  is   a  double   one:  that   he  will   give   undue    weight   to 

:XeVneting  questions  -^X^:" r^^l::  u^rd 

-.ir  f ::  ':r'::r^^^'p^^^^  -^y  -r. .. 

^"-.reror-I  re:^;r;hrb\:arst;e  here  ....   .the 
,L  selection  of  the  entire  route  between  term.n.,  or 
r'ircafe:  :f  ttHermini  -.se.v.    js  -lyjeft  enu^ 

1^^  t^rrthl  ral"Va:;r:rerro! tr  Caching  „.. 
•mponance  to  some,  at  the  expense   of  other,  governing  con- 

"'r'T°heart  of  correctlv  discerning  in  advance    by   merely 
ocu^l;  ex  mination,  assisted  only  by  maps  and  a  few  portable 

instruments,  the  physical  P--''>''''-/f  ^'^j^f  ^  most  ad- 
•     .  A  r.,'  r^r^<^\h\e  railway  route,  and  of  making  tne  moi>t  <x^ 
rnUeelTselect  on%;"L  t^^  poss'ib.e  routes  (which  are  always 
rr sT  Tor  further  Instrumental  examin^^^^^^^^^^^^^  someumes 

^'^twitrmost%opular  impressions,  there  is  a  foundation  of 
V      Z.     Certain  natural  qualifications  and  a  considerable 
''        '?    fnracticTare  essential.     Nevertheless,  the  acquirement 
amount  of  practice  are  esseuui  ,    _,  „   jurharee   of    this 

r.f  reasonable  skill  and  competency  for  the   discha.ge   01 
moirresponsible  of  all  duties  connected  with  laying  out  a  ra.l- 
1;  i    o"ly  to  a  limited  degree  depen.lent  upon  practice  alon 

r^ncre"sed  by  long  practice,  and  is   hardly  dependent    ,t  all 
or  increasea  oy        S  F  „  ^       ^  ^^^^,.^i  g,ft  for 


almost  as  certainly  as  if  the  art  of  reconnoitring  were  an  exact 
science,  and  which,  if  they  be  mastered  in  advance,— not  simply 
^y  reading  them,  but  by  acquiring  a  habit  of  observation  and  of 
applying  them  to  hypothetical  instances,— will  enable  the  young 
engineer  of  very  limited  experience  to  go  into  the  field  better 
guarded  against  error  than  by  long  years  of  field  practice  alone  ; 
for  the  latter,  in  location,   as  in  most  other  matters  which  re- 
quire   something    more    than    the    mechanical    application  of 
methods  learned  by  rote,  is  quite  as  apt  to  confirm  erroneous 
opinions  as    to  inculcate  good   ones.     The  first  necessity    is  to 
form  correct  and  definite  ideas  as  to  what  a  railway  should  be, 
what  kind  of  a  railway  we  are  to  build,  what  are  the  conditions 
which  contribute  most  to  its  prosperity,  and  to  what  extent  they 
so  contribute,  in  order  that  the  reconnoitring  engineer  may  be 
prepared  to  form  on  the  instant  an  .approximately  correct  idea, 
not  only  as  to  what  he  can  do,  but  as  to  what  he  ought  to  do,  in 
any  given  case,  and  to  decide  which  of  two  incompatible  ends 
should  be  sacrificed  to  the  other,   and  what  approximate  sum 
represents  the  difference  in  value  between  them.     Otherwise  the 
experienced  and  inexperienced  man  alike  are  in  imminent  dan- 
ger of  failing  even  to  discern  or  consider  what  are  really   the 
most  promising  possibilities— not  from  lack  of  an  "  eye  for  coun- 
try"  or  training   in  the  field,  but  from  wrong  ideas    of    expe- 
diency. 

19.  It  necessarily  results  from  the  preceding  that  the  re- 
connaissance is,  of  all  his  duties,  the  one  which  the  responsible 
engineer  in  charge  should  personally  discharge,  and  never  un- 
der any  circumstances  delegate,  in  part  or  whole,  to  less  expe- 
rienced subordinates,  where  the  final  decision  may  be  seriously 

affected  thereby. 

The  greater  portion  of  this  volume  will  be  devoted  to  the 
presentation  of  data  as  to  the  first  and  most  important  of  the 
duties  connected  with  the  reconnaissance  and  subsequent  sur- 
veys, determining  what  ought  to  be  done  ;  afterwards  con- 
sidering the  comparatively  simple  matter  of  how  to  do  it. 

20.  To  reach  entirely  correct  decisions  as  to  what  ought  to 


I  i 


I    i 


24 


CHAP.    1. -INCEPTION  OF  RAILWAY  PROJECTS. 


be  done  requires,  it  is  plain,  that  we  should  not  only  have  a 
correct  idea  of  the  nature  of  a  railway  corporation's  finances  and 
of  railway  traffic,  but  that  we  should  foresee  exactly  the  volum^ 
and  sources  of  the  future  traffic,  and  the  details  and  probable 
amount  of  the  future  operating  expenses,  as  well  as  in  part  of 
the  future  revenues  ;  for  the  larger  the  probable  traffic  the  more 
perfectly  adapted  to  its  cheap  handling  can  we  afford  to  make 
every  detail  of  the  line  ;  the  larger  the  probable  revenue,  the  less 
will'the  burden  be  felt  of  paying  interest  on  present  expendi- 
tures, etc.,  etc.  r      ,     • 

21.  This  we  cannot  do.     To  foresee  such  details  perfectly  is 
impossible.     To  foresee  them  in  any  degree  we  are  obliged  to 
do  that  most    hazardous  thing— to  look  forward   to  and  "dis- 
count" the  future  ;  to  make— and  act  upon— what  is,  after  all, 
nothing  more  than    a    guess   at  the  probable   course  of   future 
events.     To  foresee  the  future  with  adequate  exactitude  even  in 
the  simple  case  of  improvements  on  an  old  road  is  difficult,  aK 
though  we  have  a  definite  past  to  guide  us.  In  the  case  of  a  new 
road  it  is  still  more  difficult  to  approximate  to,  and  still  less  pos- 
sible to  reach,  an  exact  and   positive  result  ;  but  nevertheless, 
especially  in  anv  countrv  where  railways  already  exist,  estimates 
of  the  financial'importance  of  doing  or  not  doing  certain  things 
can   always  be   made,  by   proceeding  on  correct  principles  and 
using  proper  care,  vhich  shall  be  a  sufficient  guide  for  location, 
and  hence,  when  made,  should  always  be  carefully  followed  m 
preference  to  mere  "judgment"  and  guesswork   pure  and   sim- 
pie.     The  uncertainty  as   to  the  exact  requirements  to  be  ful- 
filled  by  the  works  when  completed  is  a  disadvantage,  indeed, 
which  cannot  be  escaped  ;  but  the  more  difficult  it  is  to  reach 
absolute  correctness,  the    greater  need  we  have  of  some  guide 
which   shall    reduce  the   unavoidable   guesswork   to   its  lowest 
terms  and  so  save  us  from  the  manifold  hazards  which  result  from 
not  only  guessing  at  facts,  but  at  the  effect  of  those  facts.  What- 
ever care  we   use,  we  can  never  attempt  with  success  to  fix  the 
exact  point  where  economy  ends  and  extravagance  begins  ;  but 
what  we  can  do  is   to  establish  certain   narrow  limits  in   either 


CHAP.  I.— THE  INCEPTION  OF  RAILWAY  PROJECTS.     25 


direction,  somewhere  within  which  lies  the  truth,  and  anywhere 
outside  of  which  lies  a  certainty  of  error.  Due  judgment  and 
caution  reqiiire  that  we  should  do  so  ;  and  this  is  what  we  do 
effect  when  we  make  as  careful  an  estimate  as  possible  of  the 
details  of  the  problem  and  accept  the  final  result  as  an  absolute 
guide. 

The  following  three  tables  (i  to  3),  while  containing  data  otherwise  useful,  and 
to  which  we  shall  have  occasion  to  refer,  bring  out  vividly  the  enormous  indi- 
rect benefits  of  railways,  which  have  much  to  do  with  the  construction  of  many 
lines  otherwise  profitless,  as  notably  in  Canada  and  Mexico,  where  the  govern- 
ment has  (very  properly  and  wisely)  paid  heavy  subsidies  to  secure  the  con- 
struction of  otherwise  profitless  lines.  The  same  has  been  true  to  a  large  ex- 
tent in  the  United  States,  both  as  respects  the  general  government,  States,  and 
private  individuals  and  corporations.  Nearly  all  the  increase  in  the  valuation 
of  the  United  States  since  1850,  as  shown  in  Table  2,  may  be  said  to  be  due  in- 
directly to  railways,  since  without  their  aid  a  much  greater  valuation  than  ex- 
isted in  1850  would  have  been  impossible. 

Table  1. 
Estimated  Total  Wealth  of  the  United  States. 

[Abstracted  from  U.  S.  Census,  1880,  Report  of  H.  Gannett,  Special  Agent.] 


Items. 


Railways  and  equipment 

Farms '. '*:  * :: 

Residence  and  business   real   estate,    mcludmg   water- 


power  

Telegraph,  shipping,  and  canals 

Live-stock,  farming  tools,  and  machinery 

Household  furniture  and  personal  clothing,  etc 

Mines  and  quarries,  including   6  mos.  average  output 

estimated  as  on  hand 

Three  fourths  of  annual  product  of  agriculture,  manu- 

.    faciures,  and  importations,  estimated  as  on  hand 

Churches,  schools,  and  public  buildings  not  taxed 

Specie 

Mechanics'  tools  and  miscellaneous 


Total 

Amount, 

I  =  I  000,000. 


Total  wealth  of  United  States,  June,  1880. 


5,536 
10,197 

9.881 

419 

2,406 

5,000 

781 

6,160 

2,000 

612 

650 


Per  cent. 


43.642 


12.69 
23-37 

22.64 
.96 

5-51 
11.46 

1.79 

14. II 

4.58 
1.40 
1.49 


100.00 


Note.— Including  the  mileage  which  was  under  construction  at  the  time  of  the  census, 
and  money  spent  on  abandoned  grading,  there  may  have  been  the  equivalent  of  some 


26     CHAP.  I.-THE  INCEPTION  OF  RAILWAY  PROJECTS. 


Table  2. 


tf-«r^  *^T^  TnTAT  True  Valuation  of  each  State  of  the 

VALUATION   ^^-^^^%'^lJ^^^ilZ':,''S.C.^....    PBK.OOS 


personal  property,  so  that 


Trub  Valuation  per  Head. 


State, 


Maine 

New  Hampshire. 

Vermont.     

Massachusetts... 
Rhode  Island. 
Connecticut 

Average . 

New  York 
New  Jersey... 
Pennsylvania. 

Delaware 

Average . 

Maryland 

Disi.  of  Columbia. 

Virginia    

West  Virginia 

North  Carolina.. . . 
South  Carolina — 

Georgia 

Florida  ...  

Alabama. 

Mississippi. 

Louisiana. 

Texas  

Arkansas. 

Tennessee 

Kentucky. 

Average. 

Ohio 

Indiana. 
Illinois  .... 
Michigan  . 

Average . 

Wisconsin 

Minnesota. 

Iowa 

Missouri 

Kansas  . . 

Nebraska. 

Average. 

Dakota. 

Montana 

Wyoming 

Colorado  .... 
New  Mexico. 

Average. 

Arizona.   .. 

Utah 

Idaho. 

Washington. 

Oregon 

Average. 

Nevada  

California 

Average  U.  S. 


Total  Trce  Valuation,  i  =  1,000,000. 


Miles  of  Railway  (1840.  2.818) 


CHAP.  I  — THE  INCEPTION  OF  RAILWAY  PROJECTS.     2/ 


95,ocx)  miles  in  the  country,  indicating  that  make  the  average  value  placed  on  it  a  little  less 
than  $60,000  per  mile.  This  corresponds  closely  with  the  aggregate  of  stock  and  bonds 
per  mile  (Table  32),  but  it  represents  value  and  not  cost,  and  the  latter  has  probably  not 
been  over  $35,000  to  $40,000  per  mile  in  cash,  which  would  make  the  actual  cost  of  the 
railways  is  not  over  7}^  to  8  per  cent  of  the  national  wealth.  Yet  at  least  three  quarters  of 
the  enormous  aggregate  may  be  said  to  be  the  direct  result  of  railways,  since  without  them 
it  could  never  have  existed.  In  other  words,  every  dollar  of  cash  invested  in  railways  has 
on  an  average  added  $6  to  $8  to  the  national  wealth;  a  fact  which  has  had  much  to  do 
with  the  construction  of  railways  which  were  not  directly  profitable. 


Table  3. 
Railway  Capital  and  Public  Wealth  of  the  World. 

[Reconstructed  and  Revised  from  Mulhall's  "  Dictionary  of  Statistics."] 


United  States 

Canada 

Australia 

United  Kingdom 

France 

Germany 

Russia 

Austria 

Italy 

Spain 

Portugal 

Belgium 

Holland 

Denmark 

Sweden  and  Norway 

Switzerland 

Turkey,  etc 

Total  Europe 

Grand  Total 


Popu- 
lation, 
1880. 


Total 
Railway 
Capital. 
Millions. 


Per 

Mile  of 

Railway. 


I  =  1,000. 

50.410 

4o40 

2,880 


34.650 
37,430 
45.260 
84.440 
37830 
28.910 
16,290 

4.350 
5,480 
4.060 
1.960 
6,560 
2.810 
17.250 


5,780 

349 
272 


312.990 
370,620 


3,740 
2,400 
2.270 
1.500 
1,286 

524 

383 

58 

296 

131 

49 

155 
160 

117 


$ 
55.300 
46. 700 
50,500 


203.000 

133.000 

102.300 

99. 500 

100.300 

94. 200 

79.600 

74,800 

109.200 

90.300 

50.000 

32.000 

97.200 

64,600 


Per 
Inhabi- 
tant. 


1X2 

83 

97 


13.069 
19.470 


117.200 
84, 700 


117 
63 
49 
19 
34 
19 
24 

15 
53 
34 
24 

24 
58 
10 


National 
Wealth. 
Millions. 


$ 

50.340 
3,160 
2.900 


39 
49 


42,300 

39,200 

30, 700 

19,860 

19.000 

10.820 

7,620 

1,648 

5.720 

5450 

1,720 

3.580 

1,502 

3,490 


Ratio  of 
Railway 
to  Total 
Capital. 


Per  cent. 
II. 4 
II. I 
9-3 


8.8 
6.1 


192  600 
249,000 


7. 
7. 
6. 

4- 

5- 
3- 
5. 


2.4 

2.8 

4.3 
10.7 

3-3 


6.7 

7.8 


The  above  statistics,  except  population,  are  mostly  for  the  year  1882.  Many  errors  and 
inconsistencies  probably  exist  in  this,  as  in  all  similar  estimates.  No  great  accuracy  is 
possible  in  them. 

According  to  Mulhali  the  wealth  of  Britain  has  more  than  doubled  in  the  past  40  years, 
and  qu2idrupled  in  70  years.  While  the  indirect  benefits  of  railways  have  been  far  less  in 
Europe  than  in  the  United  States,  it  is  tolerably  certain  that  at  least  40  per  cent  of  the 
present  wealth  of  Europe  would  not  exist  except  for  them. 


CHAPTER  IL 


THE    MODERN    RAILWAY    CORPORATION. 

22.  Modern  railway  corporations,  even  the  strongest  of  them, 
have  but  a  narrow  margin  for  mistakes.  It  is  important  that 
we  should  have  that  fact  clearly  before  the  eyes,  and  the  reasons 
why  it  must  be  so,  in  order  that  the  atmosphere  of  wealth  which 
surrounds  the  period  of  construction  may  not  beguile  us  into 

folly. 

The  origin  of  most  modern  railway  corporations  is,  in  its 
economic  aspects,  about  as  follows  :  A  certain  number  of  men 
conclude  that,  for  anyone  of  the  reasons  before  considered,  there 
is  sufficient  need  of  a  railway  in  a  certain  region  to  make  it,  when 
completed,  worth  more  than  it  has  cost  to  those  who  have  built 
it,  so  that  a  "  profit,"  or  creation  of  a  greater  value  than  the 
expenditure,  will  accrue  to  them. 

Ordinarily,  this  sanguine  expectation  is  at  least  so  far  justi- 
fied that  the  property  when  completed  is  worth  to  some  one,  in 
one  way  or  another,  all  or  nearly  all  it  has  cost,  although  there 
may  be  no  great  profits.  In  any  rapidly  growing  country,  like 
the  United  States,  the  general  rule— subject  to  numerous  and 
painful  exceptions— has  been  and  is  that  railway  properties,  like 
other  enterprises  of  the  kind,  tend  to  be  very  productive,  and  to 
eventually  rise  in  value  far  above  their  real  cost,  often  to  many 
times  their  cost. 

23.  For  this  reason  it  has  very  frequently  happened  in  the 
United  States  that  enterprises  have  appeared  to  be  of  so  sound 
a  character  that  they  have  been  almost  immediately  able  to 
borrow  on  mortgage  their  entire  capital  for  construction,  or 
even    a   still  larger  sum,   and   the  original  projectors   and   true 


CHAP.   II.— THE  MODERN  RAILWAY  CORPORATION.       29 


"owners"  of  the  property  have  not  been  required  to  invest  any- 
thing whatever  in  the  property  themselves  beyond  their  original 
sagacity  in  initiating  the  enterprise— a  quality  which  has  its 
value  in  railway  business,  as  in  most  other  human  affairs.  In 
all  cases  they  can,  if  they  choose,  borrow  on  mortgage  whatever 
sum  they  can  make  capitalists  believe  is  or  will  be  the  minimum 
value   of   the  property.     Usually  they  not  only  choose,  but  are 

compelled  to  do  this. 

24.  The  original  projectors,  who  alone  appear  in  the  manage- 
ment of  the  enterprise,  and  who  alone  constitute  what  is  known 
as  "the  Company,"  then  simply  make  good  the  deficiency,  if 
there  is  any  deficiency,  in  the  means  for  construction;  assuming 
what,  in  the  general  opinion,  is  the  whole  risk  of  the  enterprise. 
For  taking  this  risk,  as  well  as  for  their  services  in  initiating  and 
carrying  on  the  enterprise,  they  obtain  nothing  more  than  what 
may  be  called  the  speculative  interest,  viz.,  that  portion  which 
fluctuates  with  and  depends  solely  upon  the  skill  and  good  judg- 
ment with  which  the  property  has  been  originally  planned  and 
is  afterwards  managed;  which  may  be  wiped  out  in  a  moment 
or  may  become  very  valuable. 

25.  This  interest  is  in  modern  times  supposed  to  be  repre- 
sented by  the  stock  or  (in  England)  "shares,"  although  the  line 
between  stock  and  bonds  or  mortgage  securities  is  not  always 
sharply  drawn.  The  proportion  which  the  stock  and  bonds 
bear  to  each  other  varies  greatly  in  different  parts  of  the  United 
States  and  of  the  world.  In  regions  where  capital  is  abundant, 
and  there  are  small  chances  of  either  great  loss  or  great  gain, 
those  who  believe  in  the  enterprise  and  would  be  willing  to  lend 
money  on  its  minimum  value  will  prefer  to  own  it  outright,  and 
few  or  no  mortgage  bonds  will  be  issued.  Such  is  the  case  in 
England  and  on  the  Continent.  In  a  country  where  the  future 
is  all  uncertain,  but  where  population  and  traffic  is  advancing, 
literally,  by  leaps  and  bounds,  and  where  the  future  is  so  "dis- 
counted "  (as  it  is  all  but  inevitable  that  it  should  be)  that  lines 
are  built,  not  for  the  traffic  which  exists  but  for  the  traffic  which 
is  to  come,  the  opposite  conditions  will  all  but  inevitably  prevail. 


30       CHAP,    II.-THE   MODERN  RAILWAY  CORPORATION. 

The  bonds  themselves  will  then  partake  of  a  speculative  char- 
acter and  will  involve  as  much  hazard  as  large  investors  can  be 
persuaded  to  consent  to.  Consequently  there  will  be  a  constant 
tendency  for  roads  to  be  "  built  on  bonds,"  the  bondholders 
being  in  fact  sharers  in  the  speculative  risk,  but  to  a  less  extent. 
The  limits  of  doubt  as  to  the  future,  between  the  maximum  and 
minimum  value  of  the  property,  being  a  large  one,  they  know- 
incrlv  assume  a  portion  of  this  risk,  leaving  it  to  the  nom.na 
-Company"  to  manage  the  property,  and  trusting  that  they  will 
manage  it  as  skilfully  as  they  can,  as  their  own  sole  chance  of 
reaping  a  profit  for  themselves. 

These  latter  conditions  are  well  known  to  obtain  more  fully 
in  the  United  States  than  in  any  other  considerable  region  of  the 
world  and  on  that  account  it  is,  and  not  primarily  from  differ- 
ence of  laws  or  business  habits,  that  the  railway  system  of  the 
United  States  has  been  built  to  so  much  larger  extent  than  else- 
where on  borrowed  capital  represented  by  bonds. 

26  Under  conditions  involving  so  large  an  element  of  specu- 
lative'uncertainty,  as  well  as  such  great  probabilities  of  ultimate 
profit  many  abuses,  much  feverish  excitement,  many  deceptive 
exaggerations  both  in  good  faith  and  in  bad  faith,  much  gaining 
of  something  from  nothing,  many  cases  of  visionary  folly,  of  sad 
disappointment  and  of  deliberate  fraud,  are  all  but  unavoidable  ; 
yet  in  the  conditions  themselves  there  is  nothing  either  surpris- 
ing or  reprehensible  or  avoidable.  We  have  seen,  in  a  much 
exaggerated  form,  the  same  causes  producing  the  same  effects 
in  the  oil  excitement  of  1863-5,  yet  they  were  but  the  collateral 
evil  effects  of  a  movement  in  itself  in  every  way  healthy  and 
normal,  and  they  ceased  with  the  period  of  rapid  expansion  and 
sudden  and  irregular  profits. 

So  with  the  organization  of  our  railways.  The  existing  con- 
ditions, with  all  their  collateral  evils,  are  in  the  main  healthy 
and  natural  ;  and  whether  good  or  bad,  cannot  be  expected  to 
materially  change  until  the  process  of  rapid  development  and 
advance  in  wealth  has  ceased,  which  will  not  probably  be  for 
many  decades.      Until   that   time  railways  will  continue  to   be 


CHAP.    II.— 7 HE  MODERN  RAILWAY  CORPORATION.        3 1 


largely  built,  as  they   are  built,  on  bonds  and   faith  and    hope, 
•with  a  narrow  margin  of  financial  safety. 

27,  Itr  is  often  claimed  that  the  existence  of  these  conditions 
is  an  evidence  and  result  of  a  greater  national  rashness  in  doing 
business,  but  this  is  true  only  to  a  limited  extent.  The  main 
reason  is  that,  owing  to  the  rapid  development  of  the  United 
States,  the  margin  of  positive  and  certain  value  has  seemed  to 
capitalists  to  be  larger,  and  the  minus  side  of  the  speculative  and 
dubious  element,  the  proper  allowance  for  possible  depreciation, 
has  appeared  to  be  less.  The  same  general  law  obtains,  and 
always  has  obtained,  throughout  the  world,  that  such  properties 
are  always  built  on  borrowed  money  up  to  the  limit  of  what  is 
regarded  as  their  positive  and  certain  minimum  value.  Tlie 
risk  only,  the  dubious  margin  which  is  dependent  upon  sagacity, 
skill,  and  good  management,  is  assumed  and  held  by  the  Com- 
pany proper  who  control  and  manage  the  property. 

Thus  it  happens  that  in  America,  and  in  an  increasing  degree 
throughout  the  world,  the  nominal  *'  Company,"  which  the  engi- 
neer and  all  other  officers  serve,  and  which  exercises  full  control 
over  the  entire  property  for  the  time  being,  although  in  theory 
it  is  the  real  owner  of  the  property,  is  not  such  in  fact.  All  it 
really  owns  is  a  contingent  interest  in  the  results  of  its  own 
sagacity  and  skill  in  creating  a  property  which  shall  be  in  fact 
worth  more  than  what  lending  capitalists  consider  its  minimum 
probable  value.  Their  small  payment  for  this  contingent  inter- 
est (if  they  pay  anything  at  all)  is  precisely  equivalent  in  its 
nature,  although  less  objectionable  morally,  to  what  is  called  a 
"  margin"  on  stocks— it  is  sufficient  only  to  cover  tlie  financial 
risk  of  the  enterprise,  or  the  difference  between  the  actual  and 
necessary  cost  and  the  general  estimate  of  the  minimum  value  of 
the  line  when  completed,  which  is  represented  by  various  forms 

•of  bonds, 

28.  The  essential  truth  of  this  general  summary  is  not  de- 
creased by  the  fact  that,  to  be  entirely  correct,  it  should  take 
•note  of  many  apparent  anomalies  and  exceptions.  Thus  it  not 
infrequently  happens  that  the  issue   of  "  mortgage  bonds,"  and 


32       CHAP.    II.— THE  MODERlSr  RAILWAY  CORPORATION. 

even  tlie  cash  received  for  them,  is  alone  far  greater  than  the 
actual  investment,  and  still  more  frequently  that  a  large  propor-^ 
tion  of  the  bonds  are  "  taken"  ("  convey"  the  wise  i£  call)  and 
held  by  the  original  incorporators.  Usually,  in  such  instances, 
the  second  or  third  or  fifteenth  mortgage  bonds  are  in  reality 
the  stocky  and  represent  the  speculative  interest  dependent  upon 
management;  which  in  that  case  very  properly  controls  the  prop- 
erty, either  in  law  or  fact.  In  that  case  too,  when  the  property 
is  not  a  productive  one  and  a  necessity  arises  for  more  capital  to 
enable  it  to  hold  its  own,  some  new  device,  "  prior  lien"  bonds 
or  what  not,  is  used  to  transfer  the  true  mortgage  interest, 
involving  no  risk,  to  new  parties,  in  lieu  of  those  who  originally 
held  it,  or  thought  they  did.  Per  contra^  when  the  property  has 
been  successful,  then  begins  the  process  of  "  watering,"  so  called,, 
i.e.,  increasing  the  stock  or  bonds  by  new  issues  until  their  total* 
amount  bears  a  nearer,  or  at  least  more  satisfactory  relation  ta 
the  present  value  or  productive  capacity  of  the  property,  as  dis- 
tinguished from  its  original  cost.  There  have  not  been  wanting 
gross  frauds  and  impositions  in  this  practice,  as  is  not  unknown 
in  other  business  matters  ;  but  in  its  essence  it  is  an  entirely 
legitimate  and  proper  business  transaction,  in  the  nature  of  a 
capitalization  or  "salting  down"  of  realized  business  profit,  and 
belonging  as  justly  to  the  holders  of  the  property. as  the  corre- 
sponding rise  in  the  value  of  other  real  property.  A  certain 
argument,  whose  force  in  certain  individual  cases  is  universally 
recognized  by  intelligent  men,  can  be  made  against  the  reten- 
tion by  the  individual  of  all  such  "  unearned  increment,"  but  in 
the  general  judgment  of  mankind  the  argument  on  the  other 
side  is  immensely  stronger.  The  only  legitimate  distinction  in 
this  respect  between  railway  property  and  any  other  real  estate 
is  that  the  nature  of  its  origin  as  a  creature  of  the  State  justi- 
fies a  demand  that  its  monopoly  powers  shall  not  be  used  op- 
pressively, to  charge  more  than  a  fair  equivalent  for  service,  as 
measured  by  practice  elsewhere  or  on  other  kinds  of  traffic,, 
under  similar  circumstances  ;  but  the  just  increase  in  value  of  a 
well-located  railway,  which  does  not  abuse  its  monopoly  powers 


CHAP.-  II.— THE   MODERN  RAILWAY  CORPORATION. 


33 


to  make  unjust  exactions,  is  fairly  the  property  of  the  owners, 
however  large,  unless  and  until  the  public  are  prepared  to  in- 
sure the  investors  a  certain  minimum  return  as  well  as  deny 
them  the  uncertain  maximum. 

It  may  be  added,  that  the  mortgage  or  bonding  process  is 
carried  on  to  a  greater  extent  in  railway  than  other  business, 
simply  because,  unlike  most  other  business  enterprises,  a  certain 


•^20,000, 


000 


Fig,  1, — Diagram  showing  the  Financial  Record  of  the  Lake  Shore  and  Michigan 

SouTHHRN  Railway  from  1870  to  1885. 

considerable  fraction,  but  only  a  fraction,  of  the  income  of  their 
property  is  in  the  nature  of  a  monopoly  which  no  conceivable 
circumstances  can  destroy. 

29.  The  annual  interest  on  these  various  forms  of  mortgage, 
together  with  fixed  rentals  of  leased  property,  which  are  of  the 
same  nature,  constitute  what  are  known  as  the  fixed  charges, 
by  which  a  lar-ee  proportion  of  net   revenue  is  always  absorbed 


34       CHAP.   II.- THE  MODERN  KAIL  WA  V  CORPORA  TION. 


CHAP.   II.— THE  MODERN  RAILWAY  CORPORATION.       35 


on  the  most  prosperous  properties-very  frequently  nearly  he 
whole  of  it,  and  not  unfrequently  a  good  deal  more  than  the 
whole  of  it,  if  all  such  charges  were  paid. 

In  tables  immediately  following,  the  fact  that  these  are  the 
conditions  which  actually  exist  is  clearly  brought  out,  and  if 
they  were  more  generally  realized  by  engineers,  and  by  railroad 
officers  generally,  during  the  period  of  construction,  it  can  hardljr 
be  doubted  that  it  would  lead  to  more  careful  study  of  the  art  of 
obtaining  the  utmost  possible  value  from  the  money  expended' 
^  -  but  there  are  few  men  who  are 

not  elated  and,  as  it  were,  in- 
toxicated by  having  their  pock- 
ets full  of  borrowed  money,  even; 
when  the    responsibility  is   all 
their  own,and  on  so  small  a  scale 
that    its    length,   breadth,    and 
depth  can  be  readily  grasped. 
When  the  further  danger  is  add- 
ed of  dividing  up  the  responsi- 
bility among  a  dozen  or  morCy 
.  ,^_^__^__^^j__j   each  of  whom  sees  millions  in, 
/7>ear_CAar^f__Xr^   sight,  which  in  his  eyes  are  "the 
^       ^    -^     ^       ^  Company's,"  and  not  the  Com- 
es pany's  creditors',  and  a  small 


Operatinf€xpeiisei 

I  M.  0) N ^ '^. 

^  ?  CM  S  o» 


SjOOOfOOO 


:; o) 


^  ^  .T  —    ^^  AJ 


;::  00 


F,o.,._D,.o..MSHow,»o™.  F.-Kc«.R^-  part  o{  which  will  suffiee  for  all 
'SlZr'.^rJ.lZ  %'Z«^,r^t'^^l     possible  requirements  of  h.s  de- 
partment, the  impulse  ta  spend 
,roney  freely  may  well  become  too  great  for  average  humaa 
Tture  to  resist ;  l  that  the  enormous  sums  of  bonded  money 
handled  during  construction  will  create  an  atmosphere  of  wealth 
leadtg  to  a  r^ash  improvidence,  which  has  been  the  ch.ef  cause 
of  the  Mnkruptcy  of  many  lines.    As  the  engmeer  has  the  first 
«  whack"  at  the  Company's  funds,  and  at  a  time  when  the  judg- 
mint  of  the  coolest  men  is  most  likely  to  be  toss.ng  about  on 
The  dancing  waves  of  a  "boom"  at  its  very  height   h.s  dagger  .s 
particulari;  great ;  and  he  especially  should  reah«e  that  th« 


RULE  with  new  American  railways  is,  and  must  continue  to  be,, 
that  a  very  moderate  percentage  of  difference  in  either  the  first 
cost,  or  the  operating  expenses,  or  (above  all)  the  revenue,  means 
to  the  original  projectors,  whom  alone  he  serves  or  knows,  all 
the  difference  between  success  and  failure. 


m      up      tOE     Spi         rj2.53    ni.Si 


/Q74      1875         76  77         78  79        /8B0       81  82         83  54        /88S       86- 


Fig.  3.— Diagram  showing  the  Financial  and  Traffic  Record  of  the  Chicago  &  North* 

WESTERN  Railway,  1874-1886. 

[Figures  in  squares,  or  points  surrounded  by  squares,  g:ive  the  receipts  per  ton-mile 
and  passenger-mile ;  the  lower  figures  being  those  per  ton-mile.] 

In  Figs.  I.  2,  and  3  is  shown  graphically  how  very  small  is  the  margin  of 
profit  which  makes  the  difference  between  solvency  and  insolvency  even  in  the 


36      CHAP.   II.-THE  MODERN  RAILWAY  CORPORATION. 

~~  ■         Tu...  iin,«  have  not  been  chosen  as  specially  mark»d 

tional  revenue. 

30  In  fact,  the  situation  is  somewhat  worse  than  if  the  Com- 
panv  merely  began  business  with  a  heavily  mortgaged  prop- 
Lu  owned  In  fee.  The  theory  that  the  Company  -  the  own- 
in  fact,  as  it  is  in  form,  of  t'>VutcrvS.":.ti  n  i:!:;^ 

rrbuTutorrcreS  rUtrasTth  ..  re.  facts  w..ici. 
prevail  in  the  United  States,  and  for  the  most  P^"  'h-;^  ^'^^^^'^ 
world  to  consider  that  the  mortgage  mterest  uself  bu.kls  and 
Zlt'Z  real  property,  as  a  man  might  build  a  '--  or  aco.-y 
to  rent  to  others,  induced  thereto  by  the  allegations  of  the  man 
Iging  Co-pany  that  in  that  case  they  can  and  will  earn  and  pay 
SorT  large  rental  on  the  property  from  the  profits  of  the 
business  which  they  propose  to  carry  on  with  the  property  and 

^"a!   Tto'lhe  truer  manner  of  looking  at  the  facts,  both  be- 

;  0,e  '  motVaKe"  is  ordinarily  far  in  excess  of  the  mort- 

Tg    .  valu^o    t'h?;roperty  as  property,  closely  "PP-imat  ng 

gagmg  va  >-  ,  ^„^  because  the  property 

Use'lflsl     but  ab  ottdy  worthless  except  for  the  one  particular 
bus  in  ss     Wch  it  was  built  to  carry  on,  so  that  the  loan  or  mo,.- 

^Se  involves  the  ^^^^^^ r,^T:::v^::^:^- 

1     r     And  as  the  full  cost  of  all  the  fixed  property  .s  then 
riwav'sfpfactalyfadvanced,  and  frequently  the  cost  of  all,  or 

most  of  the  portable  plant  (rolling  stock)  in  addition,  the  nom.- 
Tl  mortgag'interest  is  so  large  that  it  really  amounts  pract,- 


CHAP,   II,— THE  MODERN  RAILWAY  CORPORATION.       37 


cally  to  an  ownership  interest  in  the  real  property  ;  and  all  that 
the  mortgage  interest  does  not  own  is  the  immaterial  franchise, 
which  necessarily  goes  with  the  property  wlien  and  if  they  as- 
sume control  of  it.  This  is  the  additional  security  which  makes 
the  nominal  mortgage  interest  a  real  one,  except  that  usually, 
the  operating  company  are  obliged  either  to  invest  some  money 
themselves  in  plant  to  borrow  the  rest  of  it,  or  to  throw  in  an 
interest  in  the  business  (stock)  in  order  to  persuade  outsiders  to 
build  the  plant.  Very  frequently, — in  fact — usually,  individuals 
in  the  operating  company  (stockholders)  also  lend  money  (buy 
bonds)  for  the  erection  of  the  plant. 

32.  The  instances  where  the  original  projectors,  even  of  lines 
which  liave  ultimately  proved  well  justified  and  highly  success- 
ful, have  been  ruined  by  depleting  their  means  too  rapidly  with 
unwarranted  or  deferable  expenditures,  and  have  been  compelled 
to  yield  their  control  of  the  property,  almost  on  the  eve  of  its 
success,  have  been  very  numerous.  A  single  instance,  selected 
almost  at  random,  of  the  startling  vicissitudes  to  which  such 
properties  are  subjected,  and  of  the  dangers  of  the  most  merito- 
rious enterprises  from  the  long  periods  of  depression  through 
which  they  usually  have  to  pass  soon  after  their  construction, 
and  from  the  scanty  means  of  the  original  projectors,  may  be  in- 
structive. 

33.  Within  a  few  years  after  its  construction,  what  has  since  become 
the  St.  Paul,  Minneapolis  &  Manitoba  Railway,  then  the  St.  Paul  &  Pa- 
cific, was  a  very  striking  example  of  such  reckless  management  of  rail- 
way investments. 

Its  construction  began  in  the  flush  times  of  1872-3.  Working  then 
318  miles,  it  earned  only  $630,000  gross  and  $166,000  net,  the  latter  being 
at  the  rate  of  only  $523  per  mile  of  road.  Its  debt  (exclusive  of  stock) 
was  then  over  $50,000  per  mile,  and,  no  interest  being  paid  on  any  part 
of  it,  a  receiver  was  appointed. 

In  1873-4  and  1874-5  ^^e  net  earnings  were  still  less. 

In  1876-7,  an  extension  of  104  miles  into  the  Red  River  Valley  hav- 
ing been  completed,  the  net  earnings  were  nearly  doubled,  and  became 
$749  per  mile. 

By  1878,  although  the  bonds  of  the  Company  had   become  almost 


38       CHAP.   II.-THEMODERN^SAJI^i^^ 

.onhless,  t>,e  receiver  succeeded  in  ^^^l^:Z:^^:7Z 
boundary,  in  time  to  save  a  large  land  g^"'' f""* '^';;^^;,  projectors, 
property  began  to  dawn  ;-five  V-s  too  la  e  fo^^^^^^^^^ 

A  new  company  was  then  "^^-''^^.'^'P^",,,  Love  specified,  and 
sale,  and  found  itse  f  tl.e  P°=^;^X° V^^,^,; g  "gt^o-less  than  $.3,000 

'«  ■"","  "TTentrst\hr  atd  r  nt  b^n  to  b;  of  immed.ate  value, 
per  m>le.  Then  fi/^'^'^.J^^^-Canada  Pacific  was  building  beyond  U. 
rr;:;:rrrrdTprope%  Which  had  been  almost  worthless. 

^"  x^bLrrtiru^i  r^rZ-and  its  progress  is  shown  in  Table  4. 

Table  4. 

FINANCIAL  HISTORY   OP  THE  St.    PaUL.    MINNEAPOLIS    &    MANITOBA 

Railway. 


CHAP.   II.— THE  MODERN  RAILWAY  CORPORATION.       39 


Rvthe  end  of  .883  the  road  was  earning  net  more  than  any  road 
-     H   nf   n^ica-'O  ex-ept  two  (the   Rock    Island   and    Ch.cago  & 
=.ld"th^';::m°.rs;t^i.  -i.-    THe  r  a.  sur^^^^^^^^^^     ast - 

^n:  t:^  'ZTS  r^t  ^m  llX  t!^  l  the  company  the 
;::ses"rn':!f  "he  trafhcof  one  of  the  most  fertile  valleys  on  the  Con- 

*'"^^u  .hh  tide  set  in      Immigration  and  the  price  of  wheat  fell  off. 


years,  which  alone  can  be  given  in  this  volume,  the  record  was  as  shown 
in  the  last  two  lines  of  Table  4,  the  contrast  between  which  and  the  last 
year  of  the  flush  period  is  notable. 

In  the  last  year,  in  spite  of  the  falling  off  in  prosperity,  which  had  in 
it  no  element  of  immediate  disaster,  bonds  to  the  amount  of  50  per 
cent  of  the  stock  were  "  sold  "  to  stockholders  for  10  cents  on  the  dollar, 
which  was,  of  course,  equivalent  to  a  dividend  of  some  45  per  cent, 
more  if  the  future  of  the  property  did  not  belie  its  promise.  From  the 
point  of  view  of  the  public  interest  there  was  no  danger  of  this.  Its 
future  was  magnificent  and  assured.  As  respects  the  individual  owners, 
great  as  had  been  their  profits  to  date  from  securing  control  of  this  for- 
merly bankrupt  property,  this  was  and  is  far  less  certain. 

34.  The  instructive  feature  of  the  example  is  that  even  now  (1885), 
failing  anyone  of  these  following  conditions,  ruin  or  serious  loss  of  all 
recent  investors  in  the  stock  of  property  would  be  near  at  hand : 

1.  The  fixed  charges  are  only  $1358  per  mile,  whereas  double  that 
iigure  or  even  more  would  be  more  usual.  At  the  latter  figure  a  com- 
bination of  many  causes  might  bring  the  net  earnings  below  it. 

2.  The  rapid  fall  of  rates,  which  otherwise  would  have  extinguished 
the  surplus,  was  met  by  important  improvements  of  the  main-line  grades, 
and  by  the  introduction  of  more  powerful  locomotives,  as  well  as  by  the 
natural  economies  resulting  from  heavier  trafliic,  so  effectually,  that  in  the 
last  year  but  one  of  the  table  24  per  cent  more  freight  was  moved  with- 
out any  increase  of  engine  mileage. 

3.  The  revulsion  occurred  at  a  time  when  the  general  depression  of 
business  was  not  marked,  when  the  Company  was  not  embarrassed  by 
excessive  obligations  for  new  construction,  and  when  the  falling  ofl[  in 
trafllic  and  revenue  was  in  no  respect  panic-like.  Otherwise,  even  as 
sound  a  property  as  this  had  proved  itself  to  be,  had  it  entered  upon 
considerable  expenditure  for  new  construction  or  improvement,  based 
on  a  standard  conforming  to  the  present  large  earning  power  of  the  prop- 
erty as  a  whole  instead  of  the  probable  earning  power  of  the  additions, 
separately  considered,  might  well  have  found  itself  again  a  bankrupt. 

35,  That  such  contingencies  and  fluctuations  are  not  excep- 
tional, is  indicated  by  the  aggregates  of  railway  foreclosures, 
shown  in  Table  5,  which  in  1885  rose  to  the  aggregate  of  2880 
miles  with  $139,658,000  in  bonds  ($48,500  per  mile)  and  $120,- 
090,000  in  stock  ($41,700  per  mile)  or  $268,213,000  in  all  ($93,136 
per  mile)  the  bonds  alone  probably  representing,  as  is  so  com- 


40      CHAP.   II.— THE  MODERN  RAILWAY  CORPORATION. 


Table  5. 
Railway  Foreclosures. 


Year. 

Miles. 

Capital  Stock. 

I    =    XOQO. 

Funded  Debt. 
I  =  1000. 

Floatinjr  Debt. 
X  —  1000. 

Total. 

X    =    IO(X>. 

1881 

2,617 

668 

1,190 

714 

2,8So 

$51,273 

20.751 

24,588 

12.894 

120,090 

$76,645 

23-999 
38.19S 

13.061 

139.658 

($10,000?) 
10.074 
2.4S2 

423 
8,465 

$137,923 

1882 

54.824. 

1883 

65.268 

1884 

26.378 

1885 

268.213 

Total,  5  yrs.. . 

8,069 

$229,601 

$291,561 

$31,444 

$552,606 

Per  mile,  average 

$28,455 

$36,135 

$3,897 

$68,487 

Per  mile.  i88^ 

$41,697 

$48,499 

$2,940 

$93.13^ 

The  above  is  compiled  from  "  Poor's  Manual,"  1886.  It  is  unquestionably  full  of  errors, 
but  no  authentic  or  complete  figures  exist.  The  general  fact  that  the  bonds  and  stocks 
of  bankrupt  lines  run  a  good  deal  higher  than  those  for  solvent  lines  is  clear,  as  the  most 
serious  errors  are  probably  in  the  earlier  years. 

The  Commercial  and  Financial  Chronicle,  in  its  October,  1884,  Investors'  Supple- 
ment presented  a  valuable  table  showing  the  railway  companies  now  in  default  on  pay- 
ment of  interest  on  bonds.  Only  railways  in  the  United  States  are  included,  Mexican 
and  Canadian  lines  being  omitted,  and  only  the  particular  issues  of  bonds  are  taken  on 
which  default  is  made,  although  the  mileage  given  includes  all  operated  by  the  defaulting: 
companies.  The  table  includes  all  companies  defaulting  during  the  period  covered,  which 
had  not  resumed  payment  in  full,  and  which  had  not  been  foreclosed  and  reorganized. 
The  totals  are  summed  up  in  the  following  table,  in  which  comparison  is  made  with  the 
defaults  of  1873-76: 


Total  defaults,  October,  1884.. 
Entire  railroad  system  of  U.  S. 
Per  cent  of  defaults  to  total. . . 


Jan.  I,  1884. 


Total  defaults,  1S73-1876 

Entire  railroad  system  Jan.  I, 
Per  cent  of  defaults  to  total. . . 


1876. 


Increase  in  mileage  and  bonds  during  five  years  pre- 
ceding Jan.  I.  1884 

Increase  in  mileage  and  bonds  during  five  years  pre 
ceding  Jan.  i,  1876 


Mileage. 

15.986 
121.592 

1314 


Amount  of 
Bonds. 

$315,283,000 

3.455,040.283 

9.12 


74,096 


39.818 
21.232 


$783,967,665 

2,175,000.000 

36.04 


$1,157,249,467 

*636,96o,o(X> 


*  Estimated  at  $30,000  per  mile. 


CHAP.   II.— THE  MODERN  RAILWAY  CORPORATION.       4 1 

The  whole  number  of  companies  in  default  in  1884  was  only  42,  against  197  in  the 
former  period.  In  the  former  period  of  defaults,  about  20  companies  out  of  the  total  197 
that  were  embarrassed  were  old  railroads  that  were  well  established  and  once  had  a  pay- 
ing business.  In  the  later  period,  out  of  42  companies  named  in  the  table,  none  can  be 
fairly  said  to  have  had  a  well-established  and  paying  business  on  the  basis  of  their  present 
lines  and  existing  liabilities,  unless  such  companies  as  Erie,  Wabash,  and  Reading  be 
classed  in  that  category. 

On  British  railways,  which  are  subject  to  far  fewer  vicissitudes  than  those  of  the  United 
States,  the  average  dividend  of  ^\  per  cent  is  divided  approximately  as  follows, — United 
States  statistics  from  the  census  of  1889  being  added  for  comparison  : 


United  States. 

British. 

18.8      1 

16. 1  per  cent 

pays 

• 

no  dividends. 

i.o  "       " 

under i 

per 

cent 

10.2 

4.9  "       •• 

"     2 

9.2 

32  '«       ii 

.         "     3 

3-1 

7-3  "       " 

.         "     4 

2.5 

23  4  "       '♦ 

.         "     5 

5.7 

21.7  "       ♦' 

"     6 

6.5 

20.0  "       " 

"     7 

<^-5 

1.0  "       " 

•'     8 

7-4 

0.4  "       •♦ 

.         "     9 

3-4 

0.4  "       •' 

"    10 

3.9 

0.6  "       ♦♦ 

about  15 

WhMe  exact  figures  on  which  to  base  a  judgment  are  not  available,  it  is  not  probable 
that  more  than  one  fourth  of  the  exi.sting  mileage  of  the  United  States  has  escaped  fore- 
closure proceedings  or  default  on  bonds  necessitating  a  receivership.  Many  roads  which 
are  now  among  the  strongest  properties  have  been  through  such  difficulties  several  times 
in  their  earlier  history;  while,  on  the  other  hand,  many  others,  like  the  Denver  &  Rio 
Grande,  Philadelphia  &  Reading,  and  other  strong  properties  whose  future  seemed 
assured,  have  been  overtaken  by  disasters  resulting  in  great  part  from  the  intoxication  of 
long-continued  success.  So  that  the  properties  are  few  indeed — and  those  mainly  the 
ones  which  build  no  new  lines — of  which  it  can  be  predicted  with  any  certainty  that  they 
may  not  become  insolvent  in  the  next  period  of  serious  depression. 


Table  6. 
Estimate  of  Futitre  Railway  Construction  in  the  United  States. 

[Prepared  by  Edward  Atkinson,  of  Massachusetts,  for  various  groups  of  States  as  described 

on  next  paee.l 


Group  of  States. 

Mileape  still 

needed  from 

Jan.  I.  i88i. 

19  years. 

Mileape  built 

from  Jrtn.  i, 

1881,  t"-.  Jan., 

1885. 

4  years. 

Per  cent 

total  estimate 

buik  in 

4  years. 

Mileape  still 

needed  before 

yv.D.  1900. 

15  years. 

Class  I 

Class  II 

36.236 

27.199 

34-472 

9  6^2 

9.8S8 

8  597 

5  282 

8351 
2.893 

5.857 

24 

I9i 

24 

30 

59 

27639 
21.917 
26,121 

6759 
4031 

Class  III 

Class  IV 

Class  V 

Totals 

"7,447 

30.980 

26.3 

86,467 

42       CHAP.   II.— THE  MODERN  RAILWAY  CORPORATION, 


monly  the  case,  somewhat  more  than  the  actual  total  expendi- 
ture to  create  the  entire  property.  This  amounts  to  nearly  three 
per  cent  of  the  mileage,  and  over  four  per  cent  of  the  capitalized 
cost  of  the  entire  railway  system  of  the  country,  and  that  too  in 
a  year  which  was  in  no  respect  a  particularly  bad  one  finan- 
cialiy,  as  will  be  seen  from  Table  5,  which  gives  similar  figures 
for  several  vears  back. 

36.  The'fact,  illustrated  by  the  history  just  given  of  a  road 
in  the  far  West,  that  the  intoxication  of  realized  success  will 
lead  even  prosperous  companies  to  assume  dangerous  and  reck-  . 
less  liabilities,  becomes  especially  important  in  view  of  the  fact 
that  in  the  future  a  large  portion  of  the  new  mileage  will  be 
constructed  by  such  lines.  A  carefully  studied  forecast  of  the 
probable  mileage  to  be  constructed,  by  Mr.  Edward  Atkinson, 
made  in  1881,  and  confirmed  as  a  moderate  and  cautious  esti- 
mate which  will  almost  certainly  be  exceeded  by  experience  up 
to  1885,  brings  out  this  fact  clearly,  in  addition  to  having  &n  in- 
terest of  its  own,  and  is  given  in  Table  6. 

Description  of  Groups,  Table  6. 

ClaS  I  "retchinK  down  the  Atlantic  coast  to  Florida,  estimated  to  have  by  .900  ^ 
""  cf^'^lil'  tl^  \f^.SX  'the  far  West  and  South,  with  one  mile  fer  .6  sg. 
"' cU'  iv"inclute  tie  5  States  of  Maine.  Nevada,  Colorado,  Oregoi,  and  California, 
^%^::.  ^Hiik^ot^l^^'^y'^l^l^^loL  Territories,  with  .«  miU per  6,  sg. 
"^^otal  united  States  mileage  whe^est^^e  -^P-Pf^'^^^^'^'J^^^Sjirio^  .^.^5 
;2?;  X?  .18^  'r5,76?miref  ^^ainsfan-^verage  of  7,745  miles  per  year  for  the  prev«>us 
4  yelrs.    The  Estimate  is  almost  certain  to  be  largely  exceeded. 

Table  7. 

PRorRESS  AND  Extent  of  the  Railway  System  of  the  World. 
Progress  AND^  i=.xi  ^^^^  j,„,h^„.,  ..  oiconary  of  Statistics."] 


Miles  Open. 

Cost  (mi 

llions,  $). 

1840 

I80O 

1860 

1870 

1880 

1850 

1800 

1870 

1880 

United  Stairs... 
United  Kingdom 

Continent 

Canada,  etc 

2.818 

838 

1,074 

9,021 
6,621 
8,311 

538 

30,635 

10,433 

21,815 

4.228 

52,914 
15.537 
49,320 

12.339 

93,349 
17,945 
86.818 

31,804 

292 
1,166 

652 

34 

2.144 

1,094 

1,685 

1.730 

243 

2,332 

2,572 

4,320 

860 

S.070 
3.640 
8.690 
2,010 

Total  .   

4-73° 

24,49^ 

67.111 

130.110 

229.916 

4.752 

10,084 

19,410 

CHAP.   II.— THE  MODERN  RAILWAY  CORPORATION.      43 


Table  8, 
Railways  of  the  World,  January  i,  1884. 

[From  Prof.  A.  T.  Hadley's  "  Railroad  Transportation,  its  History  and  its  Laws."] 


Miles. 


America. 
Europe. . 
Asia  . . . . 
Africa. . . 
Australia 


140,000 

114,000 

11,600 

3.400 

6,500 


275,500 


Capital  Invested. 


$8,400,000,000 

16,110.000.000 

775,000,000 

240.000,000 

325.000,000 


$25,850,000,000 


Per  Mile. 


$60,000 

115.000 

66,000 

70,000 

50,000 


$72,200 


Germany 

Great  Britain  and  Ireland 

France 

Russia 

Austria  and  Hungary 

Italy 

Spain 

Sweden 

Belgium 

British  India . 

United  States 


Length, 
Jan.  I,  1884. 


22,300 

18,600 

18,500 

15.700 

12,800 

5.900 

5.100 

4,000 

2,600 

10.500 

120,000 


Per  cent 
Increase 

in 
5  years. 


8 

5 
18 

7 
12 

13 
16 

14 
6 

20 
43 


Miles  of 
Road 
to  100 

sq.  miles. 


10.6 

15-2 

9- 
o. 

5- 

5- 
2. 

2. 

23.2 

0.7 

3-4 


.0 

,8 

•3 
,1 
,6 

3 


Miles  of 

Road  to 

10,000 

inhab. 


4 
5 
4 

I 

3 
2 

3 

8 

4 

o 

22 


9 
3 
9 
9 
4 
o 
o 

7 

8 

4 
5 


Cost 

per 

mile. 

Dollars. 


105.000 

204.000 

128  000 

80,000 

105,000 

92,000 

78,000 

30.000 

132.000 

66,000 

61,000 


Equipment  per  100  miles. 

Pass. 

Moved 

(Millions). 

Tons 
Moved 

Locom. 

Pass.  cars. 

Freight. 

(Millions). 

Germany 

1882 
1882 
1881 
1881 
1882 
1882 
1880 
1881 
1881 
1883 
18S3 

51 
76 
46 
40 
30 
29 
26 
16 
72 
24 
22 

95 

232 

105 
50 
62 

88 

77 
36 

139 
65 
21 

I.oSi 
2,298 
1,207 

775 
716 

510 

468 

401 

1,840 

436 

663 

224 

655 
180 

33 
47 
34 
15 
7 
57 
65 
313 

198 

Great  Britain 

291 

France   

93 

Russia 

14 

Austria 

70 

Italv 

II 

Spain 

9 

Sweden ... 

5 

Belgium 

British  India 

37 
19 

United  States 

400 

Comparison  with  Table  10  and  others  will  show  that  there  is  considerable  uncertainty 
in  these  figures.  It  should  be  remembered  that  American  rolling-stock  is  much  heavier 
and  larger  than  foreign,  and  that  the  average  distance  over  which  each  passenger  or  ton  is 
moved  is  far  greater. 


44       CHAP.   II.— THE  MODERN  RAILWAY  CORPORATION, 


Table  9. 

Progress  of  American  Railway  Construction  by  Groups   of  States» 

AND  OF  Foreign  Railway  Construction. 


1850 

1855 

1860 

1865 

1870 

1875 

1880 

1885 

^iT  N#*Av  Rnc^land  Stales 

2,508! 

2,807 

395 

1,620 

4'5 
1,256 

20 

3,469 

4.849 
624 

3-294 
X.523 
4.>73 

394 

40 
8 

3,660 

5.841 
865 

5.1" 
3.726 
8,684 

2,380 

345 
23 

3.834 
7.594 

945 
5.228 
3,901 
9,646 

3,201 

503 
233 

4.494 

9.709 
1,282 

6,094 

5.»35 

I3,»77 

9,506 

1.5S3 
1.934 

5.638 

12,639 

i,8i6 

7.047 
6.240 

18,879 

14.903 

3,966 
2,968 

5-977 

13.865 

2,005 

7,803 
7,008 

21,964 
23,259 

6,582 
5.886 

6,310 

New  York,  N«w  Jersey,  Penna.. 

Delaware,  Maryland,  W.  Virginia 

Virginia,  N.  Ca.,  S.  Ca.,Ga.,  Fla. 

Alabama,  Miss.,  La.,  Tenn.,  Ky.. 

Ohio,  Michigan,  Indiana,  Illinois. 

Wisconsin,    Minnesota,     Dakota, 
Iowa,  Nebraska,  Kan.,  Mo 

Indian  Ter.,  Arkansas,  Texas,Col- 
orado,  Wyoming,  Montana 

Pacific  States  and  Territories 

i6,97J^ 

2,366 

11,127 

9.675 
27,101 

31,527 

13-734- 
9-954 

Total  United  States  

9,021 

18,374 

30,635 

35.085 

52.914 

74,096 

93.349 
f_    1  . 

128,967 

t  „.v.:#>k 

The  above  was  compiled  trom  me  taoies  in  various  issuer  ^^   »  -v..  ^ 
are  full  of  numerical  errors.     These  have  been  corrected  as  far  as  possible. 

Foreign  Countries. 


1840 

1845 

1850 

1855 

1860 

1865 

Great  Britain 

Franre         

838 
271 
340 

2,536 

551 

1.429 

6,621 

1.879 

3.747 

38 

8.335 
3.459 
5.138 
1,218 

10.433 
5.900 
7,212 

2,173 

13,289 
8,477 
9,105 
2,231 

frermanv 

Canada. 

T„TA,   Mil  FAfiE  OF  RAILWAY  CONSTRUCTED  AND  IN  OPF.RATION  IN  THE  UNITED. 
STATE^    FOR  EACH  YEAR  FROM  THE  BEGINNING  OF  RAILWAY  CONSTRUCTION. 


isao 

1840 

1850 

1860. 

1870 

1880 


23 

3,818 

9,021 

30.635 

52.914 

93.349 


95 

3.535 

10,982 

31,286 

60,293 

103,145 


2 

229 

4.026 

12,908 

32,120 

66,171 

114.713 


8 


380 

4.185 
15.360 

33.170 
70.268 

121,454 


4 

633 

6 

1,098 

6 

m 
4 

8 

9 

1.273 

1.497 

1.913 

2,302- 

4.377 

4.633 

4.930 

5- 598 

5.996 

7.36s 

16.720I   18,374 

22,016 

24.503 

26,968 

28.789 

33.908 

35.085    36,801 

39.250 

42,229 

46,844 

72,385 

74,096    76,808 

79,088 

81,717 

86,46j 

I  5.3791128,967! 

ANNUAL    INCREASE. 


134 

151 

253 

465 

175 

224 

416 

389 

49  > 

159 

192 

256 

297 

668 

398 

1,369 

1,926 

2,452 

1,360 

i.6S4 

3.642 

2,687 

2,465 

1.821 

834 

1.050 

738 

1,177 

1,716 

2,449' 

2,979 

4,615 

5.878 

4.097 

2,117 

1,711 

2,712 

2,280 

2,629 

4,74^ 

11,568 

6,741 

3-825 

3.588 

CHAP.  II.— THE  MODERN  RAILWAY  CORPORATION.       45 


Table  10. 

Mileage,   Cost,   etc.,   of    European    Railways,   with    Total   Cost    of 
Construction  and  Average  Cost  per  Mile. 

[Rearranged  and  recomputed  from  the  Revue  Generate  des  Chemins  de  Per,  1886.] 


Country. 


United  Kingdom. 


Belgium 

France 

•Germany 

Austro- Hungary. 


Switzerland. 

Spain 

Portugal 

Russia 

Italy 

Holland 

Sweden  ... . 
Denmark.. .. 
Norway 


Germany  in  detail — 

Prussia 

Bavaria 

Sa.x  3ny 

Wurtemburg , 

Baden     

Alsace-Lorraine 

Other  German  States  .. 


Total  Germany 


Minor  European  Countries — 

Bosnia  and  Hertzegovina 

Bulgaria 

Finland 

Greece  

Luxemburg 

Rou  mania 

Turkey 


Miles. 

1883-5. 


x8,864 


1.885 
16,578 

21,785 

12,603 


X.795 

4.550 

927 

14,226 

5-871 
1.406 

3.975 
926 
970 


Cost. 
Millions. 


106,361 

12,636 

2,833 

1.434 

968 

818 


3.096 


21,785 

Kilos. 
370 

222 

X,l8l 

22 

366 
1,503 

i.'73 


4.837 


$3,895.10 


334-45 
2,232.20 

2,248.40 
1,279.80 


184  88 

442 . 26 

90.  II 

1,382.30 

554  50 

12734 

59-34" 

37.00 

3351 


Ay.  Cost 
Per  Mile. 


$12,901.19 

1,309  40 
268.39 

149  35 

110.95 

99.70 

310.61 


2,248.40 


(some  3.000 


$206,490 


177.420 
134,640 
103,210 

101,550 


103,000 

97,200 
97.200 
97,168 
94,448 
90,918 

41.563 
39.961 

34,548 


$121,300 

103,620 
94.7-28 
104.150 
113.140 
121,880 

100,328 


103,210 


miles). 


Sq.  Miles  per 
Mile  Ry. 


Eng... 
Scot.. 
Ire..  .. 


Aus... 
Hung. 


4-4 
10.3 
13.0 

~5 
4-2 

XI    I 

9-4 

14.7 

24.0 


18.8 
9.2 

38 

37 

130 

18 

9 
41 
13 

127 


Per  Cent 

Increase, 
One  Year. 


32.9 

X0.2 
9-4 
4-4 
8.4 
7.0 


8.4 


9-4 


87.0 

179  o 

196  o 

xSoo.o 

4  4 

53  9 

XII. 5 


2.03 
1.29 
2.01 

1. 91 

2.13 
2.05 

2.07 
2.98 
3.12 


3  04 
3.66 

330 
4.98 
5  72 
4.86 
3.21 

I. 13 
1.80 
1.97 


307 

a. 13 

X.76 
2.36 
2.24 
1.95 

1.96 


a. 07 


5- 
14 
2. 
147  00 
0.97 
5- 
7 


•14 

55 

•92 


•73 
54 


*  There  is  an  error  in  this  sum,  which  should  be  about  $100,000,000  greater — 150.66. 

The  last  three  columns  are  taken  (converting  metric  into  English  units)  from  the 
Statisque  des  Chemins  de  Fer  de  V Europe,  1882.     Vienna,  1885. 

According  to  other,  and  perhaps  more  authentic  figures,  the  railways  of  Great  Britain 
have  cost  $205,842  per  mile  of  road  ;  the  Belgian  State  Railways,  $123,986;  for  the  French 
railways,  $124,642;  for  the  German  State  Railways,  $105,204;  the  German  private  roads, 
$71,877 ;  the  Austro-Hungarian  roads,  $104,420.  The  cheapest  system  of  Europe  is  the 
State  Railways  of  Finland,  $30,102;  the  other  Russian  railways  stand  at  $82,244,  against 
$63,250  per  mile  for  the  railways  of  the  United  States. 

The  whole  cost  of  the  railways  of  the  world  has  been  more  than  $24,000,000,000,  which. 


46      CHAP.   II,— THE  MODERN  RAILWAY  CORPORATION-. 


however,  is  only  about  $24  per  inhabitant.  In  this  country  the  expenditure  has  been 
about  $133  per  inhabitant;  in  Great  Britain,  $107;  in  Germany,  $47;  in  France,  $57;  in 
Austria-Hungary,  $33;  in  Italy,  $19;  in  Belgium,  $41;  in  Sweden,  $25;  in  Spain,  $29; 
in  Russia,  $14 ;  in  Canada,  $89. 

In  France  and  Germany  railways  pay  about  5  per  cent  on  the  capital  invested,  as  an 
average ;  in  Great  Britain,  4  to  4Mi;  in  all  Europe  and  in  the  United  States,  about  4  per 
cent. 

Table  11. 

Extreme  Fluctuations  in  Price  of  the  Stocks  of  Various  Companies 

OF  Great  Natural  Strength. 
The  lowest  points  in  times  of  depression  (distinguished  by  an  1)  and  the  highest  price 
in  times  of  activity  (distinguished  by  an  h)  are  alone  noted,  except  that  in  the  last  column 
is  given  the  price  in  November,  1886.  The  list  has  been  selected  almost  at  random, 
regardless  of  their  actual  financial  status,  to  include  the  more  prominent  companies  which, 
from  the  nature  of  their  traffic  or  other  strategic  advantages,  might  naturally  be  expected 
to  be  (as  for  the  most  part  they  are)  least  subject  to  erratic  fluctuations  of  value. 


Company. 


New  York  Central 

Erie  

Pennsylvania 

Baltimore  &  Ohio 

Central  of  New  Jersey. . 

Boston  &  Albany 

Lake  Shore 

M  ichiuan  Central 

Canada  So 

Piitsburp  &  Ft.  Wayne. . . 

Chicago  &  Alton 

Ch.,  Burlinjrton  &  Q 

Ch.,  Milw.  &St.  P 

Ch.  &  N.  Western 

Ch..  Rocklsl.  &P 

111.  Central •  •  ■ 

Atchison.Topeka  &  St.  F 
Denver  &  Rio  Grande.. . 

Central  Pacific 

Union  Pacific 

Louisville  &  Nashv 

New  York,  N.  H.  &  Hartf 
No.  Pacific 


1878. 


1to3?^ 


'% 


1879. 


1880.      1881. 


I75 
IrM 
1  129 

155% 

158}^ 

I38 

I85 

166^ 

1  32 

I98' 
172% 


16.^ 
1 153M 


11155% 
196" 


ih204 

i8i%hi525^ 


I16 


16i^hii3>4 
1  63      h  102^)^ 

1  79 
b  190 


hi74 


1152% 
hi4oV4 

lt2IO 

ll  TI2 

h<75Vlf 
1»«3594 
hi3oV6 
h  90 
h  142 
hi56 
hi82H 
ll  izgj'^ 
hi36 


h ioo9^ 
I168 
b54% 


The  above  extremes  are  in  many  cases  brought  about  temporarily  only  by  the  machi- 
nations of  speculators.  In  many  cases  permanent  changes  in  the  nature  of  the  company 
have  also  had  great  influence.  On  the  other  hand,  these  fluctuations  of  stock  are  far  less 
than  the  fluctuations  in  the  productiveness  for  the  time  being  of  the  properties  represented 
bv  them  for  the  price  of  a  stock-neglecting  the  mere  momentary  fluctuations  of  a  few 
points  forced  for  the  sake  of  a  -  turn"-is,  at  the  most,  merely  this  :  It  is  the  speculators 
^timate  of  what  permanent  investors  feel  for  the  time  being  to  be  the  permanent  aver- 
AGE  value  of  the  stock.  For  there  are  always  large  holders  who  keep  in  mind  the  average 
value  of  the  property  during  good  times  and  bad  times  alike,  and  who  will  buy  or  sell  in 
quantities  large  enough  to  immediately  affect  the  price  if  THEY  THINK  it  is  falhng  below 
the  present  worth  of  its  future  chances,  all  uncertainties  included. 


CHAP.   II.— THE  MODERN  RAILWAY  CORPORATION.       47 

Table  12. 
Rolling  Stock  Per  Mile  in  the  United  States  and  British  Colonies. 


Name  of  Railway. 


New  England  States,  1883 

Middle  States,  1883... 

Southern  States,  1883 

Western  States,  1883 

Pacific  States,  1883 

Canadian  Pacific,  1885 

Intercolonial  of  Can., Halifax  to  Quebec,  1884 

Indian,  5  feet  6  inches  gauge 

India,  metre  gauge,  18S4 

Ceylon  Government,  1883 

Mauritius  Government,  1884 

Queensland  Government,  1882 

New  South  Wales  Government,  1881 

Victorian  Government,  1882 

South  Australia  Government.  1881 

New  Zealand  Government,  1883 

The  Cape  Government,  1882 

Average  of  totals 


Per  100  Miles  of  Railway  Of>en. 


Loco- 
motives. 

28.76 

41.93 
13-32 
16.23 

9-63 
10.9 
19.2 
27.2 
20.4 
31.8 
40.9 

7-9^ 
23-4 
16.8 
13. 6^ 
15-0 
23-4 


Passenger 
Cars. 


19.86 


48.31 

45.34 
12.06 

13.74 
12.06 
10. 1 

28.4 

66.5 
69.2 
95.6 
131. 8 
II. 6 

53.2 
33.6 
22.1 
42.7 
41.2 


23.89 


Freight 
Cars. 


635.9 

1714.5 

283.2 

4834 
191. 8 

276.2' 

513.3* 
512.2 

369.7 
296.1 

500.53 
112. 8 
487.1 
291.6 

344.9 
■453.2 
374.8 


590-5 


'  Only  partially  open  for  traffic.  »  Opened  about  1876. 

•  Freight  traffic  heavy  during  crop  season. 

*  Report  states,  *'  We  have  been  extremely  short  of  engines  all  through  the  year." 
'  Report  states  that  more  locomotives  are  required. 

Condensed  from  a  paper  on  "The  Laying-out,  Construction,  and  Equipment  of  Rail- 
ways in  Newly-Developed  Countries,"  by  James  Robert  Mosse,  M.  Inst.  C.E.,  in  Trans- 
actions Inst.  C.E.,  1886.    See  also  Table  8. 


f 


CHAP,   III.— CAUSES  MODIFYING  VOLUME  OF  REVENUE.   49 


CHAPTER   III. 

THE     NATURE     AND     CAUSES    CONNECTED     WITH     LOCATION     WHICH 
MODIFY    THE    VOLUME    OF    RAILWAY    REVENUE. 

37  With  the  invention  of  the  railway  began  a  new  industry 
—the  MANUFACTURE  OF  TRANSPORTATION.  Transportation,  in- 
deed existed  before  its  invention,  just  as  cotton  cloth  existed 
before  the  invention  of  modern  machinery,  but  it  was  in  eacli  case 
mainly  produced  on  a  small  scale  by  each  consumer  for  his^own 
use  and  his  immediate  neiglibors'.  With  the  invention  o  the 
railway  first  began  the  manufacture  of  transportation  for  sale  on 
a  large  scale  and  by  modern  processes. 

38    A  railway  corporation  such  as  has  been  just  considered 
—the' typical  modern  corporation-exists  for  this  purpose.     It 
finds  itself,  on  completion  of  its  works,  in  possession  of  a  certain 
piece  of  improved   real  estate,  of  certain    buildings  and   fixed 
machinerv  (the  track),  and  of  certain    tools   and  machines  (the 
rolling-stock)  for  the  manufacture  of  its  commodities,  together 
with  certain  establishments  (the  locomotives  and  car-shops)  for 
the  maintenance  and  repair  of  its  machine-tools,  which  the  extent 
of  its  business  requires.     In   many  instances  it  has  not  a  dollar  s 
worth  of  ownership  interest  in  all  this  costly  plant,  excepting  a 
portion  of  the  minor  machinery,  but  simply  controls  it  at,  in  ef- 
fect a  fixed  rental  (interest and  other  fixed  charges).     All  that  it 
really  owns  is,  commonly,  a  portion  of  the  business  or  franchise  ; 
and  this  latter  has  likewise  been  hypothecated,  or  pledged,  in 
the   mortgage   bonds  as  security   for  the   payment  of    its  rent 
charges      As  this  business  has,  from  the  nature  of  railway  busi- 
ness, assurance  of  always  amounting  to  a  certain  minimum  at 
least   this  franchise  alone  has  a  value  as  security  which  no  ordi- 
nary  business  would  have,  and  in  a  rapidly  growing  country  its 


existence  enables  all  or  nearly  all  of  the  actual  cost  of  the  entire 
premises  and  plant  to  be  borrowed,  or  rented,  from  others. 

On  the  premises  so  rented,  the  corporation  carries  on,  for  its 
own  benefit,  the  business  of  manufacturing  and  selling  transpor- 
tation, so  to  speak,  at  wholesale  and  retail,  in  lots  to  suit  the 
purchasers.  Since  it  owns  the  business  only,  and  has,  as  a  cor- 
porate body,  no  interest  or  ownership  in  the  property  itself,  it 
will  be  clear,  and  should  be  fully  realized,  that  all  its  interests 
are  limited  to  the  narrow  debatable  ground  which  lies  between 
doing  the  best  possible  and  doing  the  worst  possible  with  the 
property  in  hand,  which  is  in  all  ordinary  cases  simply  lent  to 
them  for  an  annual  consideration. 

39.  Now,  continuing  the  parallel,  which  will  perhaps  help  to 
enforce  the  truths  required,  and  referring  only  to  sales  of  trans- 
portation, or  revenue  :  if  a  manufacturing  company  in  such  cir- 
cumstances should,  in  planning  its  works,  so  plan  them  as  to  cut 
itself  off  from  disposing  of  certain  lines  of  goods  which  it  manu- 
factures, or  should  place  its  retailing  establishments  (stations)  at 
inconvenient  points,  it  is  clear  that  it  would  have  seriously  hand- 
icapped itself,  even  if,  perchance,  justifiably.  This  a  railway 
company  does  when,  by  failing  to  run  close  to  any  accessible 
towns,  it  is  prevented  from  furnishing  them  with  transportation, 
or  is  so  far  away  that  sales  are  inconvenient.  If  it  strives  to 
shorten  its  line  it  is,  for  certain  parts  of  its  traffic,  trying  to  sell 
\^s>s  yards  of  its  goods,  at  a  certain  price /^rj^n/,  in  order  to  save 
the  cost  of  its  manufacture  ;  .forgetting  that  by  the  same  act  it 
also  loses  the  selling  price  and  hence  the  profit  on  them.  If,  on 
the  contrary,  it  builds  an  over-long,  or  crooked,  or  otherwise 
objectionable  line,  it  is  in  effect  fitting  itself  to  produce  only  an 
inferior  article,  which  will  command  a  lower  price. 

40.  The  force  of  this  parallel  is  still  further  and  greatly 
strengthened  if  we  remember  that,  with  much  that  is  similar, 
there  is,  in  one  respect,  a  momentous  and  broad  distinction 
between  the  seller  of  transportation  and  the  seller  of  most  other 
commodities.  The  production  or  partial  production  of  trans- 
portation is,  from  the  necessity  of  the  business,  considerably  in 

4 


50   CHAP.   III.-CAUSES  MODIFYI^NG  VOLUME^  OF  REVENUE. 

:a  rthereto.     Every  time,  for  example,  a  P^-nger  tram  s^a.  u 
out  there  is  "manufactured,"  so  to  speak,  several  hund.ed  pas 
senee    tls      If  they  be  not  sold,  they  cannot  be  stored  away  on 
hfshe     fo    the  nex't  day's  trade,  like  the  remnants  of  a  lot  o 
d  v-goods.     They  are  simply  wasted   and   thrown  away      I    -s 
wUh  the  railway  much  as  if  tradesmen  were  conu,elled  to  cut  a 
Tew  piece  of  each  kind  of  goods  each  day  and  then  throw  away 
the  part  remaining   unsold    each    night.     We  should    probably 
under  such  circumstances  observe  a  conspicuously  greater  zea 
^ven  than  now  exists  for  regulating  and  increasing  sales  so  a 
Tsell   the  whole  of  every  piece   of  goods  ;  whatever  pnce  the 

remnants  might  bring  being  so  much  clear  gam. 
remnant  mg  g^  ^^^^  ^^^^^^   ^^^  ^^^^^^  ^^  ^ 

tant  degree  the  conditions  here  suggested  exist  w.th  respect  to 
every  part  aid  kind  of  railway  traffic.  We  see,  therefore,  how 
vtal  and  peculiar  is  the  interest  of  railways  in  neglect.ng  no 
!on  ideration  which  bv  ever  so  little  affects  its  revenue.  It  .s 
on  si  Jht  differences  of  traffic  and  revenue  that  the  corporation 

'Tran^lig:  before,  that  no  probable  effect  upon  tramc  and 
Oraniing.  ^^cur  from  the  decisions  reached  in 

re^-^irai'tc^tro^Toui:  be  neglected   it  will  be  obvious,  a 
already  hinted,  that  such  effects  are  possible  from  any  one  of  the 

following  ""^«  =  ^^   „,   LINE-Even  slight   variations 

42.  I.    THE    LENGTH   u  revenue,   as  well  as  the 

ratio  thereto.  ^       .u^rpfore  varying  in  almost  every  case, 

up  to  a  ««-"P;;:^",i,f:  a     .'e  net  revenue  frequently,  will 
t.e  gross  revenueta.  ad   ^^^^  ^^  ^^^  ^^^^^^^^  ^ 

Bi;Tf':htrotsVbe  carried  too  far,  the  traffic  will  be  overbur- 


CHAP.   III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE.    5  I 

dened,  discouraged,  and  decreased.  The  questions  thus  raised 
will  be  separately  discussed  in  Chapter  VII.,  on  Distance.  It  is 
one  of  extreme  importance. 

Such  effects  on  revenue  may  also  occur  from — 

2.  The  comparative  weight  allowed  to  securing  way 
TRAFFIC,  the  quantity  which  may  be  expected,  and  the  sacrifices 
which  may  or  must  be  made  to  reach  certain  additional  traffic 
points.     Also, 

3.  Allied  to  the  latter,  is  the  question  of  how  near  to  run 

TO   CITIES,    TOWNS,     AND    OTHER     SOURCES    OF     TRAFFIC,    which    are 

already  upon  the  line,  and  how  much  the  traffic  and  revenue  will 
be  thereby  affected. 

4.  Still  other  similar  questions  arise  in  connection  with 
BRANCH  LINES  *.  whether  to  build  a  branch  at  all,  or  take  the 
main  line  through  the  given  point ;  whether,  if  a  branch  be  de- 
cided on,  the  connection  should  be  made  at  this  or  that  point, 
there  being  often  much  choice,  and  the  decision  governed  by 
commercial  considerations  to  an  unusual  extent,  or  at  least  by 
very  different  laws  from  those  which  might  govern  the  laying 
out  of  longer  lines,  owing  to  the  shortness  and  isolation  of  most 
branches. 

5.  All  of  these  questions  together  arise  on  a  grand  scale  in 
the  laying  out  of  great  systems  of  railway  at  once  or  in  the 
connection  of  a  number  of  isolated  lines  into  a  single  system,  as 
liappens  with  increasing  frequency  in  modern  times. 

In  a  certain  sense,  indeed,  every  line,  even  nominally  inde- 
pendent, and  no  matter  how  short,  is  a  part  not  only  of  one  but 
perhaps  of  several  great  systems  of  roads.  On  this  account,  and 
because  of  the  great  importance  of  the  questions  which  arise  in 
connection  with  the  laying  out  of  branch  lines  and  systems,  a 
separate  chapter  (XXI.)  is  devoted  hereafter  to — not  a  general 
discussion,  for  that  is  impossible — but  to  the  presentation  of 
certain  suggestions  intended  to  illustrate  the  laws  which  govern 
their  solution.  Much  of  the  chapter  referred  to  has  likewise  a 
direct  bearing  on  the  remainder  of  this  chapter. 

43"  It  is  unfortunate   that  the  very  great  and  often  decisive 


$2   CHAP.   III.-CAUSES  MODIFYING  VOLUME  OF  REVENUE. 

effect  which  differences  of  location  may  have  upon  the  revenue 
of  railways  is  not  susceptible  of  more  exact  analysis,  for  it  is 
very  often,  in  properly  conducted  work,  a  consideration  of  such 
importance  as  to  sink  differences  of  engineering  details  into 
insignificance.  The  most  that  can  be  done  is  to  lay  down  with 
all  possible  care  the  general  principles  which  govern  this  effect, 
with  the  caution  that  the  very  difficulty  of  determining  exactly 
what  weight  should  be  given  to  it  creates  too  great  a  tendency 
to  neglect  it  altogetlier. 

44.  The  traffic  of  railways  is  often  spoken  and  thought  of 
as  for  the  most  part  a  monopoly.  In  a  certain  sense,  of  a  cer- 
tain small  part  of  its  traffic,  this  is  true,  as  already  noted,  to  the 
extent  that  there  is  a  certain  fraction  of  the  traffic  of  all  railways 
which  no  folly  can  destroy  or  throw  away.  But  in  a  larger  sense^ 
the  traffic  of  any  and  all  railways  is  only  to  a  very  limited  ex- 
tent  a  monopoly  of  such  nature  that  to  secure  it  the  Company 
has  nothing  more  to  do  than  to  put  up  its  buildings,  and  station 
a  man  at  the  receipt  of  customs.  The  selling  of  transportion  is 
governed  to  a  very  large  extent,  whether  there  be  nominal' com- 
petition or  not,  by  the  same  laws  which  govern  the  selling  o£ 
any  other  commodity;  and  these  laws  require  that  the  railway 
company,  like  any  one  else  with  something  to  sell,  shall  consult 
the  convenience,  and  even  sometimes  the  unreasonable  whims, 
of  the  buyer,  if  it  would  sell  its  goods  to  him. 

45.  For  only  a  small  proportion  of  the  traffic  of  any  railway- 
is  in  the  strict  sense  of  the  term  necessary  traffic,  which  must 
come  to  it  anyway,  under  all  circumstances.  The  amount  of 
such  traffic  is  measured,  when  a  railway  system  is  first  coming 
into  existence,  by  the  stage-coach  travel  as  respects  passenger 
business,  and  by  the  carting  on  the  common  roads  as  respects 
freight  business.  Under  the  stimulus  which  the  bare  existence- 
of  a'ny  kind  of  railway  facilities  gives  to  the  development  of  any 
country,  the  volume  of  this  strictly  necessary  travel  is  no  doubt 
increased  many-fold.  Nevertheless  no  railway  is  so  prosperous, 
and  so  favorably  situated  that  it  would  not,  in  literal  truths 
Starve  to  death  on  it.     The  traffic  would  be  so  very  greatly  de- 


CHAP.   I IL— CAUSES  MODIFYING  VOLUME  OF  RE  VENUE  ^    53 


creased  that  on  most  lines  it  would  not  be  possible  to  run  the 
trains  at  all.  Neglecting  altogether  the  traffic  which,  as  respects 
any  one  company,  is  not  necessary,  because  it  has  a  choice  of 
routes,  and  one  line  has  to  fight  for  it  with  others,  a  very  large 
proportion  of  the  business  of  the  railway  system  as  a  whole  is 
made  up,  as  respects  passenger  business,  not  only  of  pleasure 
travel  pure  and  simple,  but  of  travel  which  is  more  or  less  a  mat- 
ter of  whim  or  of  fancied  or  partial  necessity;  and  even  as  respects 
freight  business,  of  freight  which  will  not  be  shipped  except  un- 
der reasonably  favorable  circumstances,  especially  by  any  one 
route,  or  shipped  only  at  a  lower  rate  :  so  that  the  rates  must  be 
solely  fixed,  not  by  the  cost  of  the  service,  but  by  the  price  it 
will  bear  without  discouraging  traffic. 

46.  It  will  be  evident  therefore  that,  since  we  have  already 
seen  the  vital  importance  to  railways  of  making  the  largest 
possible  sales  of  their  wares,  and  since  a  large  part  of  their 
sales  are  of  such  nature  that  they  may  be  easily  discouraged  and 
prevented,  any  failure  to  facilitate  traffic  to  the  utmost  is  a  se- 
rious matter.  The  question  of  encouraging  or  discpuraging 
traffic  by  the  facilities  offered  will  depend  in  the  main,  no  doubt, 
upon  the  manner  of  operating  the  road  after  it  has  opened;  yet 
in  one  respect  at  least  (postponing  for  the  present,  as  noted,  the 
■discussion  of  the  first,  fourth,  and  fifth  considerations  above)  it 
is  possible  in  the  beginning  to  seriously  and  J>er ma fienf/y  aflect 
the  future  traffic  of  the  line  :  viz.,  by  going  on  the  principle, 
which  has  often  been  followed  in  the  practice,  that  "  if  the  rail- 
way DOES  NOT   GO   TO   THE    TRAFFIC,  THE    TRAFFIC  WILL   COME    TO 

THE  RAILWAY."  This  argument  is  sometimes  gravely  advanced 
in  support  of  the  plea  that  it  is  of  no  particular  importance 
whether  the  line  pass  through  a  town  or  a  mile  or  two  off 
from  it,  because  in  either  case  the  line  will  get  "  all  the  business 
there  is."  From  the  very  fact  that  there  is  a  grain  of  truth  in 
this  plea  lending  a  certain  support  to  that  cheapest  of  all 
ways  of  saving  money, — and  perhaps  saving  a  little  distance 
and  curvature  at  the  same  time, — keeping  the  line  off  all  land 
which  is  worth  any  considerable  price,  it  is  important  that  it 


54   CHAP.   III.— CAUSES  MODIFYING  VOLUME  OF  REVENUE. 

should   be  fully  realized  why  it  is  a  dangerous  and  fallacious 

argument. 

47.  It  is  particularly  easy  to  see  that  the  argument  is  both 
dangerous  and   fallacious  when  there  is,  or  is  liable  to  be,  com- 
petition for   the  traffic,  or  any  part  of  it,  as  may  be  said  to  be 
always  the  case,  at  least  potentially,  in  the  United  States.    In  that 
case,  the  only  safe  rule  is,  that  any  considerable  difference  in  haul 
to  the  station  or  in  any  other  convenience  to  the  public  will  al- 
most wholly  destroy  the  possibility  of  profit  from  the  traffic  to  be 
competed  for,  even  if  a   portion  be  secured.     For  it  might  be 
proved  by  many  instances  that  it  requires  but  a  very  slight  dif- 
ference in  the   convenience   of  access  to   practically  destroy  all 
equality  of  competition.       Except  for  the  very   numerous  in- 
stances  of  entire  neglect  of  this   danger  it  would    hardly  seem 
necessary  to  speak  of  the  matter  at  all  ;  for  it  is  evident  that,  as 
respects   freight   traffic,  rates    must  in  the    long-run    be  made 
equal,  not  simply  from  station  to  station,  hwX.  from  the  door  of  the 
consignor  to  the  door  of  the  consignee :  in  other  words,  all  additional 
cost  for  cartage   or   switching  service,  and   something  more   as 
compensation  for  the  trouble  (usually  a  very  considerable  addi- 
tion), must  be  borne  by  the  railway  before  it  is  in  a  position  to 
compete  at  all.     As  respects  passenger  traffic,  to  a  certain  class 
ot  long-trip  travel  such  minor  differences  are  of  less  importance, 
but  there  is  a  considerable  fraction  even  of  long-trip  travel  on 
which  they  have  a  recognized  and  important  influence  ;  and  de- 
vices of  all  kinds— free  omnibuses,  more  or  less  open  concessions 
on  rates,  etc.,  etc.— are  required  to  counteract  what  may  have 
been  a  mere  oversight,  or  bit  of  indifferent  negligence,  in  the 
original  laying  out  of  the  line. 

48.  Let  us  imagine  an  instance  which  has  frequently  hap- 
pened already,  and  still  more  frequently  will  happen  :  A  num- 
ber of  good-sized  towns,  ten  to  fifty  miles  apart,  served  by 
two  competing  lines  ;  one  of  them  coming  appreciably  nearer 
to  the  average  centre  of  population  than  the  other.  It  is  abun- 
dantly established  by  experience  that  in  such  a  case  the  favored 
line  can  by  a  moderate  amount  of  effort— which  may  be  counted 


CHAP.   III.— CAUSES  MODIFYING  VOLUME  OF  REVENUE.    55 


on  with  some  certainty — not  simply  cripple,  but  almost  destroy, 
its  rival's  local  traffic.  For  "  to  him  that  hath  shall  be  given," 
with  short-haul  traffic  especially.  If  one  line  start  with  any  ad- 
vantage, that  very  fact  will  tend  to  increase  it.  It  will  have  a 
better  reputation.  It  can  offer  better  facilities.  The  tendency 
of  the  traffic  of  all  kinds  will  be  to  concentrate  itself  upon  it — 
just  as  water  always  seeks  the  level  point,  however  little  lower  it 
may  be.  Even  when  a  railway  can,  or  thinks  it  can,  count  on 
permanent  immunity  from  competition,  it  should  naturally  fol- 
low from  what  has  preceded  that  it  is  still  exceedingly  dangerous 
to  put  the  public  to  permanent  inconvenience  and  expense  under 
the  false  idea  that  "  it  will  cost  the  Company  nothing."  Under 
the  best  of  circumstances  there  will  always  be  some  loss;  and  the 
slighest  addition  to  receipts,  which  might  have  been  secured  but 
is  not,  would  have  gone  almost  in  gross  to  swell  the  surplus. 
The  slight  additional  trouble  and  expense  to  shippers  of  all 
freight,  and  the  horse-car  and  cab  fares  of  passengers,  must  be 
paid  for  sooner  or  later,  in  one  form  or  another,  by  the  corpora- 
tion, if  in  no  other  form  than  in  a  decrease  of  traffic.  _  It  is  not 
true  that  nothing  which  will  still  leave  rates  at  so  much  a  mile, 
without  immediately  affecting  them  at  this  or  that  non-competi- 
tive point,  is  of  importance  to  the  Company  or  has  effect  upon 

its  revenue. 

49.  The  universal  law  of  trade  ultimately  obtains  with  sales 
of  transportation  as  of  everything  else.  The  selling  price,  the 
amount  sold,  and  the  profit  realized  on  all  articles  of  bargain 
and  sale  is  ultimately  regulated  by  the  quality  of  the  article  and 
the  price  the  consumer  is  willing  and  able  to  pay,  and  this  again 
is  greatly  affected  even  by  trifling  differences  of  convenience. 
We  may  see  this  illustrated  every  day  by  the  difference  in  price 
of  the  same  article  at  fashionable  and  unfashionable  stores  ;  and 
even  when  there  is  but  one  point  at  which  a  certain  desired  ar- 
ticle can  be  bought,  it  is  a  truth  universally  admitted  among 
business  men  that  minute  differences  in  the  price  or  the  quality 
of  the  article,  or  in  convenience  of  access  to  the  place  of  sale,  do 
have  a  material  influence  on  the  volume  of  sales,  especially  if 


56   CHAP,  III.— CAUSES  MODIFYING  VOLUME   OF  REVENUE, 


CHAP.   III.— CAUSES  MODIFYING  VOLUME  OF  REVENUE.    5/ 


such  articles  as  are  to  be  sold  in  great  numbers  to  the  general 
public.  That  precisely  the  same  argument  applies  to  railways 
can  be  denied  only  by  asserting  that  the  patronage  of  a  railway 
is  strictly  a  matter  of  necessity — a  pure  monopoly,  except  as 
competed  for  by  another  railway  ;  but  this,  even  if  it  were  true 
of  the  greater  portion  of  traffic,  would  certainly  not  be  true  at  all 
of  the  remaining  fraction,  and  it  is  ordinarily  this  remaining 
fraction  which  alone  makes  the  business  of  operating  the  prop- 
erty worth  carrying  on  by  the  company  controlling  it :  for  let  us 
suppose  that  by  systematic  negligence  at  several  points  in  the 
original  laying  out  of  a  line  a  corporation  should  succeed  in  af- 
fecting its  gross  yearly  revenue  so  much  as  one  per  cent.  It 
would  represent  certainly  five  to  ten  per  cent,  and  very  possibly 
one  hundred  per  cent,  of  the  value  of  the  franchise  owned  by  the 
corporation,  which  is  usually  all  they  do  own,  and  sometimes  a 
good  deal  more. 

60.  If  it  should  seem  improbable  that  any  possible  error  of 
this  kind  could  so  affect  revenue,  it  must  be  admitted  that  it  is 
difficult  and  in  fact  impossible  to  produce  statistical  proof,  nor 
would  such  proof,  even  if  produced  for  one  locality,  be  applicable 
elsewhere;  but  a  striking  example,  among  many,  of  the  natural 
effect  of  such  reckless  neglect  may  be  found  at  the  town  of 
Springfield,  Ohio.  A  dispute  about  a  trifling  sum  (about 
$50,000)  of  town  aid  to  the  Atlantic  &  Great  Western  Railway, 
now  the  New  York,  Pennsylvania  &  Ohio  Railroad,  caused  the 
manager  of  the  road  to  run  the  line  two  or  three  miles  from  the 
town — and  this  with  a  slight  increase,  if  anything,  in  the  dis- 
tance, curvature,  and  cost.  This  town  has  since  become,  as  even 
then  was  probable,  one  of  the  best  shipping  points  in  the  State; 
and,  purely  in  consequence  of  its  inconvenient  location,  the 
Atlantic  &  Great  Western  secures  only  an  inconsiderable  frac- 
tion of  this  traffic,  both  freight  and  passenger.  Its  annual  loss 
of  net  revenue  is,  beyond  all  question,  considerably  larger  than 
the  whole  sum  originally  in  dispute;  and  the  disadvantage  was 
so  serious  that,  very  recently,  arrangements  to  run  into  the 
town  over  another  line  were  made  at  heavy  cost,  while  still 
leaving  the  line  at  an  immense  disadvantage. 


51.  In  this  occurrence  there  is  nothing  exceptional,  even  in 
degree.  There  is  hardly  a  town  of  any  importance  in  the 
United  States  in  which  some  one  of  the  lines  running  to  it  has 
not  done  precisely  the  same  thing  ;  so  that  it  is  known  of  all 
men  to  be  at  grave  disadvantage  in  respect  to  some  portion  of 
its  natural  traffic,  whether  long-haul  and  short-haul,  and 
whether  passenger  and  freight.  That  natural  and  not  unreason- 
able  trait  of  human  nature  embodied  in  the  homely  proverb, 
*'  Give  a  dog  a  bad  name  and  hang  him,"  then  comes  in  to  inten- 
sify this  disadvantage.  This  in  turn  begets  a  poverty  of  means, 
which  begets  a  poverty  of  service,  which  still  further  increases, 
and  justifies  on  rational  grounds,  what  may  have  been  in  the 
beginning  a  rather  unreasonable  popular  prejudice;  and  the  end, 
in  all  probability,  is  a  receivership.  It  will  be  found,  on  looking 
over  a  list  of  roads  which  have  failed  in  this  way,  that,  almost 
without  exception,  they  are  those  which  merely  skirt  the  edges  of 
the  towns  which  they  nominally  reach. 

62.  The  effect  on  short-haul  traffic  of  negligence  of 
this  kind  is,  as  already  hinted,  far  more  serious  proportionally 
than  in  the  case  of  longer  haul — not  only  because  it  is  far  more 
likely  to  drive  the  traffic  to  other  lines,  when  such  exist,  but  be- 
cause it  is  far  more  likely  to  have  the  still  further  effect  of  de- 
stroying a  portion  of  the  potential  traffic  completely.  The 
longer  the  journey  or  the  haul,  evidently,  the  less  effect  will  any 
trifling  inconveniences  have,  and  the  proportional  as  well  as  ab- 
solute loss  will  naturally  be  less  at  small  towns  than  large  ones— 
especially  than  at  very  large  ones  where  there  is  a  regular  and 
established  suburban  traffic.  Nevertheless  no  town  is  so  small 
that  the  short-haul  local  traffic  is  not  materially  affected  by  tri- 
fling difference  of  convenience  of  access.  Differences  which 
originate  in  the  subsequent  management  of  the  operating  de- 
partment, better  cars,  time,  meals,  train  employees,  surer  con- 
nections, etc.,  may  have,  it  has  been  admitted,  relatively  much 
more  effect  than  a  mere  difference  in  convenience  of  access  to 
the  station  ;  but  the  latter,  unlike  the  former,  cannot  be  cor- 
rected at  any  time,  and  in  trips  of  ten  to  twenty  or  fifty  or  even 


58   CHAP.   I  I  I. -^CAUSES  MODIFYING  VOLUME  OF  REVENUE, 


one  hundred  miles,  the  mere  fact  that  the  station  is  (or  is  not) 
convenient  for  taking  and  leaving  the  train  is  alone  enough  to- 
have  a  powerful  influence  upon  the  number  of  such  trips,  es- 
pecially in  bad  weather,  but  to  an  important  extent  in  all 
weather,  with  the  weaker  three  quarters  of  the  population  at 

least. 

53.  In  very  much  less  degree  even  the  volume  of  non-com- 
petitive FREIGHT  SHIPMENTS  is  similarly  affected;  besides  the 
fact  that  it  must  be  assumed,  for  reasons  already  stated,  that  the 
rates,  in  the  long-run  and  in  some  direct  or  indirect  form,  will 
certainly  be  affected  likewise.  Sooner  or  later,  in  one  form  or 
another,  the  railway  will  be  compelled  to  make  concessions 
equivalent  to  paying  for  the  cost  and  annoyance  of  cartage  on 
much  of  its  traffic,  and  lose  altogether  more  than  enough  to  pay 
for  carting  the  whole  of  it.  There  is  no  clearer  moral  than  this 
to  be  drawn  from  recent  railway  history. 

54.  It  is  also  unmistakably  evident  from  recent  history  that  it 
is  impossible  to  maintain  more  than  a  reasonable  ratio  of  dispro- 
portion in  rates  between  competitive  and  non-competitive  rates, 
and  between  rates  on  one  class  of  freight  and  another,  even  for 
those  classes  of  freight  which  do  not  seem  to  be  affected  by  any 
immediate  cause  tending  to  have  this  effect.  A  clear  indication 
of  the  existence  of  this  law  may  be  found  in  Tables  93-5.  It  is 
now  too  well  known  and  generally  admitted  to  require  more  pre- 
cise evidence. 

55.  There  is  one  peculiar  phase  of  the  question  of  running  by 
A  TOWN  TO  SAVE  DISTANCE  which  may  be  more  appropriately  con- 
sidered in  this  connection,  as  illustrating  what  has  preceded, 
than  in  the  chapter  on  Distance. 

Let  us  suppose,  to  take  definite  figures,  that  we  have  run  by  a 
town  of  ten  thousand  inhabitants  in  order  to  save  a  deviation  of 
five  miles  from  an  air  line,  involving  a  loss  of  a  mile  or  two  of 
distance.  As  we  have  already  seen  in  part,  and  shall  more  fully 
see  (Chap.  VII.),  the  railway's  revenue  account  suffers  heavy  loss 
due  to  the  decreased  mileage  on  most  of  its  local  and  through 
business,  competitive  and  non-competitive.     Per  contra,  its  ex- 


CHAP.   III.— CAUSES  MODIFYING  VOLUME  OF  REVENUE.    59 


pense  account  is  decreased  indeed,  but  in  very  much  less  ratio. 
The  probabilities  are  very  strong  that  there  will  be  a  net  loss  to 
the  revenue.  This  might  well  be  borne  if  it  meant,  as  in  ordi- 
nary cases,  simply  *a  reduction  of  the  transportation  tax  upon 
the  traveller  or  shipper  of  freight,  but  how  stands  it  with  the 
latter?  They  save,  indeed  (in  the  case  of  local  traffic  only,  buf 
not  in  the  case  of  through  traffic),  the  two  or  three  cents  per 
mile  which  the  railway  loses,  owing  to  its  shorter  line  ;  but  they 
lose  the  entire  direct  cost  of  cartage  or  switching  charges  on 
their  freight  and  carriage,  express  or  horse-car  fares  for  their 
own  conveyance,  besides  suffering  an  annoyance  and  inconveni- 
ence in  both  cases  which  they  will  surely  estimate  at  a  good 
round  sum:  In  money,  when  by  the  existence  of  competition  they 
are  able  to  throw  the  whole  of  both  of  these  losses  on  the  rail- 
way which  seeks  their  patronage  from  a  distance  ;  in  refusal  of 
patronage,  except  under  great  concessions  or  the  compulsion  of 
necessity,  when  through  absence  of  competition  they  cannot 
otherwise  shift  the  burden  from  their  own  shoulders. 

Thus,  under  any  possible  conditions,  in  such  a  case  there  is  a 
triple  loss:  The  tax  on  the  public  is  greater,  the  receipts  of  the 
railway  are  less  per  passenger  or  ton,  and  the  number  of  pas- 
sengers or  tons  is  decreased. 

56.  The  net  losses  might  be  estimated  something  in  thisway^ 
assuming  the  town,  say,  to  be  in  Ohio : 


Loss  TO  THE  Railway. 

Loss  of  traffic  per  head,  by  being  5  miles  instead  of  i  from  centre  of 
population  (say  40  per  cent :  Table  13),  on  a  natural  revenue  per 
head  of  $10,  or  $100,000  from  the  town $40,000 

Loss  of  revenue,  due  to  one-mile  haul  on  $60,000  of  traffic — say  three 

per  cent • 1,800 

$41,800 
Per  contra  :  saving  of  expense  on  same,  at  40  per  cent  on  the  total  ex- 
penses, or  26f  (40  X  I)  per  cent  on  the  total  revenue 11,148^ 

Net  loss  to  railway $30>652 


6o  CHAP.   in.—CAUSES  MODIFYING  VOLUME  OF  REVENUE. 


Loss  TO  THE  Individual  Patrons. 

Expenses  of  reaching  the  railway  from  a  point  5  miles  off,  at  50  cents 

per  passenger  or  ton,  probably  about $25,000 

Less  saving  by  reduced  payments  to  the  railway,  as  above 1,800 

Net  loss  to  the  public  $23,200 

Destroyed  business,  which  the  public  would  have  been  glad  to  enjoy 
and  pay  for,  as  shown  by  experience,  and  which  hence  would  have 
been  worth  its  cost  to  them — say  one  third  of  the  40  per  cent  (as 
above)  of  $100,000,  the  rest  going  to  some  other  line 13,300 

Net  loss  special  to  the  public,  per  year $36. 500 

Net  loss  special  to  the  railway,  per  year 30.652 

Aggregate  loss  to  the  community,  per  year $67,152 

Which  means  from  the  point  of  view  of  political  economy, 
and  as  a  plain  statement  of  a  fact  which  would  appear  in  the 
census  statistics,  that  the  capital  of  the  country  and  the  world 
is  less  than  it  otherwise  would  be  by  the  capital  sum  of  which 
$67,152  represents  the  interest,  or  (at  six  per  cent)  $1,119,200  ; 
the  whole  of  which  is  clear  loss,  by  which  no  one  is  benefited. 

57.  A  few  hackmen  and  expressmen  are,  indeed,  diverted 
from  working  elsewhere,  where  they  would  be  true  producers, 
into  earning  a  support  by  performing  what  might  have  been  a 
needless  service.  It  is  plain  that  by  tliis  diversion  they  are, 
individually,  neither  benefited  nor  injured,  so  that  they  simply 
•do  not  enter  into  the  question  at  all,  even  from  the  point  of  view 
of  political  economy.  We  are  not,  however,  studying  political 
•economy,  but  the  art  of  directing  private  investment  in  railway 
property  so  as  to  be  profitable,  not  primarily  to  the  general 
public,  but  to  the  projectors. 

Making'all  allowances  for  possible  errors  in  the  precise  fig- 
ures used  above,  it  represents  an  immense  loss  to  all  parties  from 
running  railways  by  towns  without  going  to  them,  so  far  as  the 
traffic  of  that  town  alone  is  concerned,  separately  considered. 
There  is,  however,  this  further  disadvantage  to  be  remembered  : 
if  we  lengthen  the  line  to  reach  a  town  we  necessitate  that  the 


CHAP.  III.— CAUSES  MODIFYING  VOLUME  OF  REVENUE.   6\ 

.. — ■ • ' ~  '  '~' 

whole  traffic  shall  be  hauled  over  this  extra  distance  in  order  to 
accommodate  the  traffic  of  one  town. 

68.  This  raises  the  general  question  of  the  value  of  distance, 
for  which  see  Chapter  VII.    It  need  only  be  premised  here,  what 
has  been  in  fact  already  said,  that  although,  as  a  mere  question 
of  political  economy,  the  cost  of  this  extra  haul  is  certainly  a  net 
loss,  conferring  no  added  value  on  the  service  rendered,  yet  to 
the  revenues  of  the  railway  only,  considered  as  a  private  enter- 
prise for  profit,  this  is  by  n*o  means  the  case,  since  there  is  always 
a  credit  as  well  as  a  debit  side   to   the   extra  haul.     It  is  not 
uncommon  to  hear  engineers  speak  and  act,  indeed,  as  if  the 
extra  haul  were  a  mere  burden  on  the  traffic  :  which  would  be 
true  enough   if  railways  were   charitable  institutions  built  by 
moneyed  philanthropists  with   the  sole  purpose  of  serving  the 
public,  and  which  is  always  true  with  respect  to  that  consider- 
able fraction  of  traffic  on  which  neither  the  amount  nor  the  dis- 
tribution of  the  gross  rate  is  modified  by  the  distance.     But,  as 
matters  actually  stand,  it  may  be  rudely  stated  here  that,  as  the 
actual  cost  of  such  trifling -extra  haul  is  very  little,  the  net  effect 
of  such  deviation  for  such  a  purpose  is  very  apt  to  have  a  favor- 
able effect,  if  any  (sometimes  a  decidedly  favorable  effect),  upon 
the  net  revenue  derived  from  the  entire  traffic,  independent  of 
that  from   the  particular  point  for  the  sake  of  which  the  devia- 
tion was  made,  as  well  as  upon  the  public  interest. 

For  one  most  important  reason  why  this  should  be  so,  see  Chapter  XXI. 

59.  It  is  true  that,  in  so  far  as  the  burden  upon  the  general 
traffic  may  be  increased,  there  is  a  tendency  to  compel  the  cor- 
poration to  reduce  rates  on  all  traffic  to  the  point  which  it  will 
bear,  instead  of  making  non-competitive  rates  strictly  according 
to  distance  ;  and  in  urging  that  a  railway  will  "  get  something 
for  nothing"  out  of  extra  haul,  the  previous  claim  (par.  46  et  seq:) 
may  seem  to  be  contradicted,  that  even  slight  burdens  on  traffic 
are  dangerous ;  but  it  is  evidently  a  very  different  matter  for  a 
railway  to  take  measures  which  make  its  own  charges  on  all 
traffic  a  trifle  higher  to  relieve  a   part  of  it  from    other   and 


62   CHAP.  III.— CAUSES  MODIFYING  VOLUME  OF  REVENUE. 


heavier  burdens,  and  to  take  a  course  which  throws  a  heavy 
burden  on  its  own  traffic  and  on  its  patrons  as  well,  by  provid- 
ing facilities  for  a  lot  of  outside  parties — teamsters,  hackmen, 
and  horse-car  lines — to  extract  a  percentage  forever  of  the  total 
payments  which  the  traffic  has  to  bear. 

60,  Admitting,  therefore,  that  differences  of  location  may 
have  a  material  effect  on  the  revenue,  it  becomes  important  to 
remember  that,  as  we  have  already  seen,  as  small  a  difference  as 
one  per  cent  in  gross  revenue  will 'ordinarily  represent  from 
three  to  six  per  cent  in  net  revenue,  and  from  six  to  twelve  or 
fifteen  percent  difference  in  profits  to  the  company  proper,  after 
their  rental  or  interest  charges  have  been  met,  even  in  the  most 
prosperous  companies,  and  from  that  up  to  many  hundred  per 
cent  in  those  less  favored.  Remembering  also  that  errors  in  the 
original  laying  out  of  the  line,  unlike  errors  in  subsequent  man- 
agement, are  mainly  irremediable, — a  kind  of  fixed  charge  for 
folly  forever, — it  will  be  seen  how  large  is  the  interest  of  the 
company  who  employ  and  pay  the  engineer  in  avoiding  all  errors 
of  the  kind,  and  how  particularly  important  it  is  that  no  possible 
difference  should  be  regarded  as  trifling  because  it  will  consti- 
tute  a  trifling  part  of  the  total  receipts  or  expenses.  It  is  only 
a  small  fraction  of  that  total  which  "  the  company"  has  even  the 
hope  of  retaining  to  itself. 

When  the  cream  of  their  traffic,  the  profit  traffic,  is  lost 
to  them,  all  is  lost  ;  and  although  it  is  often  true  that  the  busi- 
ness sagacity,  or  lack  of  it,  with  which  the  enterprise  as  a  whole 
has  been  planned  will  overcome  all  that  the  engineer  can  do  to 
make  or  mar  it,  so  that  the  enterprise  will  succeed  or  fail  in  spite 
of  him,  yet  it  is  always  true  that  a  heavy  percentage  of  the 
surplus  or  deficit  which  alone  concerns  the  company  proper — 
enough,  for  instance,  to  make  all  the  difference  between  a  great 
success  and  a  small  success,  or  a  great  failure  and  a  small  fatlure 
— is  strictly  dependent  upon  the  engineer  and  upon  those,  by 
whatever  name  they  may  be  called,  who  decide  with  him,  or  for 
him,  the  semi-engineering  and  semi-commercial  questions  which 
we  have  here  considered. 


CHAP.  III.— CAUSES  MODIFYING  VOLUME  OF  REVENUE.   63 


61.  Therefore,  with  an  end  so  important  before  us,  any  guide 
is  better  than  none,  in  order  that  we  may  reduce  the  unavoida- 
ble uncertainty  to  its  lowest  terms  ;  and  under  these  circum- 
stances a  rule  which  the  writer  has  formulated  as  a  sort  of  gen- 
eral average  to  estimate  exceptions  from  is  this  : 

As  A  MINIMUM  :  At  the  smallest  and  most  inert  non-competitive 
points  the  annual  loss  of  revenue  from  placing  the  station  at  a  distance 
Jrom  town  may  be  taken  as  equivalent  to  10  per  cent  of  the  revenue  tiat- 
urally  originating  from  such  a  to7vn,  with  the  station  in  afty  given  loca- 
tion, for  each  additional  mile  that  the  station  is  moved  off  from  the 

xentre  of  the  town. 

As  A  MAXIMUM  :  At  centres  of  considerable  manufacturing  or  com- 
mercial activity,  exposed  to  considerable  actual  or  potential  competition, 
a  fair  and  moderate  estimate  of  the  probable  loss  of  revenue  from  re- 
moving the  station  to  a  distance  will  be  25  per  cent  of  the  revenue 
naturally  originating  at  such  a  toivn,  for  each  additional  mile  tliat  the 
station  is  moved  off  from  the  centre  of  the  town  ;  and  this  is  frequently 
liable,  in  cases  of  very  sharp  competition,  to  amount  to  as  much  as  ^o 
per  cent  of  the  natural  revenue,  including  all  the  indirect  effects  of  such 

disadvantages. 

The  first  of  these  estimates  the  writer  has  considered  to  be 
applicable  to  such  towns  as  the  average  of  interior  Mexico.  It  is 
below  any  class  of  towns  in  the  United  States  or  Canada,  ex- 
cepting the  strictly  rural  regions  consuming  and  producing  little 
freight  shipped  by  rail.  The  last  is  a  fair  average  (varying  how- 
ever within  wide  extremes)  of  all  the  busier  towns  and  cities  of 
the  United  States. 

62.  The  causes  of  variations  are  : 

1.  Manufacturing  and  especially  mining  towns  are  usually 
heavy  shippers. 

2.  Towns  which  are  the  seats  of  special  industries  often  make 
payments  to  railways  out  of  all  proportion  to  their  apparent  size 

and  activity. 

3.  The  number  of  competing  lines  will  greatly  affect  the  pro- 
portion tributary  to  any  one  lin,e. 

And  many  other  like  causes.     Nothing  definite  can  be  pre- 


64   CHAP.   IIL— CAUSES  MODIFYING  VOLUME  OF  REVENUE, 

dieted  about  any  one  town  from  any  figures  in  this  chapter,  but 
for  the  average  town  they  are  believed  to  be  fair. 

They  are  the  result  of  much  comparison  of  earnings  by  dif- 
ferent lines  at  large  and  small  towns  made  by  the  writer  at  dif- 
ferent times,  with  an  effort  to  estimate  the  true  cause  of  their 
disadvantages  ;  but  to  attempt  to  defend  them  in  detail,  except 
as  the  volume  as  a  whole  may  do  so,  would  occupy  too  much  space. 

Table  13. 

Estimated  Effect  on  Revenue  of  Removing  Stations  from  the  Centre 

OF  Population  of  Towns. 


CHAP.  I  I  I. -CAUSES  MODIFYING  VOLUME  OF  REVENUE.   6$ 


Distance. 

Minimum. 
lo  per  cent  per  mile. 

Ordinary  Maximum. 
as  per  cent  per  mile. 

K.VTRRMR    MaYIMITM 

Miles. 

Difference. 
Per  cent. 

Per  cent. 

Difference. 
Per  cent. 

Per  cent. 

O 

I 

2    

3 

4 

5 

6 

7 

8 

9 

lO 

lO.O 
9.0 
8.1 

7.3 

6.6 

5-9 
5.3 
4.8 

4.3 

3.8 

100. 0 
90.0 
81.0 
72.9 
65.6 
59.0 

53.1 
47.8 
430 

38.7 
34-9 

25.0 

18.75 
14.06 

10.55 
7.91 

5-94 
4.45 
3-34 
2.50 
1.87 

100. 0 
75.0 
56.25 
42.2 

31.65 
23.74 
17.80 

13.35 
10.01 

7.50 
5.62 

Very  materially 
greater  under  certaia 

circumstances, 

especially  with  sharp* 

competition,  so  that 

a  difference  of  two  or 

three  miles  often 

means  the  loss  of 

nearly  the  whole 

traffic. 

Av.   revenue 
per  head 
per  year. 

j.  $2.00    to     $3.00 

$8.00    to     $15.00 

Column  I. — Average  distance  of  station  from  centre  of  population. 

Columns  2  and  4.— Loss  per  cent  of  total  natural  revenue  for  each  additional  mile  of 

distance. 

Columns  3  and  5.— Remaining  per  cent  of  natural  revenue  left  to  the  company. 

The  effect  of  this  rule  is  presented  numerically  in  Table  13^ 
the  percentages  being  in  geometrical  ratio  to  each  other,  so  that 
any  number  in  the  column,  divided  by  the  first  or  second  or  third 
number  above  it,  gives  always  the  same  quotient. 

Under  this  table,  the  percentage  of  loss  for  each  additional 
mile  the  station  is  moved  away  is  the  same  under  all  circum- 


stances, although  the  absolute  loss  is  much  less  as  the  distance 

increases.  «•       . 

63.  The  above  rule,  it  should  be  repeated,  is  not  offered  as 
in  any  way  precise,  or  perhaps  even  safe.  Such  an  estimate 
must  always  remain,  for  the  most  part,  a  question  of  judgment. 
That  is  tlie  author's  judgment.  He  claims  no  more  solid  basis 
for  it  than  that  in  many  single  instances  there  has  been  an  actual 
difference  in  the  receipts  of  competing  lines  at  the  same  point, 
or  in  the  receipts  of  the  same  line  at  points  at  different  distances 
from  it,  but  otherwise  very  similarly  situated,  which  closely  cor- 
respond with  the  figures  given. 

64.  As  example  of  the  working  of  the  above  rule,  to  run  two 
miles  off,  instead  of  one,  from  the  centre  of  a  town  of  10,000 
people  would  involve  as  a  minimum  a  loss  of  9  per  cent  of  the 
natural  revenue  from  such  a  town,  or  froq?  $1800  to  $2700  per 
vear.  If  the  town  were  an  active  business  place  this  might 
easily  be  several  times  this  amount,  and  if  competition  were 
a  factor  of  the  problem  it  would  be  very  certain  to  be.  If 
it  were  a  question  of  running  into  a  town  instead  of  a  mile 
away,  the  loss  would  also  be  liable  to  be  very  much  greater  than 
the  Uble  above  indicates,  since  the  stimulating  effect  of  better 
transportation  might  change  the  whole  character  of  the  town, 
besides  the  natural  effect  of  a  given  difference  of  distance.  The 
question  would  be  affected  likewise  by  the  character  of  the  ter- 
mini, etc.,  etc. 

65.  As  an  instance  from  actual  practice,  two  important  Mexi- 
can  towns,  of  a  population  of  about  100,000  and  60,000  respec- 
tively,  and  about  forty  miles  apart,  with  considerable  natural 
traffic  between  them,  were  left  distant  respectively  two  and  a 
half  miles  and  four  and  a  half  miles  from  the  nearest  point  of 
the  projected  line.  It  was  a  question  whether  to  bring  the  rail- 
way nearer  to  the  town,  in  which  case  both  stations  would  be 
half  a  mile  from  the  centre  of  population  : 

If  we  might  assume  the  above  minimum  to  be  correct,  the 
certain  loss  on  all  the  traffic  contributed  to  the  railway  by  these 


^   CHAP.  III.— CAUSES  MODIFYING    VOLUME   OF  REVENUE, 


towns,  and  not  simply  on  ihe  traffic  between  them,  would  be  an. 

nually — 

$200,000  X  o  19       =  $38,000 

120,000  X  0.344     =    41,280 


Total  ($217  per  day)  $79,280 

For  Mexican  towns,  in  their  present  condition  of  imperfect 
material  development,  this  is  possibly  large  enough  ;  but  for 
American  towns  of  equal  size  and  importance  it  would  almost 
certainly  be  far  too  low.  If  it  were  to  be  considered  as  solely 
affecting  the  passenger  traffic,  and  of  such  traffic  only  that  exist- 
ing between  the  two  towns,  it  would  amount  to  the  loss  of  sixty- 
five  to  seventy  round  trips  per  day,  and  this  in  the  United  States, 
between  two  active  business  points  at  that  distance  from  each 
other,  would  be  far  from  an  exaggerated  estimate. 

It  would  in  such  a  case,  however,  be  extremely  erroneous  to 
consider  only  the  traffic  between  the  two  points.  All  the  traffic 
originating  or  terminating  at  each  point  is  more  or  less  affected, 
the  importance  of  the  effect  decreasing  with  the  length  of  tiie 
haul.  The  freight  traffic  will  also  be  materially  affected,  in  some 
slight  degree  in  volume,  and  a  large  proportion  of  it  in  average 
rates,  for  reasons  already  pointed  out,  the  chief  of  which  is  that 
the  railway  sooner  or  later  pays  for  the  cartage. 

66.  Yet  all  these  arguments,  like  almost  everything  else  con- 
nected with  the  laws  of  trade,  require  to  be  applied  with  great 
caution,  and  are  subject  to  many  exceptions,  such  as  these  which 
follow : 

Towns  will  in  many  cases  move  to  the  railway,  if  the  railway 
does  not  come  to  the  town,  with  ultimate  benefit  to  all  parties 
concerned.  This  is  especially  common  and  probable  in  the 
United  States,  but  it  is  more  or  less  true  everywhere.  In  pro- 
portion as  the  population  and  traffic  may  be  expected  to  increase, 
the  importance  of  accommodating  the  line  to  that  which  already 
exists  becomes  less  and  less. 

Even  in  a  region  tolerably  well  settled,  but  heretofore  unde- 
veloped by  railways,  or  imperfectly  developed,  a  bold  neglect  of 


CHAP.   III.— CAUSES  MODIFYING  VOLUME  OF  REVENUE.   67 


existing  centres,  especially  those  of  minor  importance,  will  be 
exceedingly  apt  to  bring  them  sooner  or  later  to  the  railway  in- 
stead of  losing  the  railway  their  traffic;  and  this  will  be  in  some 
cases,  where  other  lines  are  not  likely  to  compete,  the  more  apt 
to  follow  the  more  completely  such  points  are  left  out  in  the 
cold. 

Especially  when,  by  taking  a  central  line  between  two  subor- 
dinate centres  of  this  kind,  about  as  much  will  be  gained  from 
the  one  as  lost  from  the  other,  the  ultimate  effect  will  probably 
be  to  build  up  a  new  town  between  both,  affording  new  traffic, 
while  still  retaining  a  good  proportion  of  that  which  remains 
at  each  of  the  old  centres,  and  could  have  been  fully  secured 
from  one  of  them  only  by  wholly  neglecting  the  other;  thus  sub- 
stantially increasing  the  aggregate  traffic  of  the  line. 

This  amounts  to  saying  that  in  seeking*  to  pass  through  the 
centre  of  the  population,  as  in  determining  the  centre  of  gravity, 
we  cannot  always  consider  one  body  alone,  but  must  consider 
several  as  constituting  one  composite  entity. 

67.  So,  too,  it  is  easily  possible,  in  laying  out  branch  lines  or 
the  parts  or  links  of  extended  systems,  to  be  so  over-anxious  to 
secure  some  trifling  advantages  of  local  traffic  as  to  seriously 
burden  and  cripple  other  and  much  more  important  interests,  or 
perhaps  lay  the  line  open  in  the  future  to  destructive  competi- 
tion. 

These  various  possibilities — con  as  well  SiS pro — are  very  fre- 
quently the  most  important  of  those  which  fix  or  should  fix  the 
location  of  a  line.  Especially  in  easy  country  it  may  almost  be 
said  to  be  the  rule  that  these  will  be  important  enough  to  over- 
rule engineering  disadvantages  of  considerable  moment,  the  ex- 
tent of  which  latter,  therefore,  it  will  often  be  waste  of  time  to 
consider;  and  even  in  the  most  difficult  country  it  will  usually 
require  marked  and  decided  engineering  disadvantages  to  justly 
overbalance  any  considerable  advantages  as  respects  probable 
traffic  and  revenue. 

68.  The  question  of  the  location  of  termini,  and  its  effect 
upon  traffic,  is  really  closely  allied  to,  and  in  fact  a  part  of  the 


68    CHAP.   III.— CAUSES  MODIFYING  VOLUME  OF  REVENUE,. 


CHAP.   III.—CAUSES  MODIFYING  VOLUME  OF  REVENUE.   69 


geneial  question  of  how  near  to  bring  the  line  to  towns,  which 
we  have  just  been  discussing.  Nevertheless,  from  the  fact  that 
the  terminal  towns  are  usually  by  far  the  most  important  on  the 
line  and  likewise  the  most  costly  points  to  approach  closely,  sound 
business  judgment  is  violated  more  frequently  and  more  danger- 
ously at  such  points  than  at  points  along  the  line.  Had  it 
not  so  often  happened  that  lines  which  have  expended  mil- 
lions for  the  construction  of  long  lines  to  a  certain  place  have 
tiien  begrudged  or  failed  to  raise  the  necessary  additional  per- 
centage to  carry  their  line  into  it,  contenting  themselves  with; 
hanging  on  to  the  skirts  of  the  town  somewhere,  where  they  caa 
be  reached  by  horse-cars  or  hacks  and  drays,  it  would  seem  in- 
credible that  business  corporations  could  so  frequently  commit 
an  act  of  folly  which  can  fairly  be  paralleled  with  that  ©f  binild- 
ing  a  long  bridge  and  erecting  every  span  but  one — assuming,, 
on  account  of  some  difficulty  with  foundations,  or  what  not,,  that 
a  ferry  would  be  good  enough  for  that,  because  it  would  be 
"such  a  little  one."  The  lines  which  do  or  have  pursued  this 
course  will  be  found  to  be  those  which  figure  most  prominently 
in  the  list  of  bankrupt  corporations  ;  and  the  evidence  of  that 
fact  is  so  patent  to  any  one  who  will  take  a  list  of  such  and  study 
it  over,  that  it  is  needless  to  add  more  to  what  has  been  already 
said  than  to  note  the  great  sums  which  successful  properties  spend 
in  reaching  the  heart  of  great  cities  to  remedy  former  errors. 

69.  In  England  hundreds  of  millions  have  been  expended  for 
this  purpose,  and  tens  of  millions  at  the  smaller  towns  alone.  In 
America  we  are  far  more  backward  than  the  best  interest  of  the 
properties  requires  :  but  many  such  works  have  been  recently 
carried  through,  one  example  of  which  is  the  new  entrance  of  the 
Pennsylvania  Railroad  into  the  city  of  Philadelphia  ;  while  at 
New  York,  Boston,  St.  Louis,  and  other  cities  similar  improve- 
ments have  been  made  or  are  being  projected  on  a  lavish  scale. 
Certainly  it  has  never  been  questioned  that  the  Philadelphia  ter- 
minus was  an  expedient  investment,  and  we  may  be  sure  that  it 
was  not  undertaken  with  any  other  view  by  the  management  of 
the  company.     It  was  executed  almost  wholly  for  the  local  con- 


venience of  Philadelphia,  and  consisted  in  carrying  in  the  com- 
pany's tracks  on  an  elevated  structure  to  a  point  very  near  to 
the  centre  of  the  city.  It  was,  moreover,  an  expenditure  to  which 
the  company  was  not  driven  by  competition,  except  as  to  a  small 
part  of  their  traffic,  for  they  had  good  facilities  for  both  freight 
and  passengers  ;  facilities  as  conveniently  accessible  as  they  well 
could  be  by  horse-cars — that  ever-ready  excuse  for  neglecting  to 
bring  railway-stations  into  the  centre  of  population.  Some  in- 
crease of  space  was  indeed  desirable,  but  it  might  have  been  se- 
cured much  more  cheaply  in  other  ways,  had  the  company 
deemed  it  expedient. 

The  Philadelphia  improvement  cost  about  $4,590,000,  of 
-which  about  half  was  for  land  only  ;  or  about  $5  per  head  of  the 
population  concerned,  the  interest  on  which  at  five  per  cent  is 
about  $225,000  per  annum,  or  twenty-five  cents  for  each  man, 
woman,  and  child  of  the  population — a  sum  which  should  be 
largely  increased,  perhaps  doubled,  for  the  indirect  loss  on  in- 
vestments already  made,  and  from  operating  expenses  for  haul- 
ing the  whole  traffic  into  and  out  of  the  new  station,  to  which  the 
system  of  roads  centring  there  had  not  been  originally  adapted. 

It  is  to  be  presumed,  of  course,  that  the  value  of  this  improve- 
ment to  the  corporation  is  expected  to  be  considerably  more 
than  this.  Nor  does  such  expectation  seem  unreasonable  ;  for, 
independent  of  all  necessity  for  competition,  experience  at  other 
points  proves  that  it  would  be  a  paying  investment,  from  its 
direct  and  indirect  effect  to  encourage  new  traffic. 

In  the  company's  report  for  1881  it  was  stated — 

"The  cost  of  this  work  is  already  having  a  marked  effect  on  the  develop- 
ment of  local  traffic  ;  and  it  is  believed  that,  in  addition  to  its  great  value  to 
through  and  competitive  business,  it  will  in  a  few  years,  by  its  promotion  of 
suburban  trains  reaching  the  park  and  other  portions  of  the  city,  and  its 
stimulus  to  the  traffic  before  referred  to,  fully  realize  all  that  was  contemplated 
at  the  lime  of  its  original  construction." 

At  the  time  of  this  report  there  were  some  two  hundred  pas- 
senger trains  into  and  out  of  Broad  Street  Station  daily.  There 
are  now  about  fifty  per  cent  more. 


5 


70  CAr<4/>.   III.— CAUSES  MODIFYING  VOLUME  OF  REVENUE, 

70.  At  New  York  a  costly  improvement  was  carried  through 
at  the  joint  expense  of  the  city  and  the  New  Yoriv  Central  and 
Hudson  River  Railroad,  costing  some  $8,000,000,  in  order  to  per- 
manently insure  the  running  of  fast  trains  to  the  Grand  Central 
Station  at  Forty-second  Street,  which  will  probably  hereafter  be 
the  heart  of  the  population  patronizing  the  railway,  although  for 
the  present  it  is  rather  far  up-town.  The  then  existing  passen- 
ger station  at  Twenty-eighth  Street  was  abandoned,  in  part  on 
account  of  the  difficulties  and  expense  involved  in  securing  room 
at  that  point  for  the  immense  traffic  to  be  handled,  and  in  carry- 
ing the  line  to  it,  but  in  part  because  the  point  selected  was 
deemed  to  be  so  near  the  future  centre  of  the  city.  An  addi- 
tional passenger  station  (mainly  for  suburban  trains)  is  still 
maintained  on  the  west  side,  at  Thirty-second  Street,  as  are  also 
freight  stations  farther  down-town  on  both  the  east  and  west 
side,  to  and  from  which  cars  are  hauled  by  horses. 

71.  At  St.  Louis,  a  union  depot  for  all  the  railways  centring 
there  was  built  in  connection  with  the  great  St.  Louis  Bridge, 
the  whole  costing  some  $7,000,000;  while  there  is  hardly  a  city 
of  any  importance  where  smaller  improvements  of  the  kind 
are  not  projected  by  some  one  of  the  lines  reaching  it,  at  a 
largely  increased  cost  over  what  would  have  been  originally  nec- 
essary;— without  considering  in  this  statement  the  heavy  losses 
of  traffic  through  the  dubious  early  years  of  the  company's  his- 
tory which  have  enforced  such  improvements.  On  the  other 
hand,  there  is  no  instance  on  record  where  adequate  terminal 
facilities  once  acquired  have  been  abandoned  for  others  more 
distant  and  less  valuable,  because  the  market  value  of  the  prop- 
ertv  was  greater  than  its  productive  value  in  the  hands  of  the 
company. 

72.  To  apply  the  same  ratio  of  expenditure  as  is  incurred  at 
the  larger  cities  to  smaller  places  might  not  in  many  cases  be 
safe  for  these  reasons : 

First,  The  average  receipts  per  head  of  population  increase 
very  much  faster  than  the  population.  (See  Chap.  XXI.,  and  the 
various  tables  giving  revenue  per  head  of  population.) 


CHAP.   III.— CAUSES  MODIFYING  VOLUME  OF  REVENUE,  7 1 


Secondly,  At  very  large  cities  like  New  York,  Philadelphia, 
Chicago,  and  Boston,  the  distinctly  suburban  traffic,  making 
daily  trips  at  commutation  rates,  is  a  large  element,  which  espe- 
cially requires  the  best  attainable  terminal  facilities  and  the 
largest  possible  saving  of  time. 

Table  14  gives  some  idea — in  part,  it  must  be  confessed,  a  deceptive  and 
imperfect  one — as  to  how  large  a  part  these  various  works  constitute  of  the 
total  cost  of  railways  of  the  first  class,  and  how  small  an  element  is  the  mere 
construction  to  sub-grade  between  stations.  See  also  Chapter  XXVI.,  on 
••Terminals." 

Table  14. 

Proportion  and  Amount  of  the  Various   Items  of  Cost  of  Road  and 

Equipment. 

New  York  Central  &  Hudson  River  Railroad,  1885,  953  miles ;  amount  of  track,  2.85  times 
length  of  line  ;  and  in  less  detail  for  Pennsylvania  Railroad,  1257  miles. 


New  York  Central  &  Hudson  River. 

Pennsylvania. 

Items. 

Per 

Mile. 

Per 
Cent. 

Itkms. 

Per 

Mile. 

Per 
Cent. 

Grading  and  masonry 

Bridge 

Superstructure  

$22,000 

31030 
32,500 
15.400 
15.740 

6,630 

1.617 
15,830 

3,160 
293 

18.9 

3.6 

37.9 

13.3- 

13.6 

5-7 

1-4 

13-6 

3.7 

•3 

Construction 

Equipment 

Real  estate  and  telegraph . . 

Total 

$30,400 
19.300 
10,130 

50.7 
323 

Sutions,  etc 

17.0 

$59,830 

TfV)    C% 

Land  and  land-damages.... 

Locomotives 

Stock  

$75,300 
53,500 

Passenger  cars 

Freight  cars 

Bonds 

•  ■  •  • 

Engineering 

Floating  Equipment 

The  Pennsylvania  owns  enormous  amounts 
of  the  securities  of  controlled  roads,  repre- 
sented by  its  securities.     Its  policy  has  been 

Total 

$116,300 

100. 0 

Stock 

Bonds 

93,800 
59iOoo 

•  •  •  • 

•  •  •  • 

to  defray  expenses  out  of  earnings  rather  than 
increase  canital  acroiint 

The  small  proportion  which  the  bare  cost  of  laying  down  the  track  bears  to  the  total 
investment,  on  lines  of  importance,  is  clear  from  the  above. 

Thirdly.  At  almost  all  points  in  the  United  States  the  proba- 
bilities of  future  growth  must  be  remembered.,  which  will  some- 
times, as  at  New  York,  bring  a  point  which  is,  for  the  time  being, 


72    CHAP.   III.— CAUSES  MODIFYING  VOLUME  OF  REVENUE. 


CHAP.  III.— CAUSES  MODIFYING  VOLUME  OF  REVENUE.   73 


i 


considerably  outside  of  the  centre  of  population  into  the  very 

heart  of  it. 

Nevertheless,  no  town  is  so  small  that  the  considerations 
advanced  are  not  more  or  less  applicable  to  it,  and  the  usual  law 
of  development,  when  topographical  impediments  do  not  forbid 
it,  is  that  the  town  spreads  equally  in  all  directions,  its  centre  of 
gravity  remaining  unchanged,  as  in  the  case  of  London,  and 
measurably  of  Chicago,  Philadelphia,  and  other  cities  ;  in  which 
case  the  disadvantages  of  having  a  terminus  at  a  distance  from 
that  centre  do  not  decrease  with  time,  but  increase  in  direct  ratio 
to  the  population. 

73.  Although  the  impossible  task  of  definite  technical  analysis 
of  the  revenue  considerations  here  discussed  has  been  passed  by, 
it  is  hoped  that  enough  has  been  said  to  impress  upon  the  minds 
of  engineers  and  projectors  that  they  are  entitled  to  great,  if 
somewhat  indeterminate,  weight,  and  that  it  is  unsafe  for  any 
engineer  to  enter  upon  the  work  of  laying  out  a  railway  with  no 
more  thought:  of  its  financial  future  than  a  vague  idea  that  the 
passenger  revenue  is  obtained  by  selling  tickets,  and  the  freight 
revenue  is  measured  by  the  sum  of  the  war-bills,  and  that  neither 
is  any  concern  of  his  ;  his  duty  being  simply  to  get  the  shortest, 
che^ipest,  and  straightest  line, — the  phrase  has  almost  hardened 
into  a  formula, — and  that  when  he  has  gotten  it  he  has  done  his 
whole  duty.  It  may  be  that  he  has,  but  it  does  not  follow  ;  and 
the  chances  are  good  that  he  will  have  not  only  completely  failed 
to  do  it,  but  will  have  involved  the  projectors  in  certain  ruin  ; 
because,  although  the  amount  by  which  the  revenue  can  be  mod- 
ified by  differences  of  location,  or  even  by  differences  in  the  sub- 
sequent management,  is,  as  a  rule,  only  a  small  percentage  of 
the  aggregate  revenue,  yet  it  is  this  small  percentage  alone  in 
which  the  original  projectors  have  a  property  interest  ;  that  por- 
tion of  the  revenue  which  goes  to  pay  fixed  charges  and  operat- 
ing expenses  being  in  no  sense  theirs. 

The  strength  of  the  argument  for  neglecting  no  effort  to 
reach  all  possible  sources  of  traffic  is  greatly  strengthened  by  the 
considerations  which  it  seemed  more  appropriate  to  discuss  in 


Chapter  XXL,  but  which  have  a  very  direct  bearing  on  the  sub- 
ject-matter of  this  chapter. 

74.  That  the  effect  of  comparatively  slight  causes  to  influence 
revenue  has  not  been  exaggerated,  may  perhaps  be  proved,  as 
effectually  as  in  any  way,  by  a  trivial  incident  which  the  writer 
knows  to  be  authentic  : 

A  certain  railway,  for  competitive  reasons,  determined  that 
some  marked  improvement  in  its  eating  stations  must  be  made 
to  meet  the  competition  of  dining-cars  on  a  rival  line.  The  pro- 
prietor of  one  of  these  establishments,  therefore,  was  instructed 
to  make  certain  decided  improvements  in  the  appointments  of 
his  table,  and  in  the  character  and  quality  of  the  viands  provided, 
at  the  expense  of  the  company,  and  to  send  in  his  bills  from 
time  to  time  for  this  additional  expenditure.  The  bills  not  com- 
ing in,  although  the  desired  betterments  had  been  (with  some 
reluctance)  made,  and  with  results  very  gratifying  to  the  com- 
pany, the  proprietor  was  again  requested  to  send  in  his  bills  ; 
when  it  appeared,  on  inquiry  as  to  each  item  in  succession  for 
which  he  had  been  specifically  instructed  to  increase  his  expen- 
diture at  the  expense  of  the  company,  that  the  proprietor  was 
*' satisfied  that  it  paid  him,"  or  that  it  was  "no  more  than  he 
ouirht  to  do,"  or  that  he  was  *'  well  enough  contented  as  it  was" 
— in  short,  that  he  had  no  bills  to  present. 

Such  an  incident,  the  details  of  which  were  precisely  as 
stated,  must  be  admitted  to  be  an  extraordinary  instance  of  the 
power  of  conscience  in  a  class  who  are  not  often  given  credit  for 
having  any,  but  it  is  also  a  proof  that  great  direct  advantages  to 
the  proprietor,  as  well  as  indirect  advantages  to  the  company, 
must  have  resulted.  To  fully  appreciate  its  bearing  upon  those 
semi-technical  questions  which  depend  more  or  less  on  the 
peculiarities  of  human  nature,  two  additional  facts  must  be 
remembered.     On  the  one  hand — 

1.  A  large  fraction  of  the  passengers  have  but  slight  reason 
to  choose  between  one  or  another  railway  before  beginning  their 
journey  ;  while,  on  the  other  hand, 

2.  The  journey  once  entered  on,  they  have  no  choice  what- 


<*/> 


1 


74   CHAP.   III.— CAUSES  MODIFYING  VOLUME  OF  REVENUE. 


ever  as  to  where  to  take  their  meals,  but  to  take  such  meals  as 
are  set  before  them  at  the  appointed  stopping-places,  or  go 
hungry.  The  railway  restaurant  business  is  pre-eminently  non- 
competitive. 

If,  therefore,  a  trifling  improvement  in  meals,  which  had  never 
been  really  bad,  could  so  materially  affect  the  non-competitive 
business  of  a  railway  restaurant,  what  is  the  probable  effect  of 
the  same  and  other  slight  causes  on  the  traffic— especially  on  the 
receipts  from  that  considerable  class  who  travel  a  great  deal  by 
rail,  but  hardly  make  a  really  necessary  trip  more  than  two  or 
three  times  in  a  lifetime  ? 

With  this  attempt  to  solve  by  a  parable  an  essentially  inde- 
terminate problem,  we  pass  to  those  branches  of  our  subject 
which  are  often  of  less  real  importance,  but  which  admit  of  more 
definite  and  technical  treatment,  and  which,  perhaps  for  that 
reason,  are,  not  unnaturally,  too  often  the  only  ones  considered 
by  members  of  a  definite  and  technical  profession. 


CHAPTER    IV. 

THE  PROBABLE  VOLUME  OF  TRAFFIC,  AND  LAW  OF  GROWTH 

THEREIN. 

75,  It  having  been  once  determined  that  a  railway  is  to  be 
built  at  all  between  any  two  points,  with  the  consequent /r/'w^- 
facie  corollary  that,  excepting  when  and  as  reasons  to  the  con- 
trary appear,  it  is  to  be  the  cheapest  line  over  which  trains  can 
be  run  with  due  safety  and  speed,  tlie  probable  nature  and 
volume  of  the  future  traffic  becomes  the  vital  question  ;  for  both 
the  revenue  and  the  operating  expenses  will  vary  in  close  ratio 
therewith,  and  only  to  increase  the  one  or  diminish  the  other 
are  we  justified  in  expending  more  money  than  proper  security 
in  handling  trains  requires.  The  more  the  traffic  of  a  railway 
the  larger  the  pecuniary  saving  from  a  given  betterment  in  the 
rate  and  distribution  of  gradients,  curvature,  or  distance — and 
the  more,  consequently,  tiie  justifiable  expenditure  to  effect  it ; 
the  criterion  beincj  :  Will  a  certain  betterment,  which  is  not  an 
essential  for  the  safe  passage  of  trains,  save  the  company  more 
per  year  in  operating  expenses  (or  add  more  to  the  revenue,  in 
the  limited  class  of  problems  in  which  that  question  comes  in) 
than  it  will  add  to  fixed  charges  by  the  capital  expended  to  effect 
it?  If  it  will,  the  expenditure  and  betterment  should  be  made  ; 
if  it  will  not,  it  should  not  be  made. 

76.  To  determine  the  probable  volume  of  traffic  with  exactness 
is  of  course  impossible  ;  nor  is  it,  fortunately,  particularly  im- 
portant to  do  so,  if  we  make  a  reasonably  close  approximation  ; 
for  the  reason  elsewhere  discussed,  that,  with  a  judiciously  located 
hne,  the  saving  by  adopting  a  poorer  line  than  one  naturally 
adapted  to  the  topography  is  ordmarily  not  so  great  that  any 


76 


CHAP.   IV.—PROBABLE  VOLUME  OF  TRAFFIC. 


CHAP.   IV.— PROBABLE  VOLUME  OF  TRAFFIC. 


77 


probable  deficiency  in  the  estimate  of  traffic  would  permit  of  it; 
while,  on  the  other  hand,  the  cost  of  defying  the  natural  topo- 
graphical conditions  is  ordinarily  too  great  for  any  probable 
excess  in  the  estimate  of  traffic  to  permit  of  it  wrongly.  In  other 
words,  the  danger  lies  in  having  no  criterion,  or  in  a  false  per- 
spective as  to  the  relative  importance  of  various  ends,  or  in 
purely  arbitrary  decisions  based  on  no  investigation  whatever, 
rather  than  in  a  certain  percentage  of  error  in  our  criterion. 

All  that  we  need  to  do,  therefore,— all  that  will  have  any 
important  bearing  on  our  action,  as  experience  will  soon  teach, 
— is  to  bring  reasonably  near  to  each  other  the  maximum  and 
minimum  probabilities, — "the  limits  of  error  in  either  direc- 
tion, somewhere  within  which  lies  the  truth  and  anywhere  out- 
side of  which  lies  a  certainty  of  error."  This  there  is  ordinarily 
no  difficulty  in  doing. 

77.  In  a  rude  way  it  can  be  done  at  once  by  any  one  at  all 
familiar  with  railroad  work.  We  know  at  once  whether  a  line  is 
more  likely  to  have  a  light  local  traffic  or  a  trunk-line  traffic.  It 
is  but  a  step  further  to  determine  with  very  approximate  exact- 
ness that  a  line  will  have  somewhat  more  traffic  than  this  or  that 
or  the  other  line  near  it,  or  similarly  situated  in  other  regions, 
and  less  traffic  than  as  many  others  ;  from  which  the  establish- 
ment of  a  mean  for  the  immediate  traffic  and  its  future  growth 
is,  with  some  knowledge  of  railroad  business,  a  simple  matter. 

78.  The  greatest  difficulty  in  making  such  estimates  is  ordi- 
narily the  fact  tiiat  to  make  them  it  is  essential  to  estimate  and 
allow  for  the  probable  future  growth  of  traffic,  since  it  is  rarely 
the  case  that  a  railway,  especially  in  the  United  States,  is  built 
simply  and  only  to  accommodate  the  traffic*' in  sight,"  as  min- 
ers say.  On  the  contrary,  it  has  been  and  will  continue  to  be 
frequently  the  case  that  the  railway  is  relied  upon  not  only  to 
accommodate  but  to  create  a  great  part  or  the  whole  of  the 
traffic  for  which  it  is  built.  Even  when  the  population  of  the 
region  traversed  cannot,  as  it  can  in  most  parts  of  the  United 
States,  be  expected  to  rapidly  increase,  experience  has  shown 
that  if  the  surrounding  territory  has  heretofore  been  but  scantily 


provided  with  railway  facilities,  (i)  the  traffic  of  the  first  few 
vears  will  be  but  a  small  proportion  of  what  would  nominally  be 
expected   from  a  similar  population  elsewhere,  and  (2)   that  it 

Table  14i. 

Earnings  Per  Head  of  Population  and  Per  Mile  of  the  Railways  of 

THE  State  of  Iowa. 


Miles  of  Road. 

Population. 

Gross  Earnings. 

Year. 

Total. 

In- 
crease. 

Actual  or 

Estimated. 

1  =  1000. 

Per  Mile 
of  Road. 

Totals. 

Per  Mile 
Road. 

Per  Head 
Popula- 
tion. 

1862 

626 

653 
727 

■  •  •  • 

27 
74 

778. 
830. 
882. 

1,243 
1,271 
1.212 

$1,109,346         $1,772 

$1.42 

i86^ 

1-570,546 

2,405 

1.89 

1864 

2.553,699           3-512 

2.89 

1865 

847 

I30 

934- 

1. 103 

3,871.783    i       4,572 

4  14 

1866 

1,060 
1,328 
1,448 
2.081 

213 
168 
220 

533 

t  986. 
+  1,038. 
t  1,040. 
t  1,142. 

930 
838 

734 
550 

4.118.006 

5,867,501 

8.024.931 

10.409.950 

3.884 
4,778 
5-541 
5.002 

4.12 

1867 

5.65 

1868 

1869  

7-36 
9.12 

1870...    .    

2,683 

602 

*  1.194.320 

445 

11,932,352 

4.447 

10.00 

1871 

3,160 

3^643 
3.728 

3.765 

477 

483 

85 

37 

t  1,231.600 
+  1,270.100 
+  1.309.800 
+  1.350.700 

389 
349 
352 
359 

1872 

i9.i-s 

i°73 

1874 

1875  

3.S50 

85 

*  1.393.000 

362 

1876 

3.939 
4.134 
4.157 
4-396 

89 
195 

23 
239 

t  1,436  500 
t  1,481.400 
+  1,527.700 
t  1.575.400 

365 
360 
368 
359 

5-903 
5-587 

^077 

1878 

(24.550,000) 
(24.500.000) 

16.08 

i879--.. 

15  54 

1880 

4.977 

58X 

•  1,624.615 

327 

(27.250,000) 

5-491 

16.80 

i88i 

5i426 

6,337 
7.01s 
7.249 

449 
911 
678 
234 

t  1,675.400 
t  1,727.7-0 
t  1,781.700 
t  1.837.400 

309 
272 
258 
253 

28,452,181 
32,023.966 

34,433,355 
35,735,272 

5-084 
5.607 
5,386 
5,481 

16.98 

1882 

18.54 

1881 

19-35 

i88a 

19.46 

♦  Actual.  t  Estimated. 

The  tendency  of  earnings  to  increase  about  as  the  square  of  the  population  tied  together 
by  convenient  means  of  transportation,  discussed  in  detail  in  Chapter  XXL,  is  very  con- 
spicuous in  this  and  the  following  table. 

may  be  expected  for  the  first  few  years  to  have  an  abnormally 
rapid  growth.  Table  14^  shows  this  clearly.  Even  in  a  com- 
paratively densely  populated  State  like  Massachusetts,  or  in  a 
country  like  England,  which  are  neither  growing  rapidly  in 
population  nor  ill  provided  with  existing  facilities,  experience 
has  shown  (Tables  15  and  16)  that  the  rate  of  growth  is  rapid 
enough  (from   5   to  8  per  cent  per  annum,  as  an  average)  to 


'-^'m- 


78 


CHAP.   IV.—PROBABLE  VOLUME  OF  TRAFFIC, 


CHAP.   JV.— PROBABLE  VOLUME   OF   TRAFFIC. 


79 


Table  15. 

Earnings  per   Head   of   Population  and  Per   Mile   of   Road    of    the 

Railways  of  Massachusetts. 


Miles  of  Road. 

Population. 

Gross  Earnings. 

Year. 

Totol. 

Per 

cent,  in 

Mass. 

Actual  and 

Estimated. 

I        1000. 

Per  Mile 
Koad. 

Total 
(Thousands). 

Per  Mile 
Road. 

Per  Head 
Popula- 
tion. 

"845 

463 

97 

837- 

1.885 

$2,8q5 

$6,350 

S3 -35 

46  

632 
715 
787 
945 

96 
95 
94 
93 

882. 
909. 
937- 
965. 

1.542 
1,336 
1,265 
i.oq6 

3.642 

4.965 
5.406 

5742 

5.850 
6,950 
6.890 
6.080 

4.23 

A1     ....••••>. 

5.19 

^8 

5.43 

49     

5-54 

1850 

1.092 

92 

994  514 

992 

6.420 

5.890 

5.770 
5.990 
6,870 
7.300 

5.94 

ri     

1,142 

1,150 
T.164 

i.«94 

9« 
90 

89 
88 

1,016. 
1,038. 
1.060. 
1,083. 

978 
1,003 
1,013 
1.024 

6.600 
6,886 

7.977 
8.696 

5  91 

3* 

<;  95 

D' 

6.70 

33 

54 •• 

7.04 

1855    

1,281 

87 

1. 107. 

972 

9.077 

7.090 

7. II 

c6  

1.325 
1.351 
1,380 
1.380 

86 

85 
84 
83 

1.130. 

1,155- 

1.180. 
1.205. 

960 
972 
973 
993 

9,750 
9-094 
8,597 
9,771 

7.370 
7.360 
6,230 

7,080 

7.42 

5"    

6.69 

0/    

eg    

6.12 

3" • • * 

59   

6.7s 

i860 

1.37' 

82 

1.231  066 

1.033 
1.063 
1,080 
1,042 
1,070 

9.936 

7.260 

6.63 

61    

1,366 
1,386 

1,475 
1.486 

81 
81 
83 

83 

1,252. 
1,273. 
1,295- 
1.317 

8.669 

9-655 
11,711 

14.981 

6.340 

6.960 

7.920 

10.100 

5.63 

63 

6.09 

61   

7.21 

"j 

64 

9  78 

1865     

1.500 

83 

1,340. 

1.108 

17-459 

11.660 

11.04 

66 . • • 

67 

1.550 
1,612 

1,749 
1.979 

84 
84 
85 
85 

1,362. 

1.385. 
1,409. 

1.433- 

1.088 

1.076 

1.023 

930 

19.242 

19.444 
20,788 

22,495 

12.430 
12,100 
11.920 

11.380 

12  16 
12.17 

68  

12.60 

69  

13-35 

1870  

1.475 

1.457  351 

988 

13.220 

13  40 

.71  ........... 

2,098 
2.194 
2.365 
2,418 

1,601 
1,658 
1.735 
1.783 

1.487. 
1,517- 
1,548. 
1.580. 

930 

914 
962 
887 

27.186 
30,879 
34.930 
34.000 

12.950 
14.080 
14.800 
14.070 

l?-94 

72 

14-30 

73 

74     

15-38 
15.88 

1875 

2.4S9 

1. 817 

1,612. 

895 

31.495 

12.820 

14-35 

76 

2,479 
2,496 

2,492 
2,626 

1.837 
1.855 
1,850 
1.862 

1.645. 
1.678. 
1.713 
1-747- 

896 
903 

927 
941 

29,856 
28.932 
38,003 
29.153 

12.070 
11.620 
11,250 
11,100 

i3-4ti 

77     

12.77 

78 

12.15 

79    

11.80 

1880 

2.667 

1.893 

1.783.085 

945 

33,662 

12.640 

•3.38 

81 

82 

2-755 
2.778 
2.783 
2.852 

1.928 
1.949 
1.953 
1,974 

1.820. 
1.859. 
1.897. 
1,937- 

944 
955 
974 
982 

35.936 
39.094 
41,636 
41.457 

13.070 
14.100 
15.010 
14,560 

13-85 
14.78 

81 

IS  40 

84 

14.86 

The  actual  mileage  in  the  State  limits  is  not  given  previously  to  1870,  and  an  assumed 
percentage  has  been  used  to  determine  the  population  and  earnings  per  mile  of  road. 
From  1870  to  1884  the  earnings  per  head  are  computed  by  assuming  that  the  average 
earnings  jjer  mile  of  road  were  no  greater  inside  than  outside  the  State  limits,  which 
is  certainly  incorrect,  and  on  an  average  will  probably  make  the  earnings  per  head  fen 
io  Jl/teen  per  cent  too  small.     From  1861  to  1870  inclusive  the  total  earnings  within 


constitute  an  element  which  might  be  legitimately  considered  in 
laying  out  a  new  line.  The  table  embodying  this  English  ex- 
perience is  very  instructive,  as  indicating  a  minimum  of  growth 
under  settled  conditions  which  no  large  section  of  this  country  is 
likely  to  fall  below  for  many  decades. 

In  all  but  the  rarest  instances,  it  would  be  absurd  to  claim 
that  no  allowance  should  be  made  for  future  growth  of  traffic, 
and  often  it  should  be  a  very  large  one.  Nevertheless,  while, 
theoretically,  large  allowances  for  this  future  traffic  are  almost 

Table  16. 
Growth  of  English  Railways  and  Railway  Traffic 


% 

Miles. 

Capital. 

No.  of 
Passengers- 
Millions. 

Ybar. 

Double 
or  more. 

Single. 

Total. 

Total. 
I     $1,000,000. 

Per  Mile. 

I  =  $1000. 

1855 

6,153 
6,690 

7,711 
8,338 
8,898 

9,803 
10,239 

2,182 
3.743 
6,143 
7.038 
7,760 
8,130 
8,625 

8,335 
10.433 
13,854 
15,376 
16,658 

17,933 
18,864 

1446. 
1692. 
2213. 

2574- 
3061. 

3537. 
3892. 

1734 
164.0 
166.6 

165-7 
183.8 
197.2 
206.1 

118.6 

I860 

1634 

1865 

251.9 

1870 

336.5 

1875 

507.0 

1880 

1884 

603.9 
695.0 

Receipts. 

Per  Cent 
Oper- 
ating 

Expenses. 

Per  Cent. 
Net 

Ybar. 

Total. 
Millions. 

Per  Mile 
of  Road. 

Per 

Train 
Mile. 

Per  Cent  from— 

Receipts 
to 

Pass.         Freight. 

Capiul. 

1855 

$ 

104.6 

134-8 
174.4 

3I0.8 

386.3 

306.0 

328.8 

% 

12,530 

12,930 
13.120 
13,570 
17,200 
17,040 
17,440 

cts. 
140.6 

131-5 
125.0 
124.4 

136.5 
127.2 

131.3 

49-7 
47.1 
46.3 
42.8 
43.0 

41-S 
43.6 

50.3 
50.9 
53-8 
53-5 
54.3 
54-6 

53.4 

47 
48 
48 
54 
51 
53 

•  •  •  • 

I860 

1865 

4  19 
4.11 

1870 

4-41 

1875 

4-45 

1880 

1884 

438 
4.16 

Compiled  from  the  Board  of  Trade  returns. 


the  State  were  given  separately.  Previously  to  1861,  the  total  earnings  divided  by  the 
population  of  the  State  was  multiplied  by  the  assumed  per  cent  of  mileage  within  the 
State  limits  for  the  earnings  per  head.  The  compilation  for  the  years  preceding  1871  was 
abstracted  from  an  old  volume  of  the  Railway  Times. 

See  also  Tables  21  to  26,  83,  and  various  others  for  indications  as  to  growth  of  traffic. 


'^^ 


80 


CHAP.   IV,-^PROBABLE  VOLUME   OF  TRAFFIC, 


CHAP.   IV.— PROBABLE  VOLUME  OF  TRAFFIC, 


81 


always  justifiable,  it  is  for  practical  reasons  so  exceedingly  dan- 
gerous as  to  amount  to  absolute  folly  for  an  average  American, 
corporation,  even  of  the  more  prosperous  kind,  to  look  ahead  for 
more  than  from  three  to— at  most— ten  years  for  the  "  rapidljr 
increasing  traffic"  which  is  to  justify  an  increase  of  present 
expenditure  over  what  the  prospects  of  the  present  and  the  im- 
mediate future  will  justify. 

79.  Let  us  see  why  this  is  so.  The  theory  of  the  subject  is 
simple:  In  Table  18  is  given  the  present  value  or  present  justi- 
fiable expenditure  to  save  $1  (or  one  unit  of  any  other  value)- 
'at  the  end  of  any  given  period  at  any  given  rate  of  interest;  that 
is  to  say,  the  sum  which,  if  placed  at  compound  interest  now, 
will  produce  $1  at  the  end  of  the  specified  period.  This  fact 
given,  it  logically  follows,  that  if  the  value  of  a  given  betterment 
for  a'given  immediate  traffic  be  $1,  the  present  value  of  the 
same  betterment  for  an  equal  traffic  which  is  to  exist  only  in  the 
future  will  be  that  sum  which  at  compound  interest  will  produce 
$1  when  the  assumed  traffic  comes  to  exist.  If,  for  example, 
we  expect  the  traffic  to  double  in  ten  years,  we  may  spend  for  a 
betterment  worth  $1  to  the  present  traffic,  $1  +  the  sum  which 
will  produce  $1  at  the  end  of  ten  years,  which  latter  is  at  7  per 
cent  (Table  18)  50.8  cents;  so  that  under  these  conditions  (which 
would  apply  to  most  new  American  lines)  we  should  be  war- 
■  ranted  in  spending  50.8  per  cent  more  money  to  effect  givea 
betterments  than  we  would  for  the  traffic  "in  sight." 

Table  17. 
Value  of  $i  placed  at  Compound  Interest  for  a  Term  of  Years. 


With  Interest  at— 

Years. 

3        i       3H 
per  cent,    per  cent. 

3H 
percent. 

4 
per  cent. 

5 

per  cent. 

6 

per  cent. 

8 

per  cent. 

10 
per  cent. 

X 

9 
3 

4 

1 
\ 

0 

X.06 
1.09 

X.X3 
1.16 
X.19 

x.as 

X.27 
1  30 

1.06 
1.10 

X.14 

1. 18 

X.32 

X.96 
J -30 

1-34 

I  03 
1.07 

I.IZ 

X.IS 
X.19 
X.23 

x.a7 
1.32 
1.36 

X.04 
X.08 
Z.12 

X.17 

1.23 
1.27 

1.39 

1-37 
1.42 

x.05 

I.IO 

X.16 

x.aa 
1.28 
1-34 

X.41 
1.48 
1-55 

x.06 
1. 12 
1.19 

i.a6 

1-34 
1.42 

x.50 

1-59 
1.69 

x.08 

1. 17 
x.26 

x.36 
x-47 
x.59 

1.71 
1.85 
2.00 

X.IO 
1.21 

».33 

X.46 
x.6x 

»-77 

1.9s 
2. 14 
2.36 

10        1        1.34     i        1-38 

i.4t 

1.48 

1.63 

I  79 

2.16 

a. 59 

Table  17. — Continued. 
Value  of  $i  placed  at  Compound  Interest  for  a  Term  of  Years. 


With  Interest  at — 

Years. 

3 

percent. 

3^ 
per  cent. 

per  cent. 

4 
percent. 

5 

per  cent. 

6 

per  cent. 

8 

per  cent. 

10 

per  cent 

10 

1-34 

1.38 

1. 41 

1.48 

1.63 

1.79 

2.16 

2  59 

II 

12 

«3 

X4 

X5 
16 

17 
18 

19 

1   38 
1-43 
1-47 

»-5» 
1.56 
1.60 

X.65 
1.70 

»-75 

1-43 
1.48 

»-53 

1.58 
1.6^ 
1.68 

1-74 
1.80 
f.86 

1.46 
1. 51 
1.56 

1.62 
1.68 
1.73 

1.79 
1.86 
1.92 

1-54 

1.60 

1.67 

1-73 
1.80 

1.87 

X.95 
2.03 
2.11 

1. 71 
1.80 
1.89 

1.98 
2.08 
3.18 

2.29 
2.41 

2-53 

1.89 
2.01 

2-'3 

2.26 
2.40 
2-54 
2.69 
2.85 
3  03 

2-33 
2.52 
2.72 

2.94 
3-17 

3-43 

3-70 
4.00 

4-31 

2.85 
3-«4 
3-45 

3-7^ 
4-»7 
4.60. 

5-05 
5-55 
6. 11 

20 

1. 81 

»-93 

1. 99 

2. 19 

2.65 

3-21 

4.66 

6.72 

21 
22 

83 

94 
25 

36 

37 
28 
2q 

1.86 
1.93 
1.97 

3.03 
3.09 
3.16 

3.32 
2.39 

2.36 

1.99 
3.06 
2.13 

3. 30 
2.37 
2-35 

2-43 
2.51 

2.59 

3.68 

2.06 
3.13 

3.21 

2.28 
2.36 

2.45 

2-53 
2.62 

2.71 

2.28 

2.37 
2.46 

2.56 
3.67 
2.77 

2.88 
3.00 
3" 

324 

2.79 

2-93 
3.07 

323 
3-39 
3-56 

3-73 
392 
4.12 

3.40 
3.60 
3.82 

4-05 
4.29 

4-55 

4.82 

5-" 
5-42 

503 

5-44 
5.87 

6.34 
6.85 

7-39 

7-99 
8.62 

931 

7-39 
8-13 
8.04 

9.83 
10. 8i 
11.90 

13.08 

14-39 
15  83 

30 

2-43 

2.81 

4  32 

5-74 

10.06 

17.41 

3« 
3a 
33 

34 

II 

37 
38 
39 

a.  50 
3.58 
3.65 

3.73 

2. 81 
2.90 

3.99 
3-07 
3X7 

3.77 
3.86 
3.96 

3.06 
3.16 
3.27 

3-37 
348 
3.60 

2.91 

301 

3" 

3-22 

3-33 
3-45 

3-57 
3  70 
3.83 

3-37 

365 

3-79 
3  95 
4.10 

4.27 

4-44 
4.62 

4-54 
476 
5.00 

525 

5-52 
5-79 

6.08 

6-39 
6.70 

6.09 

6.45 
6.84 

7.25 
7.68 
8.15 

8.63 

9-15 
9.70 

10.86 
11.74 
12.67 

13-69 
14.78 
15.96 

17.24 
18.62 
20.11 

21.72 

19-15 
21.06 
23.17 

25-45 
28  03. 
30.83 

33-91 
37  •  ^0 
41.02 

40 

3.26 

372 

3  96 

4.80 

7.04 

TO. 28 

45-12 

4» 

44 
46 
48 

3.67 
3.90 

4»3 

3-97 
4-23 

4.83 

424 

4-54 
487 

5-2' 

5-'9 
5-62 
6.07 
6.57 

7.76 
8.56 

9-43 
10.40 

11.56 
12.98 

14  59 
16.39 

25-33 
29-54 
34-46 
40.19 

54-59 
66.04 

79.90 
96.67 

60 

4.38 

5  »5 

5.58 

7. II 

11.47 

18.42 

20  70 
23.25 
26.13 
29.36 

46  88 

117.0 

5a 
54 

^\ 
58 

4.65 
4-93 
523 

5-55 

5-So 
587 
6.27 
6.70 

5  98 
6.41 
6.87 
7-35 

7.69 

8.31 
8.99 

9-73 

12.64 
1394 
15-37 
16.94 

54.68 
63.78 

74-39 
86  77 

i4»S 

171.2 
207.1 
250-5 

60 

589 

7   IS 

7.88 

10.52 

18.68 

32 -99 

101 .2 

30?-! 

6a 

«4 
66 

68 

6.25 
6.63 
7  03 

7.46 

7.64 
8  15 
8.71 
930 

8.44 

9.04 

9.68 

10.37 

11.38 
12.31 

13-31 
14.40 

«5-57 

20.59 
22.70 

25-03 

27  60 

37.06 
41.65 
46.79 
52.58 

118.0 

137-7 
160.6 

187-3 

366.7 
443-6 

536- r 

649-4 

TO 

7.Q2 

9-93 

11.11 

.30.43 
3883 
40-56 
63.25 
80.73 

5Q-o8 

218.5 

785  6 

2 
85 

QO 

9.18 
10.64 
12-34 
M-30 

It. 69 

1378 
16.23 

»9  »3 

13.20 
15.68 
18.62 

22.11 

18.95 
23-05 
28.04 

3412 

79.06 
105.80 
141.58 
189-47 

321.0 

471.6 

693.0 

1018.1 

1265. 

2036. 
3278. 
5277- 

100 

19  22 

26  55 

31.19 

50.50 

131  50 

339-30 

2197-9 

13677- 

Formula:  5"  =  (i  +  r)«,  in  which  r 
amount  of  $1  at  compound  interest. 


z=  rate  of  interest,  n  =  number  of  years,  and  S  = 


82 


CHAP.  IV. -PROBABLE  VOLUME  OF  TRAFFIC, 


Table  18. 
Present   Justifiable   Expenditure  to  se- 
cure A   RETURN    OF    |l  AT    THE   EnD  OF 

ANY  Number  of  Years. 


With  Interest  at — 


Table  19. 
Saving  per    Annum   which 
WILL  IN  THE  Aggregate 

AMOUNT     TO     |I     at     THE 

End  of  a  Term  of  Years. 


With  Interest  at— 


5    I    e 

per       per 
cent.    cent. 


CHAP,   IV.— PROBABLE  VOLUME  OF  TRAFFIC, 


83 


Table  18. — Continued. 

Present   Justifiable   Expenditure   to   se- 
cure A  Return   of   $i   at  the  End  of 
ANY  Number  of  Years. 

Table  19. — Continued. 

Saving   per  Annum   which 
WILL  IN  THE  Aggregate 

amount     to     $I     AT     THE 

End  of  a  Term  of  Years. 

With  Interest  at — 

Years. 

With   Interest  at — 

Years. 

3 

per 
cent. 

4 

per 

cent. 

5 

per 
cent. 

6 

per 
cent. 

7 
per 
cent. 

8 

per 
cent. 

10 

per 

cent. 

.009 

3 

per 
cent. 

4 

per 

cent. 

5 

per 
cent. 

6 

per 
cent. 

60 

.228 

141 

087 

.054 

•034 

.021 

50 

.009 

.006 

.005 

.004 
.004 
.cx)3 
.003 

.003 

52 

58 

•215 
.203 

130 
120 
lit 
103 

079 
072 
065 
059 

.048 

.043 
.038 
.034 

.030 
.026 
.023 
.020 

.018 
.016 
.013 
.012 

.007 
.006 
.005 
.004 

52 
54 
56 
58 

.008 
.008 
.007 
.006 

.006 
.005 
.005 
.004 

.003 
.003 
.002 
.002 

60        !   .170 

095 

053 

.030 

.027 
.024 
.021 
.019 

017 

.010 

.003 

60 

.006 

.004 

.003 

.002 

63 

64 

66 
68 

.160 

•'5» 
.142 

•134 

088 
o8r 
075 
069 

049 
044 
040 
036 

.015 

•o»3 
.011 

.010 

.008 
.007 
.006 
•  005 

.c»3 
.002 
.00a 
.002 

62 

64 
66 
68 

.006 
.005 
.005 
.005 

.004 
•  003 
.003 
.003 

.002 
.002 
.002 

.CX32 

.002 
.001 
.001 
.001 

70 

.  126 

064 

033 

,  .017      .009 

.004 

.001 

70 

.004 

.003 

.002 

.C»I 

75 
80 

85 
90 

.109 
.094 
.081 
.070 

053 
043 
036 
029 

026 
020 
016 
012 

.013 
.009 
.007 
.005 

.006 
.004 
.003 
.002 

.003 
.002 
.001 
.001 

.oot 
.000 
.cwo 
.000 

75 
80 

85 
90 

.004 
.003 
.003 
.002 

.002 
.002 
.001 
.001 

.001 
.001 
.CXJI 
.001 

.001 
.001 
.000 
.000 

100 

.052 

020 

008 

.003 

.001 

.000 

.000 

100 

.002 

.001 

.000 

.000 

Table  20. 

Showing  the  Justifiable   Present  Expenditure  to  save  $i  per  Annum 
FOR  various  Terms  of  Years  at  various  Rates  per  Cent  for  Capital. 


Term 

Justifiable  Present  Expenditure  with  Interest  at — 

OF 

Ybaks. 

3 

per  cent. 

4 
per  cent. 

5 

per  cent. 

6 

per  cent. 

7 

per  cent. 

8 

per  cent. 

9 

per  cent. 

10 
per  cent. 

I 
2 
3 

$o-97 
1.91 

2.83 

$0.96 
1.89 
2.78 

$0.95 
1.86 
3.72 

$0.94 
1.83 
2.67 

$0.93 
1. 81 
2.62 

$0.93 
2.58 

$0  93 
1.76 
2.53 

$0.91 
1-74 
2.49 

4 

1 

3.72 
4.58 

542 

363 
4-45  • 
524 

3-55 

3-47 
4.21 
4.92 

3-39 
4.10 

4-77 

3-31 
3-99 
4.62 

3  24 
389 
4-49 

3-17 
3-79 
4.36 

\ 

9 

6.33 
7.03 

7-79 

6.00 
6.73 
7-44 

.S.79 
6.46 
7. II 

6.21 
6.80 

5-39 
5-97 
6  52 

5-21 

5-75 
6.25 

5-03 
5-53 
6.00 

4.87 
5. 34 
5.76 

10 

8.53 

8. II 

7.72 

7  36 

7.02 

6.71 

6.42 

6.14 

II 

13 

»3 

925 

9-95 

10.64 

8.76 

9-39 
9.99 

8.31 
8.86 

9-39 

7.89 
8.38 
8  85 

7-50 
7-94 
8.36 

7-14 
7-54 
7.90 

6.81 
7.16 

7-49 

6.50 
6.81 
7.10 

16 

XI. 30 

"•94 
13.56 

10.56 

II. 13 

11.65 

9.90 
10. 38 
10.84 

930 

9.71 

10. II 

8.75 
9. II 

9-45 

8.24 
8.56 
8.8s 

7-79 
8.06 

8.31 

7-37 
7.61 
7.8J 

»7 
18 

«9 

13.17 

»3-75 
«4-32 

13.17 

13.66 
1313 

11.27 
11.69 
12.09 

10.48 
10.83 
11.16 

9.76 
10.06 
10.34 

9.12 

9-37 
9.60 

8.54 
8.76 

8.95 

8.0a 
8. 30 
8.37 

20 

14.88 

^3-59 

12.46 

11.47 

10.59 

9  82 

9.13 

8.51 

84  CHAP.   IV.-^PROBABLE  VOLUME   OF   TRAFFIC. 


Term 

OF 

Years. 


20 


31 

aa 
"3 

26 

27 
38 
29 


30 


31 
32 
33 

34 
35 
36 

38 

39 


40 


41 
42 
43 

44 
45 
46 

47 
48 
49 


60 


55 
60 

65 

_7^ 

76 


3 

per  cent. 


80 

85 
90 

95_ 

100 


Perpetuity 


14  88 


15  42 

15-94 
16.44 

16.94 
17.41 
17.88 

18.33 
18.76 

19.19 


19.60 


20.00 
ao.39 
20  77 

21.13 

21.49 
21.83 

22.17 

22.49 
22.08 


23.12 


23.41 
23.70 

23.98 

24 -25 
24-52 
24.78 

25-03 
25.27 

25-50 


25-73 


26.77 
27.68 

28.45 
29.12 


29.70 


30.20 

30-63 
31-00 
31^32 


33-33 


Table  iq,— Continued. 


Justifiable  Present  Expenditure  with  Interest  at— 


4 

per  cent. 


31-60 


13-59 


1403 

14-45 
14.86 

15-25 
15.62 

15  98 

16.33 
i6.66 
16.98 


17.29 


17  59 
17.87 
18.15 

18.41 
18.67 
18.91 

19.14 
19-37 
19-58 


19.79 


19.99 
20.19 
20.37 

20.55 
20.72 
20.89 

21.04 
21.20 
21.34 


21.48 


92.11 

22  .62 
23-05 
23.40 


23.68 


5 

per  cent. 


23.92 
24.11 
24.27 
24.40 


24.51 
25.00 


13.46 


12.82 
13.16 
13-49 

13.80 
14.09 
14-38 

14.64 
14.90 
15-M 


'5-37 


15-59 
1580 
16.00 

16.19 

i6-37 
16.55 

16.71 
16.87 
17.02 


17.16 


17.29 
17.42 

17-55 

17.66 

17-77 
17.88 

17.98 
18  08 
18.17 


18.26 


18.63 
18.93 
19.16 

19-34 


19  49 


6 

per  cent. 


19.60 
19.68 

19-75 
19.81 


^9-85 


20.00 


11.47 


II  76 
12.04 
12.30 

12.5s 

12.78 
13.00 

13.21 
13.41 
13-59 


1377 


13-93 
14.08 
14.23 

14-37 
14  50 
14  62 

14-74 
1485 
14-95 


1505 


1514 
15-23 
I5.3« 

15-38 
1546 
15-52 

15-59 
15-65 
15-71 


15-76 


15-99 
16.16 
16.29 
16.39 


16  46 


16.51 

16.55 
16.58 
16.60 


16.62 


7 
per  cent. 


8 

per  cent. 


16.67 


10.59 


10.84 
11.06 
11.27 

11.47 
11.65 
11.83 

11.99 
12. 14 
12.28 


12.41 


12-53 
12.65 

12-75 

12.85 
12.95 
13-04 

13.12 
13.19 
13.26 


»3-33 


13-39 
13-45 
13-51 

1356 
13-61 

1365 
13.69 
13-73 
13-77 


13.80 


13-94 
14.04 
14.10 
14.16 


14.20 


14.22 
14-24 
14-25 
14.26 


14.27 


14.29 


9.82 


10.02 
10.20 
10.37 

10.53 
10.67 

10.81 

10  94 
11.05 
11.16 


9 

per  cent. 


11.26 


11-35 
II  43 

11.51 

"•59 
11.65 
11.72 

11.78 
11.83 
11.18 


11.93 


11.97 
12.01 
13.04 

12.08 
12.11 
12.14 

12  16 
12.19 
12.21 


12.23 


12.32 
12.38 
12.42 
12.44 


13.46 


12.47 
12.48 
12.49 
12.49 


12.49 


12.50 


9-13 


ID 

per  cent. 


8.51 


9-29 
9-44 
9.58 

9.71 
9.82 

9-93 

10.03 
10.12 
10.20 


10.27 


8.65 

8.77 
8.88 

8.99 
9.08 
9.16 

9-24 
9-31 
9-37 


943 


10.34 
10.41 
10.46 

10.52 

10.57 
10.61 

10.65 
10.69 
10.7? 


48 
53 
57 

.61 

,64 
.68 


10.76 


10.79 
10. 8r 
10.84 

10.86 
10.88 
10.90 

10.92 
10  93 
10.95 


9.71 

9-73 
9.76 


io.96_ 

11.01 
11.05 
11.07 
IJ.08 


09 

10 

10 

11 

.11 

.11 

9-78 

9.80 
9.83 

9.83 

9.85 
9.86 
9.88 

9.89 
9.90 

9. 91 


9-92 


II. IX 


9-95 
9-97 
9.98 

_9:99. 
9-99 


10.00 
10.00 
10.00 
10.00 


10.00 


xo.oo 


This  table  gives  simply  the  capital  sum  which  will— 

(I)  Return  $i  per  annum  in  interest  during  the  given  term  ;  and, 

(2    Return  an  additional  sum  in  interest  each  year  which,  placed  at  compound  interest 

at  the  same  rate,  will  extinguish  the  principal  at  the  end  of  the  given  term. 

At  10  per  cent  for  capital  it  is  worth  spending  but  twice  as  much  to  ensure  a  saving  of 

$,  p^r  anrum  for  ever  as  to  ensure  it  for  7  years  only.    At  the  much  higher  rates  whid. 

people  often  wish  to  be  assured  of  before  spending  money  in  new  enterprises  it  is  worth 

practically  nothing  to  save  money  more  than  6  or  8  years  ahead. 


CHAP.    IV.— PROBABLE  VOLUME   OF   TRAFFIC. 


85 


80.  All  this   is  undeniably  correct  in   theory,  except,  indeed, 

that   it   understates   the  case  ;  for  we  might  enter  into  further 

mathematical  subtleties,  and  prove  that  if  the  ratio  of  growth  of 

traffic  is  greater  than  the  rate  of  interest  on  capital,  the  present 

justifiable  expenditure  to  provide  for  such  increase  of  traffic  is 

infinite.     But  this,  while  an  excellent  exercise  for  the  student,  we 

shall  not  attempt  to  do  ;  confining  ourselves  instead  to  the  more 

profitable    work    of    pointing   out    the    reasons    why,    with    any 

•ordinary  corporation,  all  such  speculations  are  wholly  delusive, 

•so  that  even  the  indications  of  Table  18  are  of  value  only  as  fixing 

a  maximum  which  should  never  be  exceeded. 

81.  The  first  and  most  vital  reason  is  that,  while  it  may  be 
taken  as  a  practical  certainty  that  the  traffic  of  any  ordinary 
Tailvvay  not  only  will  grow,  but  that  it  will  grow  at  an  average 
rate  of  something  like  5  to  8  per  cent  per  annum  east  of  the 
Alleghenies,  and  7  to  10  or  15  or  even  20  per  cent  per  year  west 
of  there,  yet  that  the  rate  of  this  growth  of  traffic  is  excessively 
variable  and  uncertain— liable  to  cease  altogether  at  any  time  for 
many  years,  and  at  periods  when  it  is  particularly  inconvenient 
to  put  interest  on  discounted  expectancies. 

For  this  cause  alone  it  is  in  general  inexpedient  to  look 
forward  more  than  at  most  five  years  for  traffic  to  justify  an 
increase  of  immediate  expenditure;  and  when,  as  is  of  course 
more  likely  to  be  the  case,  a  new  project  is  floating  upon  the  top 
of  a  "  boom"  or  upward  wave  in  the  tide  of  business,  it  is  unsafe 
to  look  ahead  more  than  two  or  three  years.  It  is  at  such  times 
especially  to  be  remembered  that  the  wave  may  begin  to  flow 
backward  at  any  time,  and  that  even  if  it  do  not,  the  line  is  built 
with  borrowed  capital,  and  that  it  is  difficult  for  the  average 
financier  to  borrow  large  sums  on  future  expectancies;  nor  can 
he  in  any  case  borrow  $2000  per  mile  as  cheaply  as  $1000  per 
mile.  Borrowed,  however,  the  money  must  be  if  the  first  supply 
gives  out,  or  the  whole  investment  of  the  original  company  will 
probably  be  lost ;  and  the  instances  are  rare  in  which  any  large 
proportion  of  the  entire  capital  has  been  positively  secured 
before  the  surveys  are  substantially  complete  and  construction 
in  progress. 


86 


CHAP,  IV.— PROBABLE  VOLUME   OF   TRAFFIC. 


CHAP.   IV.— PROBABLE  VOLUME  OF  TRAFFIC. 


87 


82.  A  sequence  of  events  which  has  been  again  and  again 
repeated  is  that  the  company  shall  enter  upon  the  work  with 
vague  visions  of  boundless  prosperity,  and  look  with  certainty 
to  securing  "  all  the  money  they  need;"  shall  encourage  their 
engineer  in  a  costly  style  of  construction  which,  with  the  natural 
preference  of  an  engineer  for  massive,  durable,  and  stately  works, 
he  is  all  too  ready  to  adopt ;  and  finally,  often  within  a  ridicu- 
lously short  time  of  the  period  of  their  brightest  hopes,  be  left 
stranded  by  the  ebb-tide  of  speculation,  a  complete  and  helpless 
financial  wreck. 

83.  Finally,  there  is  another  and  still  stronger  reason  why  the 
growth  of  traffic  should  not  be  counted  on  for  many  years  ahead 
in  designing  the  works.  It  is  usually  a  simple  matter  to  so 
design  large  parts  of  the  line,  including  most  of  the  more  expen- 
sive works,  that  their  construction  may  be  postponed  until  a 
more  convenient  season— a  possibility  so  important  that  it  is 
separately  discussed  hereafter  (Chap.  XXIII.).  By  so  doing  we 
at  least  make  sure  of  keeping  the  capital  account  at  a  minimum 
and  of  (usually)  retaining  the  line  in  the  hands  of  the  original 
company;  while,  when  all  causes  are  considered,  the  loss  from 
postponing  the  execution  of  all  more  costly  work  which  can  be 
postponed  will  not  be  very  great,  even  if  one's  brightest  dreams 
are  realized — which  will  rarely  be  the  case. 

84.  We   may  conclude,   therefore,   that   although   a    railway 
corporation   which   has  in  truth  as  well  as  in   imagination  un- 
limited means  ;  which  is  able  to  look  ahead  with  certainty  for  a 
long  period  of  years  ;  which  is  able  without  doubt  to  tide  over 
long  periods  of  depression  without  danger  to  its  stability,  and 
which  has  no  anxiety  to  realize  present  profit,  or  even  avoid 
present  losses,  on  investments  which  will   be  ultimately  profit- 
able ;— although  such  a  corporation  may  legitimately   make  a 
large  increase  in  its  investments  for  the  sake  of  a  traffic  which  is 
still  in  the  distant  future,  yet  that  no  ordinary  corporation  can 
afford  to  look  ahead  more  than  two  to  five  years  for  the  traffic 
to  pay  interests  on  increased  investments,  and  that  even  in  that 
case  they  take  much  risk  in  doing  so.     Traffic  should  therefore. 


in  ail  cases,  be  rather  under-  than  over-estimated,  to  the  end  that 
in  no  case  extravagant  expenditures  shall  be  made  for  a  costly 
perfection  of  alignment  which  the  traffic  will  not  justify  :  bearing 
in  mind  that  an  under-estimate  of  admissible  expenditure  is 
simply  a  failure  to  invest  a  small  (or  it  may  be,  large)  additional 
sum  of  money  which  would  have  earned  good  interest,  but  which 
may  be  invested  later  at  nearly  if  not  quite  as  good  advantage  ; 
whereas  an  over-liberal  investment  of  additional  sums  on  which 
interest  cannot  be  earned  greatly  endangers,  in  the  trying  years 
which  usually  come  soon  after  the  line  is  opened,  the  permanency 
of  the  whole  investment. 

In  the  one  case,  our  economy  only  tndangers  a  minor  loss,  if 
the  enterprise  as  a  whole  turns  out  well  ;  and  if  it  does  not,  may 
save  it  from  ruin.  In  the  other  case,  our  extravagance  only 
gives  us  a  fair  investment  for  a  little  more  money  if  all  goes 
well,  and  if  it  does  not,  may  be  the  ounce  of  additional  load 
which  breaks  the  back  of  the  enterprise.  Our  only  grave  dan- 
ger, therefore,  is  of  error  in  one  direction  only  ;  which  makes  it 
the  easier  to  make  an  estimate  of  traffic  sufficiently  exact  for  all 
important  purposes — that  is  to  say,  one  which  will  be  certainly 
not  too  large. 

85.  Tables  21  to  27  give  various  statistics  of  the  growth  of 
American  railway  traffic,  such  as  are  likely  to  be  useful  for 
checking  in  a  rude  way  the  estimated  growth  of  traffic  on  any 
line.  The  most  accurate  and  satisfactory  method  for  estimating 
both  traffic  and  expenses  in  any  given  case,  however,  is  com- 
parison with  the  experience  of  neighboring  roads  of  the  same 
general  character,  because  it  is  much  easier  to  count  on  a  line 
doing  so  much  better  or  worse  than  another  line,  than  to  esti- 
mate the  absolute  traffic  independently. 

Tables  23  to  27  inclusive,  for  the  groups  of  States,  cover  a  period  extending 
from  one  period  of  business  activity  to  another,  with  a  severe  depression  be- 
tween. Table  28,  for  the  whole  United  States,  covers  two  preceding  and  four 
following  years  likewise,  and  by  comparison  with  this  table  the  general  course 
of  traffic  and  earnings  for  the  same  additional  years  can  be  determined  with 
approximate  accuracy. 

All  these  tables  were  computed  from  the  statistics  of  Poor's  Manual. 


88 


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C/M/'.   IV.— PROBABLE  VOLUME  OF   TRAFFIC. 


CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC. 


The  groups  of  States  are  those  of  Poor's  Manual,  which  see  for  the  years  1882  and 
1886  for  details.  The  population  used  for  the  first  part  of  the  Table  (1881)  was  that  of 
the  Census  of  1880,  which  was  about  three  per  cent  too  small.  .  ^      ..  r 

By  a  different  estimate,  the  number  of  inhabitants,  of  acres  m  gram  and  cotton,  of 
bushels  of  grain  and  bales  of  cotton  produced,  per  mile  of  railway,  have  been  as  follows 
for  the  last  seven  years,  in  all  cases  taking  the  mileage  and  population  at  the  close  of  the 
year  and  the  crops,  etc.,  of  the  previous  summer  : 


Popu- 
lation. 

Acres. 

Bushels  of 
Grain. 

Bales  of 
Cotton. 

1879 

1880    

581 
545 
509 
473 
466 

458 
461 

1,565 
1,466 

1.359 
1,236 

1,204 

1,216 

1,216 

31,600 
28,932 
19,804 
23.405 
21,563 
23,690 

23,241 

67-73 
70-53 
52.65 
60.18 

47.00 
45-44 

1881  

1882    

1883....   

1884    

1885  

50.41 

Table  22. 
Statistics  of  Revenue  Per  Head  of  Population  and  Per  Mile 

FOR  Each  State  Separately— 1881. 
[These  statistics  are  based  upon  the  same  figures  as  those  given  for  groups  of  States  onlr 
in  the  first  part  of  Table  21.     The  division  of  the  miles  of  road  operated  between  the  dif^ 
ferent  States  is  not  exact,  so  that  the  figures  can  be  regarded  as  approximations  only.] 


Per  Mile  Railway. 


Maine 

New  Hampshire. 

Vermont 

Massachusetts. . . 
Rhode  Island... 
Connecticut 


Square 
Miles. 


32.0 
10.3 
12.2 

3-47 
8.55 
5- II 


New  England. 


New  York 

New  Jersey 

Pennsylvania 

Delaware 

Maryland  and  D.  C. . . . 
W.  Virginia 


Popula- 
tion. 


II. O 


Middle  States. 


7.67 
5.00 
6.81 

9-75 
9.60 
100.5 


8.60 


593 
387 
397 
793 
1,810 
670 

650 


Per  Cent. 
Sidings. 


19.0 
17.6 

15.4 
63.0 

46.5 
35.0 


Per  Cent. 

Operating 

Expenses. 


848 
679 

633 
677 

485 
271 


775 


37-4 


75-3 
79.6 

64.6 


69.0 
64.0 
80 

71 
61 

64 


70.0 


Gross  Revenue. 


Per  Mile 
Railway. 


Per  Head 
Populat'n. 


$4- 130 
5.200 
4.690 

10.200 
9.200 
9.650 


$6.54 
10.90 

12.40 

16.50 

5-90 
16.00 


52.2 
193 


67-3 


61.0 

63.9 
61.5 

70 
60.7 

83-4 


8.420 


62.9 


13.000 
6.850 

15.800 
2.880 

5-490 
3.670 


14.000 


13-10 


15.90 
28.10 

23.70 

4.08 

12.30 

13-60 


18.50 


91 


Table  22. — Continued. 


Per  Mile  Railway. 

Per  Cent. 
Sidings. 

Per  Cent. 
Operating 
Expenses. 

Gross  Revenue. 

Square 

Miles. 

Popula- 
tion. 

Per  Mile 
Railway. 

Per  Head 
Populat'n, 

Virginia 

15.3 
31-4 
25.2 
22.1 
70.7 
22.0 
100.3 
26.0 
24.0 

13-4 

602 
228 

738 
586 

344 

551 

2,470 

594 
811 

569 

13.0 
6.4 

7-1 
7.7 
5-0 
8.6 

5-4 
II. I 
22.0 

13. 1 

65.6 
66.5 
68.0 
60.7 
62.8 
69.9 

65.9 
71.0 

67.7 

55-8 

5-590 
2-590 
3-250 
3.740 
3.210 
4.150 
3-320 
8.080 
4.500 
5-590 

7.00 
2.70 
4.04 
6.14 
1. 61 

N.  Carolina 

S.  Carolina 

Georgia '. 

Florida 

Alabama 

6-43 
1.03 
10.40 
4.36 
5.90 

Mississippi 

Louisiana 

Tennessee 

Kentucky 

Southern  States 

25.7 

681 

10.9 

65.0 

4-550 

5.20 

Ohio 

5.08 

13.9 
5.65 
5.20 
10.2 
21.0 

14.3 
24.2 

202 
400 

331 

288 

249 
199 

478 
718 

29.6 
29.6 
27.0 
27.0 
10.6 

7.0 
II. 4 

9.9 

62.8 
68.2 

76.5 
54-7 
59-7 
61.4 

54-0 
64.0 

8.790 
5-850 
5-750 
7.560 

3 -930 
4 -370 
7.000 

3-570 

20.50 
12.40 
17.30 

29-05 
14.70 
15.90 
13.60 

3.92 

Michigan 

Indiana 

Illinois 

Wisconsin 

Minnesota. 

Missouri 

Iowa 

N.  W.  Central  States. 

9.90 

351 

21.3 

60.9 

6.520 

17.60 

Nebraska 

226 

303 
254 

283 

95 
1,200 

309 

17.0 

53-7 

1. 160 

Wvomincr 

Dakota 

Kansas 

7-5 
5.9 
5-9 
3-9 

62.8 
61. 1 

58.5 
68.0 

5-170 
6.530 
3.960 
4.480 

Colorado 

46.90 

Arkansas 

Texas 

FarW.  andS.  W.... 

61.9 

310 

7-1 

60.2 

6.420 

16.10 

New  Mexico 

230 
104 
148 
140 
301 
230 

Arizona 

Utah 

13-7 

49-3 
53.8 
49-5 
56-4 

Nevada 

California 

8.620 

Oregon 

Pacific  States 

181. 0 

261 

9.6 

49.9 

(7.500) 

23.15 

United  States 

29.0 

481 

25.1 

61.9 

7.690 

14.50 

'■( 


92 


CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC. 


CHAP.   IV.— PROBABLE  VOLUME   OF   TRAFFIC. 


93 


Table  23. 

Main  Results  op  Operation  of  the   Railways  of  the   New  England 

States,  i 873-1881. 


Yka«. 

Popula- 
tion. 
1  = 

1,000,000. 

Miles 

Railway 

Operated. 

Revenue. 

X  —  $1,000,000. 

Divi- 
dends. 

Revenue  per  head. 

Rev. 

per 
Mile. 

Pass. 

Fght. 

Total 

Net. 

Pass. 

Fpht. 

Total 

1=  1,000 

3873 

74 

3-644 
3.696 

5.303 

5.617 

22.36 
22.11 

29 -3J 
27-95 

51-68 
50.06 

15-06 
16.71 

9.00 
8.51 

6-15 
6.00 

8.03 
7-55 

14.18 

1355 

9-73 
8.91 

1875 

3748 

5.732 

21.78 

26.55 
25.24 

24-52 
23.29 
23.81 

48.33 

15-32 

8-79 

5.80 

7.10 

12.90 

8. 41 

X876 

77 

78 

79 

3.801 
3-853 
3905 

3-958 

5.783 
6,036 

5.760 
6,156 

20.52 
20.07 

»7-97 
17.52 

45-76 

44-59 
41.26 

41-33 

»5-38 
»3  74 
13-69 

15-59 

7.61 

6.98 

7-57 
7.24 

5-44 
5-21 
4.60 

4-45 

6.67 
6.36 
6.00 
6.02 

T2.II 
11.57 
10.60 
10.47 

7.90 

7.38 
7.18 

671 

1880 

4.010 

6,071 

19.32 

29  44 

48.76 

17.19 

8.00     1  4.82 

7-37 

12.19 

8.00 

1881 

4.063 

6,261 

20.17 

32-71 

52.88 

15-92 

11.14 

4.98 

8.0s 

13-03 

8.43 

Tabi"?:  25. 

Main  Results  of  Operation  of  the  Railways  of  the  Southern  States,, 
(South  of  Potomac  and  Ohio),  1873-1881. 


Yhar. 

Popula- 
tion. 

1,000,000. 

Miles 

Railway 

Operated. 

Revenue. 

1  ~  $1,000,000. 

Divi- 
dends. 

Revenue  per  head. 

Rev. 

per 
Mile. 

Pass. 

Fght. 

Total 

Net. 

Pass. 

Fght. 

Total 

1—  1,000 

1873 

74 

11.022 
II. 196 

13,908 
»3.505 

15-30 
14.13 

38-39 
38  13 

53-70 
52.26 

18.13 
17.27 

0.90 
1.07 

1-38 
1.26 

3-49 
3-41 

4-87 
4.67 

4-44 

3-86 
3-86 

J875   

H.370 

13.522 

13-86 

36-53 

r.40 

50.74 
39.81 
42.80 
43  92 

16.74 

1.50 

1.22 

3-22 

3-73 

1876 

77 

78 

79 

"•544 
11.718 
11. 892 
12  066 

13.948 
11,272 
12,498 
13.389 

11.88 

9-95 
11.22 
11.32 

38.87 
29.86 

31-58 
32.60 

17.12 
12.66 

14-38 
14.67 

1.86 

2.74 
2.81 

2-13 

1.03 
0.84 

0-99 
0.94 

3-37 
2.54 
2.66 
2.70 

4.40 
3-38 
365 
3-64 

3-64 

3-53 

3-43 
3.28 

1880 

13.241 

13.548 

10.45 

37.87 

48-32 

18.12 

3-53 

0.86 

3-IO 

3  96 

3.56 

1881 

xa.415 

14,002 

17.11 

46.63 

63.74 

22.24 

3-59 

1.38 

3-76 

5-14 

4.72 

Table  24. 

Main  Results  of  Operation  of  the  Railways  of  the  Middle  States, 
with  Maryland  and  West  Virginia,  1873-1881. 


Year. 

Popula- 
tion. 
1  = 

1,000,000. 

Miles 

Railway 

Operated. 

Revenue. 
1  =  $1,000,000. 

Divi- 
dends. 

Revenue  per  head. 

Rev. 

3\?ile. 

Pass. 

Fght. 

Total 

Net. 

Pass. 

Fght. 

Total 

I  —1,000 

1873 

74 

10.915 
11. 123 

12,441 
12,874 

42.36 
41.70 

151.7 
144.8 

194.1 
186.5 

693 
90.2 

36.5 
37-6 

3.88 
3.26 

13.90 
13.00 

17.78 
16.26 

15.6 
14.5 

1875 

"-331 

i3.»73 

40-77 

«34-9 

175-7 

65  6 

39-4 

3.60 

11.84 

'5  44 

133 

1876 

77 

78 

79 

11.540 

11.749 
11.95S 
12.167 

13.647 
13,607 
14,600 
14.941 

47-48 
39.26 

35-95 
43  20 

130.1 
116.7 

119.5 
127.1 

177.6 
«55-9 
155-5 
170.3 

69-4 
61.0 
61.6 
70.4 

33-7 
24-9 

31.1 

23-9 

3-58 
4.10 

3-34 
3-00 

3-55 
3-63 

12.91 

11.30 

9.90 

10.00 

10.45 

16-49 

15-40 
13  24 
13.00 
14.00 

14-5 

13-3 
II. 4 
10.6 

11.3 

1880..    .. 

12.376 

14,882 

44-97 

I1540 

U;a.s 

199.0 

83-9 

38.5 

12.40 

16.03 

13-3 

1881 

12.585 

16,213 

49-92 

228.4 

84.9 

33-3 

3-97 

14.30 

18.17 

14.1 

Table  26. 

Main  Results  of  Operation  of  the  Railways  of  the  Western  and- 
Southwestern  States  (all  North  of  Ohio  and  West  of  the  Missis- 
sippi AND  East  of  the  Rocky  Mountains),  1873-1881. 


Year. 

Popula- 
tion. 
I  = 

1,000,000. 

Miles 

Railway 

Operated. 

Revenue. 

1  =  $1,000,000. 

Divi- 
dends. 

Revenue  per  head. 

Rev. 

per 
Mile. 

Pass. 

Fght. 

Total 

Net. 

Pass. 

Fght. 

Total 

1=  1.000 

1873 

74 

16.025 
16.589 

32,973 
35.639 

51.62 
56-78 

160. 1 
158.1 

211.7 
214.9 

72.5 

75-5 

75-6 

19.06 
16.61 

3-23 
3-42 

10.00 

9-53 

13.23 
12.9s 

6.43 

6.02 

1875 

17.154 

36,058 

54-99 

151.2 

206.2 

19.23 

3-21 

8.80 

12.01 

5-73 

1876 

77 

78 

79 

17.718 
18.282 
18.847 

19411 

36.753 
39.136 
41,605 

44,104 

43  36 

44-44 
49.00 

54-45 

142-9 
148.8 
160.9 
177.9 

189.2 

193-2 
209.9 

232-4 

63-9 
66.1 
78.0 
99.0 

17.39 
14.56 
19.34 
23.56 

2.45 

2-43 
2.60 

2.80 

8.07 
8.13 
8.53 
9.16 

10.52 
10.56 

11.13 
11. 96 

5-95 
4-95 
5-05 
5-27 

1880 

19.976 

45.911 

1 
64.10  226.5 

290.6 

125.2 

33.12 

3-21 

11.30 

14-51 

6-34 

1881 

20.540 

53.224 

71.40273.0 

344.4 

134-8 

40.85 

3.48 

13.3c 

16.78 

6.49 

94 


CHAP.   IV.— PROBABLE  VOLUME   OF  TRAFFIC. 


CHAP.   IV.— PROBABLE  VOLUME  OF  TRAFFIC. 


95 


,••1) 


Table  27. 

Main  Results  of  Operation  of  the   Railways   of  the  Pacific  States. 

1S73-1881. 


YSAK. 

Popula- 
tion. 
I  = 

1,000,000. 

Miles 

Railway 

Operated. 

Revenue. 
X  r=  $1,000,000. 

Divi- 
dends. 

Revenue  per  head. 

Rev. 

per 
Mile. 

Pass. 

Fght. 

Total 

Net. 

Pass.l 

Fght. 

Total 

14-43 
14.12 

1_  l.OOO 

1873 

74 

1. 124 

1.185 

1,612 

1,639 

(5.9) 
6.27 

(10.3) 

TO.  48 

(16.2) 
16.77 

(9-3) 
985 

(2.6) 
3.26 

5.26 
5-99 

9.17 
8.83 

10.2 
10.2 

1875 

1.346 

1,790 

6.70 

15-74 

16.37 
16.56 

17 -35 
18.08 

19.92 

22.44 

12.23 

5-43 

5-39 

12.60 

17-99 

12.5 

1876 

77 

78 

79 

1-307 
1.368 

X.429 

I.4QO 

1,867 

3,109 
3,617 
3-663 

7.64 
7.89 

8.53 
8.86 

34.01 
24  65 
26.88 
26.44 

11. 75 

11.32 

12.97 

9  97 

4.53 

458 

(6.0) 

1.63 

3-99 

S-85 
5.76 
5-97 
5-93 

12.50 
12.10 
12.07 
12.17 

18.35 
17.86 
18.04 
18.10 

12.9 

7-9 
7.4 
7.24 

1880 

I.55I 

3,813 

8.82 

28.74 

10.79 

5.68 

12.77 
16.40 

18.45 

7.53 

1881 

I.6I2 

5,418 

10. II 

26.43]  36.54 

18.64 

7-79 

6.28 

23.68 

6.75 

Table  28. 

Main  Results  of  Operation  of  the  Railways  of  the  Entire  United 

States,  1871-1885. 


Ybak. 

Popula- 
tion. 

1,000,000. 

Miles 

Railway 

Operated. 

Revenue. 

X  =  $1,000,000. 

Divi- 
dends. 

Revenue  per  head. 

Rev. 

per 
Mile. 

Pass. 

Fght. 

Total 

Net. 

141.7 
165.8 
183.8 
189.6 

Pass. 

Fght. 

Total 

I—  1,000 

1871 

72 

73 

74 

39.585 
40.640 
41.72a 
42.834 

44,614 
57,323 
66,237 
69,273 

108.9 
132.3 

1374 
141.0 

294.4 
340.9 
389.0 

379-5 

403.3 
465 -2 

526.4 
520.5 

56.5 
64.4 
67.1 
67.0 

2.76 
3-24 
330 
3.30 

7-44 
8.40 

9-30 
8.85 

10.20 
11.64 

13   60 

12.15 

9.04 
8.10 
7.93 
7-53 

1875 

43.976 

71,759 

139 -» 

364-0 

503-1 

185-5 

74-3 

3.16 

8-27 

11.43 

7.03 

1876 

77 

78 

79 

45-»47 
46.350 
47.585 
48.853 

73,508 

74,112 
78,960 
82,223 

136.1 
125.2 
124.6 

142.3 
147.7 

361.1 
347-7 
365-5 
386.7 

497-3 
472 -9 
490.1 
529.0 

186.5 
171.1 
187.6 

219.9 

68.0 
58.6 
53.6 
61.7 

3.01 
2.71 
a.6x 
3.93 

8.00 

7.50 
7.62 

7.92 

11.01 
10.31 
10.33 
10.84 

6.77 
6.39 

6.3Z 

6.43 

1880 

50.155 

84,225 

467.7 

615-4 

255.2 

77- » 

2.93 

9.32 

13.35 

7-31 

1881 

8a 

83 

84 

51.491 
52.863 
54.271 
5S.7»7 

94,486 

95.752 
106,938 

"3,173 

173-4 
188. 1 
206.8 
206.8 

200.9 

5520 
485.8 
544-5 
502-9 

725 -3 
728.0 
807.1 
763 -3 

276.7 
264.8 
391.6 
366.5 

93-3 

97.3 

101.6 

93. • 

77-7 

3-37 
3-56 
3.80 

3.71 

10.73 
9.30 

10.03 
9.06 

14.09 
13.80 

14.83 

13-70 

13-38 

7-67 
7.60 

7-54 
6.76 

1885 

57.202 

123,110 

5197 

765-3 

266.5 

3-50 

9.09 

6.33 

86.  Experience  has  shown  that  the  probable  number  of 
TRAINS  PER  DAY  is  at  once  the  most  convenient  and  the  most 
exact  basis  for  arriving  at  estimates  of  probable  future  traffic, 
and  especially  expenses.  It  is  the  most  convenient,  because  it 
can  be  more  easily  and  more  correctly  anticipated  than  any  other 
item  of  future  business, — as  tonnage,  for  example, — and  also  be- 
cause we  use  the  same  unit  for  all  our  traffic,  both  freight  and 
passenger  ;  and  it  is  the  most  exact,  because  it  is  by  very  much 
the  most  uniform,  measure  of  operating  expenses,  the  cost  of  a 
train-mile  being  very  nearly  the  same  whether  the  trains  are  run 
full  or  empty,  or  long  or  short,  and  not  being  materially  differ- 
'Cnt  for  freight  or  passenger  service,  although  usually  less,  by 
-one  third  to  one  fourth,  for  the  latter,  as  we  shall  see  hereafter. 

Assuming,  therefore,  this  basis  for  estimates,  it  may  be  al- 
ways anticipated  that  there  will  be  one  passenger  train  per  day 
each  way,  and  that,  unless  the  traffic  be  exceedingly  limited,  this 
train  will  be  exclusively  for  passengers.  Mixed  trains,  so  called, 
.are  in  but  little  and  decreasing  favor  with  railway  managers,  al- 
though it  is  not  always  possible  to  avoid  them.  When  used  at 
.all,  they  are  usually  nothing  more  than  freight  trains  under  an- 
other name — accommodations  for  a  few  passengers  being  added 
chiefly  as  a  convenience  to  special  classes  of  travel,  in  the  hope 
that  such  additional  convenience  may  have,  as  it  usually  does,  a 
favorable  influence  on  the  volume  of  travel.  With  freight  traffic 
•of  course  no  such  motives  intervene  to  modify  the  number  of 
trains,  so  that  mixed  trains  are  always  freight  trains  carrying  a 
few  passengers,  and  never,  in  regular  service,  passenger  trains 
carrying  freight. 

87.  Therefore,  under  the  most  unfavorable  circumstances 
there  are  pretty  sure  to  be  two  regular  trains  per  day,  one  pas- 
senger and  one  freight  or  "  mixed"  train,  over  lines  of  any  length. 
Less  than  this  is  certainly  never  contemplated  on  lines  built  as 
private  business  enterprises,  unless  on  very  short  branches  built 
as  feeders. 

88.  The  point  at  which  it  becomes  reasonable  to  anticipate 
Tunning  two  regular  passenger  trains  daily  is  more  difficult  to  de- 
termine. 


96  CJ/AP,   IV,-PROBABLE  VOLUME  OF  TRAFFIC, 


CHAP,   IV.— PROBABLE  VOLUME  OF  TRAFFIC. 


97 


m 


m 


I 


In   the  Northeastern  third  of  the  United  States,  as  may  be 
seen  by  examining  any  railway  guide  only  a  very  small  propor- 
tion of  the   minor   branch  lines  run  only  one  passenger  tram  a 
dav  and  but  a  very  few  of  the  lines  run  as  few  as  two  passenger 
trains   a  day.     In   the  North   Central    United    States,  including 
both  slopes  of  Mississippi  Valley,  two  passenger  trains  per  day 
may  be  said  to  be  the  rule,  exceeded  only  in  the  more  populous 
regions  and  on  the  important  trunk  lines;  but  only  a  small  pro- 
ponion   of    the  lines  run   as    few  as  one   train    a  day.     In    the 
Southern  and  extreme  Western   States  the  mileage  may  be  said 
to  be  about  equally  divided  between  one  train  per  day  and  two, 
only  a  few  leading  lines  or  sections  of  lines  running  more   than 
two  trains  per  day.     In  England  and  on  the  Continent  the  aver> 
age  number  of  passenger  trains  per  day  is  much  greater  than  m 
the  United    States,  except  in  the  extreme   Northeast  :  but  this 
distinction  is  constantly  growing  less  with  the  rapid  increase  of 
population  and  wealth    in    the  United    States.     Tables  29  to  7S 
give  many  statistics  of  the  average  number  of  trains  per  day  oa 
single  roads,  and  in  groups  of  States. 

89.  There  are  immense  local  fluctuations  in  every  State  and 
Territory,  but  as  a  rule,  when  the  conditions  are  at  all  favorable 
for  the  development  of  passenger  travel,  a  minimum  of  two- 
trains  per  day  may  be  looked  for  with  some  confidence.  This  is 
especially  probable  because,  in  order  to  encourage  and  develop- 
traffic,  it  becomes  expedient  to  put  on  two  trains  a  day  long  be- 
fore a  single  train  becomes  so  crowded  as  to  actually  compel  it. 
The  greater  facilities  so  offered  are  almost  certain  to  add  a  con- 
siderable percentage  to  the  aggregate  travel  and  revenue  ;  and 
as  the  actual  additional  cost  of  the  extra  train  is,  on  the  contrary, 
but  a  small  percentage  of  the  average  cost  per  train-mile,  such  a 
train  is  almost  always  put  on  long  before  the  mere  statistics  of 
tickets  sold  begin  to  indicate  that  it  is  a  necessity.  It  is  impos- 
sible, in  fact,  until  the  volume  of  travel  becomes  large  and  the 
number  of  passenger  trains  at  least  two  or  three  per  day,  to 
make  anv  attempt  to  regulate  the  number  of  trains  so  as  to  have 
them  run  full,  without  serious  injury  to  net  revenue. 


90.  Beyond  three  or  four  trains  per  day  there  is  much  less 
necessity,  as  a  rule,  to  add  trains  to  accommodate  and  develop 
travel  until  the  seating  capacity  itself  becomes  too  small  ;  this 
being  one  of  the  many  cases  in  which  '*  tiie  destruction  of  the 
poor  is  their  poverty."  Nevertheless  the  results  of  experience 
with  even  the  heaviest  traffic  is  that  it  does  not  pay  to  scrimp 
train  facilities.  Certain  trains  carry  enormous  loads  and  bring 
up  the  average  materially,  but  a  multitude  of  trains  carrying 
much  lighter  loads'are  run  with  the  heaviest  traffic,  at  frequent 
intervals,  bring  about  the  close  correspondence  in  average  train- 
load  on  roads  of  widely  different  character,  shown  in  Table  29. 


Table  29. 

Average  Freight  and  Passenger  Train-Load,  Haul,  Train  Service,  etc., 
FOR  THE  United  States  and  Groups  of  States,  1885. 


Freight  Traffic. 

Passenger   Traffic. 

Aver- 
age 
Train- 
Load. 

Aver- 
age 
Haul. 
Miles. 

No. 

Trains 

per 

day. 

Miles 

per 

Engine. 

I  —  1000 

Ton- 
Miles 

per  Car. 

I  =  1000 

Aver- 

Train- 
Load. 

Aver- 
age 
Haul. 

No. 

Trains 

per 

Day. 

A.  New  England 

B.  Middle 

102 
179 
139 
93>^ 
125 
118 
148 
"5 

60 

145 
108 

103 
132 

159 
162 

3-74 
7.42 

4-44 
2-43 
2.31 
2.17 
2.13 
I  81 

19.8 
21.3 
26.3 
19.8 
21.0 
20.6 
17.9 
14.4 

424 
53-9 
72.8 
60.9 

61.3 
58.1 
69.6 
51.8 

59 

44^ 

2,m 

32 

43 

36 

47M 
69>^ 

16 

i8l^ 

37% 

39H 

48 

49 

60 

31H 

4  52 
4.64. 

C  No.  Central. .... ...... 

2.3T 

D.  So    Atlantic 

1.52- 

E.  Gulf  and  Miss.  V.   ... 

F.  So.  Western 

1.64 
1.36 

G.  No.  Western 

H.  Pacifc 

1. 21 

1.35 

Total  U.  S.,  1885... 
1884... 
1883... 
1882... 

M3 
»34 
126 

129 

112 
112 
no 
109 

3-8t 
4  OS 
448 
S.32 

21.6 

22.1 
22.8 

2i.3 

57-4 
56.0 

56.6 

53-8 

43H 
42^ 
46% 
45^ 

26 

26H 

27^ 
26 

2.36 
2.51 
2.41 
2  37 

U.  S.  Census,  1880.. 

129 

III 

3-91 

22.4 

•  •  •  • 

4i« 

21 

2.16 

Excepting  the  figures  for  1880  from  the  U.  S.  Census,  the  above  is  computed  from  the 
statistics  of  Poor's  Manual.  In  this,  as  in  all  other  tables  in  this  volume,  the  railroad 
year  is  taken  at  365  days,  owing  to  the  regrettable  fact  that  the  distinction  between  Sun- 
day and  week  days  is  fast  disappearing.     The  "  number  of  trains"  always  means  each  way. 

7 


CHAP.   JV, 


.^PROBABLE  VOLUME  OF  TRAFFIC. 


o 

en    2 


—       c  *>  A 


^'S 

% 

$ 

CO 

« 

O 

« 

N 

et 

c« 

C4 

H 
M 

NO 

CO 

<o 

CO 

w 

c« 

c« 

M 

« 

M 

'^  ,8 


CO     w     <^ 


00 


CHAP,  IV.— PROBABLE  VOLUME  OF  TRAFFIC. 


99 


Table  32. 

Traffic  Statistics,  Lake  Shore  and  Michigan  Southern  Railway 


Year. 


1870. 


71- 
72. 

73- 
74. 


1875. 


76. 

77.- 
78.. 

79 


1880. 


81. 
82, 

83 
84. 


1885. 


Miles 
Road. 


1. 013 


1,074 

1,136 

1. 154 
1.178 


1. 178 


Per  Milr  Operated. 


Earnings. 


Expenses 
and  Taxes. 


13.336 


13.872 
16.682 
16,824 
14-592 


12.284 


1. 178 
1,178 
1,178 

1,178 


1,178 


1,178 

1,274 
1,340 
1,340 


11,851 
11,484 

11,877 
12.975 


15,922 


15261 
14.306 
13.817 
11.075 


1.340 


10.545 


8,261 


9,106 
11,177 
11,928 

9.491 


8,963 


8.135 
7,622 
7.210 

7.591 


8.846 


9577 
8,679 

8. 211 
6.815 


6,929 


Net 
Earnings. 


5.075 


4,766 

5.505 
4.896 
5.101 


3.321 


3.716 
3.862 
4.667 

5.384 


7,076 


5.684 
5.627 
5,606 
4,260 


3,616 


Dividends. 


Earned. 


9.60 


Paid. 


8.37 
8  55 
6.10 
6.04 


2.20 


3  26 

3-57 
5.61 

7.24 


11.28 


8.02 

8.37 
8. II 
4.02 


1.98 


8.00 


8.00 
8.00 
4.00 
3-25 


2.00 


3-25 
2.00 
4.00 
6.50 


8.00 


8.00 
8.00 
8.00 
5.00 


The  Lake  Shore  and  Michigan  Southern  Railway  being  one  of  the  few  im- 
portant lines  which  have  been  operated  under  substantially  similar  conditions 
and  with  substantially  the  same  mileage  and  motive-power  for  fifteen  years,  its 
statistics  have  an  especial  interest,  and  Tables  30,  31,  and  32  are  added  for 
that  reason. 


It  is  not  expedient,  nor  indeed  possible,  therefore,  to  base 
estimates  of  the  probable  number  of  passenger  trains  on  esti- 
mates or  statistics  of  the  probable  number  of  passengers  to  be 
carried,  further  than  to  assume  that  the  smaller  the  traffic  the 
smaller  will  be  the  average  number  of  passengers  per  train. 

91.  The  same  is  true,  in  less  degree,  even  of  estimates  of  the 
probable  number  of  freight  trains.  It  is  not  correct  to  assume  a 
certain  tonnage  to  be  moved,  divide  that  by  the  load  of  a  car  to 
get  the  number  of  loaded  cars,  divide  that  again  by  the  number 
of  cars  per  train,  and  so  get  the  number  of  trains.     There  is 


CHAP.  IV.-PROBABLE  VOLUME  OF  TRAFFIC. 


lOO 

"1  TTn^i^^^XTr^i^^rr^^rt^wastage  of  capacity  amount- 
always,  in  the  fi--^'  P'^"'  ^i,.  cent,  according  to  cu- 
ing to  -"y-'>«;\^7.'"''",^ffiei     to  be  estimated  on  the  basis 

fie  the  obtaining  of  full  loads  .s  '^f'^'^%^^^^^,,\,  Lrly 

Table  33. 
Growth  of  Average  FRE.oHT-TKAm  Load  or  Various  Roads, 

1873  TO  1885. 


N 

[ew  York  Trunk  Lines. 

Year. 

N.Y. 
Cent. 

N.Y., 
L.  Erie 

&w. 

Penna. 

B.& 

Alb. 

129   

Ill 
122 

75 

1073 

74 

139 
166 

•  ■  ■   •  •  •  • 

81 

75 

»34 

128 

82 

-ft       

180 
166 
186 
191 

219 

138 
145 
146 
i8s 

132 
137 
154 
170 

87 

7" 

77 

78 

79  

88 

93 

94 

80 

311 

184 

97 

jIt    

218 
319 

300 

196 

304 

ai8 
228 

311 
213 

184 

189 

189 
205 

209 

102 

0-     

104 

9~        

J03 

"3 

84 

106 

85 

227 

109 

Minor  Trunk  Lines. 


Del., 
Lack. 
&W. 


Can. 

So. 


Mich. 
Cent. 


Pitts., 

Ft.  W. 

&C. 


P..C. 

& 
St.  L. 


79 


83 


83 
78 
93 
77 


88 
89 


«35 


96 


T55 
190 


147 
158 
167 

J95 


90 
80 

99 
99 


208 


275 


301 


97 

96 

116 

120 


I2S 


186 
173 


184 
198 


132 
132 

131 

'39 


89 
«3 

98^ 

116 
129 
140 
t56 


166 


155 
16s 

160 
161 


107 


303 


138 


i8s 


CHAP.  IV.-PROBABLE  VOLUME  OF  TRAFFIC, 


lOI 


pacity.  Nevertheless,  even  on  such  lines,  fluctuations  and  irreg- 
ularities of  traffic  are  always  so  great,  that  it  is  no  infrequent 
spectacle  to  see  trains  running  light  in  the  direction  of  heaviest 
traffic  ;  and  the  difficulty  of  fully  filling  up  trains,  of  course,  be- 
comes much  greater  as  the  tonnage  is  less,  or,  as  already  stated, 
when  it  is  nearly  equal  in  each  direction.  There  is  also  always 
one  train  per  day,  the  way-freight,  which  averages  little  more 
than  one  half  an  ordinary  train-load,  owing  to  the  irregular 
service. 


Table  33. — Continued, 
Pennsylvania  Railroad,  by  Half  decades. 

<For  the  fig:ures  for  each  year,  and  for  direction  of  heaviest  traffic  only,  see  Index.) 


1853-5. 

75-4 


1856-60. 

83.2 


1861-4. 

94-3 


1865-70. 

104.4 


1871-4. 

116. 8 


1876-80. 

155-5 


1881-5. 

196.0 


These  fig^ures  not  unfairly  represent  the  general  law  of  gjowth  in  train-load  in  the  past 
30  years  under  favorable  conditions. 


Year. 


«873. 
74- 
75- 
76. 

77- 
78. 

79 
80. 
8z. 
83. 

83. 
84. 
85. 


Chicago  Roads. 


III. 
Cent. 


83 
94 
90 
97 
97 

ZI3 

"5 
1x0 

103 

120 


100 
1 30 

XI6 


C. 
R.I. 
&P. 


81 
80 

99 


85 

95 
107 
104 
109 
106 
105 
105 


Ch.  & 

Alt. 


119 
124 
142 

»39 
138 
161 

»77 
184 
189 
188 
190 
184 


CM. 

& 
St.  P. 


76 
74 
87 
86 

87 
83 
80 


C.& 
N.  W. 


Minor  Western  Roads. 


0.& 

M. 


55 
72 
81 
86 

93 
9t 


X07 

lOI 

99 
X08 
1 10 

123 
122 
132 
X33 
133 
121 
126 
132 


"5 

121 

133 
X29 
XO7 
126 

103 
152 


L.  & 

N. 


120 


Z3X 


137 


c.c, 

C.&L 


79 
81 
86 

89 
90 

99 
112 
122 

191 
205 
218 
205 

3X2 


Wise. 
Cent. 


53 
60 

55 
73 
96- 


1X3 


XOO 


Below  the  cross-lines  in  the  second,  third,  and  fifth  columns  there  was  a  large  increase 
of  mileage  operated,  as  also  in  some  cases  not  marked.  Most  of  the  other  cases  in  which 
the  train-load  h<is  decreased  are  due  to  a  falling  off  in  total  ton-mileage. 


^^ra 


CHAP,   IV, -PROBABLE  VOLUME   OF   TRAFFIC, 


CHAP,   IV.— PROBABLE  VOLUME  OF  TRAFFIC, 


103 


102 

^  ~  ~  .o,r*.  fr^iaht-train  loads  which  has  taken  place 

The  enormous  increase  .n  average  f  eight  ^^^^"  J  ^  ^f^^.„  ^.i^^out 

Table  30  and  others. 

TL      So  many  freight  trains,  usually  from  two  to  six.  are  put 
^he  tL?table     ff  more  are  needed.  "  extras"-a  train  run- 

r;re:ir:rHer  -- -  - --:;- ef :: t-r. 

rr:  it"rtrt;:rdTer^e..nt,  ^       -; 
rrrS'?r:7-"L^?ra\:;TrfanX  ;r.a.„.  u; 

time-table  "rights"  is  ^f^^        ^^^  „^,,,,  ,,,„  appear  on 

required  by  the  tonnage,  and  often  more,  the  office  of  the  extra 
trains  being  simply  to  serve  as  equalizers. 

made  up.  they  are  started  off  as  e   her     r^gu lars    o^  ._^^^^^  ^^ 

whichever  will  give  quickest  despatch  •  "-"^  ^^  ''  ;^;  ^„  ,„„„„t  of  the 

send  out  at  least  one  -in  on  each      hedu,     tra.n  '  '       ;  ^^  ^^^^^^    ^^^  ^^^ 

practical  inconvenience  ^""^  f ".«"  °' ^7.""""';,  „„,  ,„  give  a  separate  time  to 

;:;;r^:s;r:rr.\rr:;rrr;.; » ..,. ... «...  ^.  - 

much  ir«g"l"''y;  p^,,„„  division  of  the  Erie,  running  often  a  hundred  train* 
p.r°:r:hra"'h!tTJorgu,ar  scheduVed  trains,  one  for  ..M.  and  one  fo, 
PM.   and  all  others  are  run  as  sections  of  th>s  tram. 


94f  It  should  be  mentioned  also  that,  in  attempting  to  draw  conclusions  as 
to  probable  traffic  from  statistics  as  to  "miles  run  by  freight  trains"  on 
neighboring  roads,  such  statistics  must  be  accepted  with  the  greatest  caution. 
An  unfortunate  custom  exists  of  comparing  locomotive  expenses  on  the  basis 
of  the  engine-mile  instead  of  the  car-mile,  and  as  a  consequence  a  habit 
has  arisen  among  master  mechanics  and  other  officers  of  exaggerating  the 
switching  mileage  (which  is  heavy  enough  at  best)  in  every  possible  manner,  by 
heavy  allowances  for  switching  at  stations,  and  for  running  to  and  from  the 
round-house.  Instances  might  be  given  in  which  the  excess  of  this  nominal 
mileage  over  that  actually  run  between  termini  amounted  to  nearly  one  fifth, 
independent  of  the  usual  and  regular  switching  allowance  of  so  many  miles  per 
hour  to  switching  engines  proper,  which  is  separately  given.  This  fact  is  im- 
portant to  remember  not  only  in  estimating  the  volume  of  traffic,  but  also  in 
estimating  locomotive  expenses  ;  for  most  roads  make  more  or  less  allowance 
for  mileage  outside  of  the  regular  revenue  distance,  and  it  is  always  more  or 
less  deceptive,  consequently,  to  use  such  data  uncorrected  for  estimates  of  cost 
per  revenue  train-mile.  Whenever  there  is  a  marked  discrepancy  in  the  cost 
per  train-mile  on  similar  roads  this  cause  may  with  some  confidence  be  regarded 
as  the  true  explanation.  Some  reasonable  approach  to  a  correct  estimate  of  the 
probable  traffic  can  thus  be  made,  by  a  little  effort,  from  published  statistics  of 
various  roads  and  towns,  unless  in  a  region  which  is  entirely  new  to  the  rail- 
ways, or  for  other  exceptional  causes.  The  following  statistics  will  also  be  of 
assistance: 

95.  The  average  payment  to  railroads  of  each  man,  woman, 
and  child  in  the  United  States  now  averages  about  $13.50,  of 
which  about  $3.50  is  for  passenger  transportation  and  $10  for 
freight.  Table  34  and  several  others  (see  Index)  give  further 
statistics  for  various  groups  of  States,  but  the  fluctuations  from 
such  averages  are  of  necessity  great.  Points  which  are  centres 
of  manufacturing  and  transportation  interests  will  have  a  many 
times  greater  traffic  than  this  to  dispose  of  ;  while,  on  the  other 
hand,  there  are  few  local  stations  which  will  fall  very  far  below 
it,  the  great  excess  of  the  few  points  being  compensated  by  the 
great  multitude  of  small  deficiencies. 


I04 


CHAP,   JV.— PROBABLE  VOLUME   OF   TRAFFIC. 


CHAP.   IV.^PROBABLE  VOLUME  OF   TRAFFIC. 


105 


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ABITANT   BY   S 

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Table  34. — Continued, 
Foreign  Countries. 


1876  .. . . 
1880-1. . 
1880    ... 
1880  . . . . 
1881..   .. 

1876-80.. 


Great  Britain  and  Ireland 

France 

*VUSll  1a  •••••••••••••••••••••i 

^  tcHjT  ■■••••••••••  •••••  «••  •  ••• 

Mexico  (one  railway  only).. .. 


So'n  U.  S.  (E.  of  Miss.  Riv.). 
N.  and  W.  U.  S 


Total  U.  S. 


Miles. 
16,658 

15^227 

7,086 

5,4»8 

293 


11,892 

66,714 


78,606 


Pass. 
5.19 

1.78 

0.5S 
0.06 


0-93 
3-35 


2.84 


Total  of  all  earnings,  $9.20). 
"  "  "         5.66). 


it 
u 


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M 


it 
it 


it 
tt 


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5.28). 

«.33)- 
0-53)- 


3.80). 
12,98). 


10.91). 


Fr'ght 
4. ox 


3-50 
0.68 


0.47 

287 

9.63 

8.07 


From  the  above  statistics  we  may  conclude  that  the  average  revenue  to  railways  from 
each  inhabitant  of  the  different  sections — bearing  in  mind  that  much  of  the  trunk-line 
freight  traffic  credited  to  the  Middle  States  is  in  reality  a  part  of  New  England  and 
Western  payments — is  (average  of  1880-85)  about  as  follows : 


New  England  States 

Middle  States 

Pass. 
$5  00 

3-50 
3-00 

550 

Freight. 
$8. 00 

zi.oo 

11.50 

14.00 

Toul. 
$13.00 

14  50 
»4-5o 
19  50 

Ranging  from 
$6.50  to  $16.50 

4.08  to     28.XO 

Western  and  Southwestern  States 

Pacific  States 

Average  of  all  Northern  and  W'n  States. 

3-50 
1. 00 

11.00 
3  50 

14.50 
4.50 

Southern  States  (E.  of  Miss.  River) 

Average  of  the  entire  U.  S 

3-00 

9  00 

12.00 

The  fluctuations  from  year  to  year  hardly  exceed  10  to  15  per  cent  more  or  less  of 
these  averages.  There  is,  however,  a  gradual  yearly  growth  in  the  payments  per  inhabi- 
tant amounting  to  an  average  of  perhaps  one  per  cent  per  annum,  due  largely  to  causes 
considered  in  Chapter  XXL 

The  fluctuations  in  the  average  payments  of  different  localities  are  no  doubt  ex- 
treme, as  may  be  seen  from  the  statistics  in  other  tables.  The  State  of  Florida  pays  but 
$1.60  per  annum  to  its  railways.  The  larger  Eastern  cities,  probably  $30  per  head  at 
least.  There  are  doubtless  considerable  sections  of  each  of  the  States  in  the  above  groups 
where  the  payments  may  be  as  low  as  half  or  as  high  as  double  the  average  for  the  whole 
group  of  States.  The  trunk-line  export  traffic  constitutes  only  an  insignificant  fraction 
of  the  total  revenue  of  United  States  railways,  lai^e  as  it  is  absolutely. 


CHAPTER  V. 


OPERATING    EXPENSES. 


96.  We  may  gain  a  profitable  insight  into  the  general  nature 
of  the  causes  which  modify  operating  expenses  and  espec.a  ly 
of  the  effect  thereon  of  differences  of  alignment  by  first  consid- 
ering them  in  a  very  general  way,  neglecting  all  detail 

We  have  previously  (Chap.  III.)  compared  the  railway  to  a 
great  manufacturing  establishment-manufacturing  transporta- 
fion     Its  operating  expenses,  to  carry  out  the  analogy,  should  be 

only  anothe'r  name^for  the  total  cost  of  P^o!'".<^'-S ^^f'^^^J^^'^l^Z 
which  it  sells  ;  but  as  a  matter  of  fact  this  is  not  the  case.    The 
Tnt  res^r  "  r  ntal "  charge  on  its  real  estate,  and  on  most  of  it 
machTnery  and  plant-the  heaviest  single  item  by  far  >«  the  real 
"oDerS"  or  manufacturing   expenses-is  never  included  m 
wh'at  aTc'alled  the  operating  expenses,  but  constitutes  the  nx.. 
rHARGE  for  interest  on  bonds  (see  Figs,  i,  2,  3).     Counting  in 
the  'fixed  charges"  as  part  of  the  "  operating"  or  manufacturing 
expenseihe  latlr  neve'r  amount  to  much  less  than  80  per  cent 
and  from  that  to  considerably  over  100  per  cent,  for   ong  periods 
of  time     The  average  for  the  whole  United  States  is  somewha 
iLToo  oer  cent  leaving  but  little  more  than  10  per  cent  profit 
^n  the  goods  sold  t^  be  listributed  to  the  managing  companies^ 
vZ  Lorable  circumstances  this  profit  is  as  much  as  ^^^^or 
20  per  cent ;  very  rarely  more.     Tables  35  ana  30  g 
;Hf»a  nf  the  law  in  this  matter. 

97    Is  these  fixed  charges  increase  in  somewhat  faster  rat,o 
than  thecost  of  construction,  and  are  the  same  per  y--JJ^^f^^[ 
the  business  be  large  or  small  or  none  at  all,  the  great  impor 
tance  of  (t)  diminishing  the  expenditure  for  construction  as  much 


CI/AP.   v.— OPERATING  EXPENSES. 


107 


Table  35. 

Stock  and  Bonds  Per  Mile  of  Road  by  Sections  of  the  United  States. 

1880. 


Groups  of  States. 

Miles. 

Stock  and  Bonds  Per  Milk. 
I  =  $1,000. 

Revenue 

per  Mile. 

I  —  $1,000. 

Stock. 

Bonds. 

Other  D't. 

Total. 

New  £ne:Iand 

5.910 
14.942 
12,978 
46,102 

4.461 

31.6 

47.5 
15.8 
24.8 
33-2 

21.5 

49-3 
19.2 
22.7 
35.8 

2.75 

2.87 

1.37 
1.48 

2.58 

55.85 
99.67 

36.37 
48.98 

71.58 

8.00 

13.30 

356 

6.34 

7-53 

Middle 

Southern 

Western 

Pacific 

United  States 

Canada 

84.393 

28.4 

27.3 

1.86 

57.76 

7.31 

1885. 


New  England. 

Middle 

Southern 

Western 

Pacific 


United  States. 


1884. 
1883. 
18S2. 


6,412 

18,595 
20,584 

74.854 
7.284 


127,729 


31.8 

57.3 
20.2 

25.2 
340 


21.9 

53.6 
24.6 

25.6 
28.5 


30  9 
30.1 
30.8 
30.7 


29  5 

293 
28.7 
28.3 


2.46 

4.87 

1.20 

56.16 
115.77 

46.00 

1.49 

2.20 

52.29 
64.70 

2.03 
2.0 

61.43 

61.4 

1.9 
1.9 

61.4 
60.9 

8.87 

11-53 
3.66 

5-25 

4-55 

6.22 
6.76 

7-54 
7.60 


1885. 

$55,100 


The  nominal  cost  of  road  and  equipment  for  the  whole  United  States  was  for  these 
years : 

1882.  1883.  1884. 

$52,790  $55,500  $55,300 

The  Canadian  railways  averag;e  but  $ri,ooo  of  bonds  per  mile,  and  $58,230  of  stock 
and  bonds  together.  Excluding  the  Grand  Trunk,  which,  with  26  per  cent  of  the  mileage, 
has  45  per  cent  of  the  capital,  there  are  only  $28,000  per  mile  of  both  stock  and  bonds. 
More  than  one  fourth  of  the  total  capital  (145  millions  out  of  558,  for  9,575  miles,  in  1884) 
was  contributed  from  governmental  sources.  Earnings  are  correspondingly  small,  being 
for  1884 : 

Canada  Southern,  )  ^^950  miles  \  $^0'6o°  P^^  mile. 
Grand  Trunk,         )    '  t      6,290  "       " 

316  remaining  lines,   6,625     "  2,010  '* 


it 


9,575  miles,       3,491  per  mile. 


io8 


CHAP,  v.— OPERATING  EXPENSES. 


CHAP,    r.— OPERATING  EXPENSES, 


109 


Table  36. 
Distribution  of  Gross  Revenue,  in  Per  Cent  of  Total  Receipts. 

1880. 


Groups  or  Statks. 


New  England. 

Middle 

Southern 

Western 

Pacific 


Per  Cent  of  Receipts  Devoted  to— 


Op'g  Exp. 


Total  U.  S. 


68.1 

62.4 

63.5 

53.9 
50.2 


Net  Rev. 


58.3 


31-9 
37-6 

36.5 
46.1 

49.8 


41.7 


Interest. 


11.25 

19-33 
16.84 
16.98 

2305 


Dividends. 


17.58 


16.83 
14.24 

7-43 
11.72 

14  50 


12.55 


1885. 


New  England 

Middle 

Southern 

Western 

Pacific 


United  States  for  each  Year  from  1879  to  1885. 


1879- 
1880. 

1881. 

1882. 

1883 
1884. 

1885. 


58.8 

58.3 
61. 1 
63.6 
63.8 
65.2 
65.1 


41.2 
41.7 
38.9 
36.4 
36.2 
34.8 
34.9 


21.18 
17.58 
18.32 
20.02 
21.00 
22.90 
24.52 


11.72 

12.55 
13.30 

13.23 
12.38 
12.09 
10.05 


as  true  economy  permits,  and  (2)  increasing  the  traffic  (sales)  so 
that  this  burden  may  constitute  a  less  percentage  of  the  entire 
business,  is  evident.  Omitting  them,  the  operating  expenses 
PROPER  (corresponding  to  the  expenses  of  simply  running  and 
maintaining  a  factory  which  has  once  been  thoroughly  equipped 
and  of  selling  the  manufactured  products)  amount  usually  to 


about  two  thirds,  or  67  per  cent,  of  the  receipts,  varying  however 
enormously  (from  but  little  over  50  to  more  than  90  per  cent) 
with  different  roads.  Table  37  and  others  give  an  idea  of  the 
general  tendency  for  a  long  period  of  years. 

As  the  ratio  of  expenses  to  receipts  may  be  made  less  either 
by  the  receipts  being  larger  or  the  expenses  being  smaller,  the 
fact  that  the  ratio  is  low  or  high  is  no  real  test  of  economy  in 
operation,  nor  of  the  value  of  the  property.  Wherever,  from 
absence  of  competition,  the  rates  are  very  high, — as  formerly 
on  the  Pacific  railways,  Panama  Railroad,  and  many  lines  in 
Europe, — this  ratio  will  be  small,  even  in  the  face  of  heavy  ex- 
penses. Wherever  all  or  nearly  all  railways  have  been  very 
costly,  as  largely  throughout  Europe,  it  will  also  be  small,  since 
the  fixed  charges  will  constitute  a  larger  proportion  of  the  tax 
on  earnings,  and  rates  will  naturally  adjust  themselves  to  pay  (i) 
all  operating  expenses,  (2)  all  rental  or  fixed  charges,  and  (3)  a 
fair  profit  to  the  managing  company. 

Wherever  several  lines  are  so  situated  that  their  business  is 
largely  competitive,  and  must  be  handled  at  the  same  gross 
price,  but  one  or  more  of  them  has  better  grades,  or  a  shorter 
line,  or  more  traffic,  or  other  special  advantages,  one  line  will 
permanently  show  a  lower  percentage  of  expense  than  the  others, 
which  will  have  no  meaning  as  an  indication  of  real  excellence 
of  management.  This  latter  law  is  strikingly  illustrated  by  the 
trunk-line  percentages  in  Table  37,  the  cause  for  the  differences 
in  which  is  explained  in  a  following  note  and  in  Chap.  XXI. 

98.  The  operating  expenses  proper  are  very  irregularly 
affected  by  the  amount  of  business  or  by  the  character  of  the 
alignment.  A  very  large  proportion  of  them  are,  like  the  rental 
or  fixed  charges,  independent  of  both  :  such  as  the  salary  of  the 
president  and  other  officers  ;  maintenance  of  works  and  plant 
against  the  deterioration  which  comes  with  time,  irrespective  of 
work  done  ;  salaries  of  local  freight  and  passenger  agents,  a 
large  proportion  of  whom  must  be  employed  anyway,  whether 
considerable  sales  are  made  or  not.  This  immense  class  of  the 
expenses  amounts,  as  we  shall  see,  to  nearly  one  half  of  the 


no 


CHAP.    V.—OPERA  TING  EXPENSES. 


CHAP,   v.— OPERATING  EXPENSES. 


Ill 


Table  37, 
Percentage  of  Operating  Expenses  to  Revenue. 


1849-50 

1851-55 
1856-60. 
1861-65. 
1866-70, 

1871-75 
1876-80 


1876 

54.6 

1879 

54-3 

I8S0 

68.0 

1880 

61.5 

1880 

51.0 

United  Kingdom. 

Prussia ' 

Italy 

Spain 

India 

Xul„crH,t  fi^ris  „  „  rtc,  indicate  the  numlDer  of  years  for  »hich  the  average  is 
givel.  th^^iTh-  ;:    The'group  of  States  are  those  of  Poor's  Manua,  for  the  years 

""'TrlTtke  atov.  MU  ^,  may  cncluJ,  that  no  mark«.  tendency  exists  to  increase  or 
dimmish  the  ratio  of  receipts  to  operating  expenses,  both  of  »hich-as  may  be  seen  from 
other  tables— have  a  tendency  to  tall  rapidly  and  about  equally. 

"rZluaUcns  .finZiual  lims  in  respect  to  this  ratio  are  often  extreme,  as  may 
be  ll\T.L^^^  the frunk  lines,  and  rarely  affords  any  trustworthy  indtcat.on  of  efiicenq^ 
oJ  Tan^ement  the  cause  almost  always  lying  deeper,  and  being  incapable  of  essential 
mo^ificaTorb"  kny  skill  of  management  without  change  of  external  cond.t^ns.  Thus  the 
PennsvTvlnia  Railroad,  having  the  shortest  haul  (and  consequently  the  h.ghest  .ece,p« 
per  mt)  on  traffic  betw'een  almost  all  points  in  the  West  and  the  Atlantic  coas  ,wll  foreve 
maintain,  under  equal  skill  in  management,  a  ratio  of  receipts  to  expenses  from  lO  to  .5 
~r  clnt  higher  ttan  the  Erie.  The  New  York  Central  would  compare  sull  more  un- 
Crably  in  this  respect  except  that  the  enormous  volume  of  its  local  traffic  favorab  y 
modifies  its  average,  which  will  on  this  account,  under  existing  conditions,  be  always  more 


Z^bL  tha:.;'e  Erie.  The  low  ratio  of  the  Baltimore  &  Ohio  as  respects  the  Pe  n- 
sylvania,  is  due  almost  exclusively  to  the  greater  relative  volume  of  its  coal  traffic,  which 
fe  alway;  carried  in  full  trains  at  low  cost.  The  same  effect  is  still  more  strikingly  visible 
rnlrWegWng  the  history  of  the  PhiladelphU  «=  Reading  Railroad.    See  Index,  and 


operating  expenses  proper — the  other  half  only  varying  more  or 
less  closely  with  the  details  of  the  line  and  grades,  and  very 
much  less  than  half  with  slight  changes  in  volume  of  traffic. 

99.  Therefore,  it  may  be  said  in  a  general  way  that  ten  per 
cent  added  to  revenue  is  as  good  as  fifteen  per  cent  taken  off 
operating  expenses  ;  and  this  again  means  thirty  per  cent  taken 
off  that  portion  of  the  operating  expenses  wliich  varies  with 
Ime  and  grades.  To  gain  or  lose  ten  per  cent  in  revenue  by 
slight  differences  in  the  route  selected  is  very  easy.  To  reduce 
the  whole  operating  expenses  fifteen  per  cent  by  differences  in 
alignment  which  do  not  increase  the  cost  of  construction,  is  not 
so  easy.  Let  us  illustrate,  by  examples  free  from  detail,  the  very 
important  moral  conveyed  in  these  facts.  We  will  assume  the 
case  of  a  fairly  prosperous  line  of  the  second  grade,  whose  in- 
come and  outgo  we  shall  find  may  be  distributed  in  something 
like  the  following  manner  : 

Per  Cent.       Per  Mile. 

Gross  revenue loo.o  $7,000 

Operating  expenses,  unaffected  by  either  alignment  or 

volume  of  traffic  (50  p.  c.  of  operating  expenses),     .     33.3  $2,333 

Ditto,  increasing  directly  with  considerable  changes  in 

alignment  or  volume  of  traffic,  but  not  with  trifling 

changes  (40  p.  c.) 26.7  1,867 

Ditto,  increasing  directly  with  the  less  important  changes 

in  alignment  or  traffic  (10  p.  c.) 6.7  467 

Total  of  nominal  operating  expenses 66.7  $4,667 

Add  to  the  latter  the  rental  or  interest  charge  (6  p.  c.  on 
$30,000  per  mile,  assumed  cash  cost  of  road  and 
plant), 25.7  1,800 

Total  of  true  operating  expenses,  or  cash  cost  of 

producing  the  transportation  sold, 92.4  $6,467 

Surplus  available  for  dividends    being   the    business 

profit  resulting  from  operation, 7.6  $533 

Let  us  now  see  the  effect  of  increasing  or  decreasing  the 
gross  revenue  ten  per  cent,  as  it  is  frequently  possible  to  do  (one 


Chapter  XXI.,  pars.  973-4- 


|.' 


112  CI/AP.   V,— OPERATING  EXPENSES. 

might  perhaps  more  fairly  say,  rarely  difficult  to  do)  by  probably 
differences  of  alignment  alone.    We  have,  if  it  has  been  mcreased: 

Per  Mile.       Per  Cent 
Increase. 

Gross  revenue  (increased  lo  per  cent) ^^'^^  ^^ 

Operating  expenses  (lo  p.  c.  only  increased  lo  p.  c),  ^  ^ 

or  $47  per  mile  increase        . ^,7^^  ^^ 

Fixed  charges  (assumed  unchanged),      ......    j — 

Total  charges  against  revenue, ^'5^3  ^^^^ 

Surplus  available, 

The  surplus  available  for  dividends  is  more  than  doubled. 
On  the  other  hand,  if  there  has  been  ten  per  cent  loss  of 

traffic,  we  have—  PerMile.     Per  cent. 

Decrease. 

.    .  $6,300           lo.o- 
Gross  revenue, 

Operating  expenses  (lo  p.  c.  of  lo  p.  c.  only  decreased    ^^^^ 

'°  P-  "=) \    .    .    1,800  0.0 

Fixed  charges, 

6  420  "■ 

Total  charges  against  revenue * 

The  expenses  are  a  little  over  the  receipts,  and  the  road  is 
on  the  way  to  a  receivership,  if  it  has  been  opened,  as  U  is  very 
apt  to  be,  in  one  of  the  years  in  which  an  ebb  in  the  business  tide 
fs  beginning,  and  there  is  no  apparent  growth  (often  a  decrease) 

in  traffic  for  several  years. 

,00.  Again:  Let  us  suppose  that,  by  an  improvement  of  or  m- 
iury  t.^  th!  line  and  grades,  we  increase  or  decrease  the  average 
rIL  load  30  per  cent-often  not  difficult  to  effect.     Our  account, 
Ifwe  htve  improved  the  grades,  will  then  stand  as  follows: 

Per  Mile.      Per  Cent. 

%n  000  0.0 

^;:::trnr:x;enses-(3;  p.  c.-  oi  5;  p.  c:  sivea.  or  \,-^i    3.967  ;5.o 

Fixed  charges  (as  above), _[ . 

5.767 
Surplus  available  for  dividends, V^33 


CHAP,   v.— OPERATING  EXPENSES. 


113 


Or,  we  have  benefited  the  line  greatly  indeed,  and  yet  but 
little  more  than  if  we  had  added  lo  per  cent  to  revenue.  On 
the  other  hand,  reversing  this  process,  we  find,  as  before,  that 
the  road  is  on  the  way  to  a  receivership. 

101.  Let  us  suppose,  by  an  unnecessarily  extravagant  scale  of 
expenditure,  for  purposes  which  do  not  really  add  much  in  dol- 
lars and  cents  to  economy  of  operation,  we  have  increased  the 
capital  account  or  rental  charge  33  per  cent,  in  a  way  which 
does  not  decrease  operating  expenses  more  than  2  per  cent, 
nor  add  anything  to  revenue — a  not  uncommon  case,  since  the 
use  of  6°  instead  of  10°  maximum  curves  will  alone  suffice  to  do 
it,  in  some  cases.     We  have  then 

Per  Mile. 

Increased  the  rental  charge  33  p.  c,  or $622 

Decreased  operating  expenses  5  p.  c,  or      ....        93 

Net  increase, $529 

Or  within  $4  of  wiping  out  the  surplus  over  expenses  and 
fixed  charges.  If  we  have,  in  addition,  adopted  a  line  which, 
instead  of  being  better,  is  really  more  expensive  to  operate 
than  another  line  which  would  have  cost  no  more — or  if,  pos- 
sibly, we  have  adopted  a  line  which,  in  addition  to  being  more 
expensive,  involves  a  certain  sacrifice  of  revenue,  a  receiver- 
ship is  practically  assured.  Both  of  these  are  very  probable 
contingencies,  but  if  we  have  escaped  them,  we  have  barely 
saved  ourselves.     The  profit  from  the  enterprise  is  destroyed. 


102.  A  great  change  has  taken  place  within  the  past  ten 
or  fifteen  years,  and  indeed  is  still  in  progress,  in  the  operat- 
ing expenses  of  railways,  as  a  result  of  the  introduction  of  cer- 
tain modern  improvements,  and  notably  the  steel  rail.  At  so 
recent  a  period  as  the  publication  of  the  first  edition  of  this 
treatise  (1877)  these  improvements  had  hardly  begun  to  tell  at 
all  upon  the  statistics  which  were  available  for  its  preparation  ; 
but  they  have  already  (1885)  modified  them  profoundly,  and 
where  the  process  will  end  it  is  impossible  to  foresee  with 
8 


CHAP,   v.— OPERA  TING  EXPENSES. 


CHAP,    v.— OPERATING  EXPENSES. 


I 


h 


114 

:^^^^^:^^^Z^:^^^^^^^  the  change  will  be  very  much  more 
^;^oi  than  even  vet  appears  upon  the  surface. 

:  ■-•  •-"..ir.::;-.:::?;  r.  its:  "/ir^s 

se  V  ce     Mogul  or  Consolidation  locomotives  are  rap.dly  super- 
seivice.     Mogui  o  ^^^^^^      supersede  it. 

;r;-r  Mr-:"  .=.t:  -  -  -— ■  •-  »■ 

client  pro>p=c..  «'  "'■'J  "",  ,„nt   „„   h..   .1.0    been 

ind.     The  capacitv  01  orainar)    ircigut 

104.    1  he  capa  ^^^^^  ^^^  ^^^^^^  ^^^^^ 

cars  have  been  b>"l  •  J^^  ^"^^^^^  .  Car-Builders'  Association 
so  far  that  a  committee  of  the  Mastei   v.- 

creosouHj,  ui  x.  or.H   Qprondlv  the  substitution  of  first- 

o«,'.ii  hilt  increasme  use);  and,  seconuiy,  m^. 

r^ba^-a'sUor  wh^t  iJs  --ofore  done  du^^or  t  at  piir^^^^^^^ 

"^"^  rre'r-taf^e^r;  r.!a7  tt^m^f  :o£t  factor  of 
to  34.  a"tl  othe.s)  has  ^^^     P         ^^^        ,  ;„  ^^^^^^^  ^f  producing 

^"'  ^"JotTmruCctur     'commodity  consumed  by  railways. 
^-aerTl^pos  -"ble  ^o.P-.  with   any ^^^^^^^^^^^^^^^  - 

;^e.    Rates  of  8,  9,  lo.  x3i  '5,  ^^nd  44  cents. 


115 


Table  38. 
Receipts,  Expenses,  and  Profits  per  Ton-Mile. 


Trunk  Lines. 

Minor  Trunk  Lines. 

Year. 

Penn'a. 

N.  Y.  C. 

Erie. 

P.,  Ft.  W. 
&C. 

B.  &  Alb. 

L.  S.  &  M.  S. 

Rec.   Exp. 

Pr. 

Rec. 

Exp.   Pr. 

Rec. 

1.95 

Exp. 
1.03 

Pr. 

•92 

Rec.  Exp. 

1 

Pr. 

Rec. 

Exp.   Pr. 

Rec. 

Exp 

Pr, 

1852 

4.64 

.  . 

.  . 

, , 

53   

3  7« 

2.50 

1.28 

1 .22 

, , 

,  , 

.  , 

•  • 

, , 

•  • 

54   

327    |2    28 

•99 

2  95 

i.3»  1-64 

2.58 

1.41 

1. 17 

,  . 

,  , 

,  , 

* . 

^  , 

»  , 

55   

2.84  I1.68 
305    il.98 

1.163.27  1.34  1.93 
1.0713. iiji. 32  1-79 
1.043.05  1.54  1.51 

2.42 
2.36 
2.48 

^•I5 
1.22 
1. 17 

1.27 
1.14 
'•3« 

•• 

•• 

•• 

Aver.iffc. 

,.       1       .  . 

1856 

2.70 

..69 

.. 

57 

2.38 

1.52 

.86,3.19;!. 70  1.49 

2.46 

.90 

1.56 

2.27 

I  •.57 

.70 

,  , 

,  . 

,  , 

58   

2    19 

1-35 

.8412.6311.37  1.26 

2.32 

•65 

I  67 

11.90 

1.32 

•.58 

,  , 

•  • 

.  , 

,  . 

59 

2.02 

1. 18 

.842  16  1.28,    .88 

i.6i 

^•-4 

.28 

1.651.18 

•47 

,  , 

,  ^ 

,  , 

,  , 

eo  

'•95   I1.17 

.782.061.34'    .72 

1. 81 

1. 00 

81 

1.67I1.18 

•49 

. 

.. 

Averaire.. 

2.25  1.38 
1-93  1   .9» 

. 87)2. 62  1.45  I. 17 
I.02  I  98  1-341    .64 

2.14 

1-77 

I.OI 

•93 

I -13 

.84 

X.87 
;i.7i 

1. 31 

.98 

•56 
•73 

•• 

..    1    .. 

•  • 

1861 

.. 

. . 

62 

2.05  (i  09 

.962  23  I  36!    .87 

1.89 

•95 

.94  1.90 

.98 

.92 

.  • 

•  • 

.  • 

63 

2.20    1.16  1. 0412. 44 

'•5»     ^93 

2.og 

.96 

I.I3;2.0lll.20 

.81 

,  , 

,  , 

, , 

,  , 

64   

2.46  11.R7    .592.76 

1.96     .80 

2.34 

1.46 

.88 

2  381I.50 

.88 

,  , 

,  , 

. . 

,  , 

,  , 

65   ..    .. 

2.66    2.28    .38  3  45 

2.54'    -91 

2.76 

1.98 

.78 

2-4411  79 

65 

Averatje.. 

2.26    I  460.80J2.57 

1.74I    .61 

2.17 
2.43 

1.26 
1.66 

.91 

•77 

2  09  1.29 
2.0211.50 

.80 
•52 

• 

•  • 

.  • 

..    1    .. 

1866.   ... 

2.28    1.82    .46 

3  09 

2  16 

■v> 

,  , 

,  ^ 

67 

209   |iS4'    •5S 

275 

1-95 

.81 

2    04 

I  47 

•57 

I  95|i^44 

.51 

•  • 

68 

1.91   I1.25     .66 

2  74 

I  80 

•94 

1.81 

'•34 

•47 

1.70JI.15 

•55 

2.81 

•  . 

•  • 

69 

1.72   ii.20,    .52 

2  39 

1.40 

•99 

154 

1. 17 

.37 

1.62  I. II 

•51 

2.43 

•  , 

•  • 

,  , 

70 

1.55    I. 00    .55 

1.88 

^•I5 

•73 

l^33 

•97 

•36 

1.45    ^86 

•59 

2.19 

• . 

1.50 

•93 

•57 

Average.. 

I. 91     1.36     .5s 

2.57 

1.69 

I.OI 

.88 
.62 

I  83 
1.44 

^•3' 

I.OI 

•51 
•43 

1.75  I  21 
1.43    .78 

•54 
•65 

2.48 
2.09 

• . 

1-39 

.. 

a87i 

t.39  1     87     .52  1.63 

.9i|   .48 

72 

1.416  .886;   530  1.59 

i.ij 

.46 

'•53 

.98 

•55 

1.40 

.81 

•59 

2.02 

1-37 

.92 

•45 

73 

I  416  .857  .559, 1-57 

1.02 

•55 

1.46 

.96 

•50 

1.40 

•95 

•45 

1.96 

1.59 

•37 

1-34 

•95 

•-39 

74 

I.2S5  .719    536  1.46 

.98 

.48 

1. 31 

.91     .40 

1.26 

•74 

•52 

1.82 

I  39 

•43 

1. 18 

•77 

.41 

75   

1.058  .616  .442 

1.27 
1.70 

.90 

I.OI 

•37 

•49 

1. 21 

1    19 

.96    .25 

•96     .431 

III 
1.32 

.69 
•79 

•42 

•53 

I  53 
1.88 

I  10 
1.48 

•43 
.40 

I.OI 

1.26 

•74 
.86 

•27 

Average.. 

i..^o7 

•790  •517! 

.40 

1876 

.892 

.582  .310  1.05 

•  71 

•.34 

1. 10 

.8q 

.21 

•93 

.61 

•.30 

1.28 

1.03 

•25 

.82 

•.S6 

.26 

77 

.980 

5.52  .428  I. 01 

.70 

•3' 

■95 

•75 

.20 

I.OI 

.67 

•34 

1. 21 

1.03 

.18 

.86 

•57 

•29 

78 

.918 

•483  -435 

•93 

.60 

••33 

•97 

.67 

•.30 

.88 

•50 

•38 

^•I3 

•99 

.14 

•73 

•47 

.26 

79 

•796 

.427    369 

.80 

•55 

•25 

.7« 

•56 

.22 

•76 

•44 

•32 

1. 10 

•78 

•32 

•64 

.40 

•24 

80  ..    .. 

.880 

.470  .406 

.88 

•54 

•34 

M 

•53 

•.30 

.qi 

•51 

.40 

1. 21 

1.02 

.19 

•75 

•H3 

•,32 

Avcrajie.. 

.873 

•503    390 

•93 

.62 

3» 

•93 

.68 

■25 

.90 

•55 

•35 

1. 19 

•97 

.22 

.76 

•49 

■  27 

x88i 

82 

84 

•799 

•437  -362 

•78 

•56 

.22 

.81 

•53 

28 

•75 

•43 

•32 

1.04 

.96 

.08 

.62 

.42 

.20 

.817 

•473    344 

•74 

.60 

•14 

•75 

•53 

.22 

•75 

•47 

.28 

1.07 

.98 

.09 

•63 

.41 

.22 

.819 

•477    342 

.91 

.68 

•23 

•99 

•53 

•25 

•79 

•55 

•24 

1. 19 

1.09 

1. 10 

•73 

•45 

.28 

.740 

.441  .299 

•83 

.62 

.21 

•7^ 

•52 

.20 

.67 

•49 

.18 

1.09 

1.07 

.02 

.65 

•43 

.22 

85  

.627 

.391  .236 

.68 

•54 

•T4 

.66 

•48 

.18 

•.S8 

•44 

•  14 

•94 

.81 

•^3 

•55 

.40 

15 

Average., 

.760 

•444    ^'fi,    .79'    •^o 

.19 

•75 

•52 

•23 

•71 

.48 

.23 

I  06 

.98 

.28 

•64 

•42 

.22 

For  the  whole  United  States  the  earnings  per  ton  per  mile  were : 

1880  1881  1882  1883  1884  1885 

1.29  1.236  I  236  1. 124  ^•057 

The  receipts  p>er  ton  per  mile  in  the  various  sections  of  the  United  States,  according  to 
the  Census  of  1880,  were  : 


Group. 

Receipts 

Average  haul— miles 

Tons  per  tram 


I. 

New 

Eng. 

II. 

N.  Y., 
D.CInd. 

in. 

Va..  Ky., 
Miss. 

IV. 

Ill,  Mo., 

Minn. 

v.* 

La.,  Ark., 
Ind.  T. 

VI. 
Far  W. 
and  So. 

1.83 

55-7 
90.6 

1.02 
106. 1 
163.6 

2.15 
103.7 

55-5 

1.36 

1533 
122.8 

12.57* 

34^6 

61.3 

2  57 
166.9 

955 

U.S. 

X.29 
III. 
129. 


ii6 


CHAP,   v.— OPERATING  EXPENSES. 


Table  39. 

AVERAGE  COST   PER   TRAm-M.LE   OF  THE   FOUR   TRUNK    L.NES  AND   ENCUSH 

Railways. 


Year. 


N.  Y.  Cent. 


Cents  per 
Train. 


Erie. 


Revenue. 
Mile. 


Penna. 


Revenue. 

Mile. 


B.  &0. 


Cents  per  Engine. 


per  K 
Mile. 


1873. 
74- 


1875 


76. 

77- 
73. 
79 


126.2 
127.3 


132-5 


116. 6 
122.0 


95-5 
89.6 


71. 1 
67.7 


II9-3 


80.1 


114. 6 

104.0 

loi  .0 

95-5 


114. 2 
102.1 

99-5 
95-6 


76.2 

74-3 
73-6 
72.0 


63  9 


1880. 

81. 
82. 
83. 
84. 


107 -3 


1885 


112. 5 
118. 3 
123.2 

108.5 


101.8 


92.6 


105.2 

108.0 

100.5 

95-7 


83.8 


60.9 

57.3 
54-5 
52.2 


67.1 


91.2 


81. 1 
88.2 

85.7 
84.4 

78. 1 


71.6 
715 
69.4 
66.3 


69.0 


'liTIi^e  Shore  &  Michigan  Southern  statistics,  Tables  30,  3.,  and  others  fo^ 

lowing.  ,    ^       ...     .,  ^„  T,-_  heen   on  the  whole,  a  decline  in 

The  above  suffices  ^<'^f^^^^:^ZX\^^J:T^o.o^y  V^r  to„.n,i,e  show» 

expenses  per  train-mTle,  yet  the  aam  part  °    '  train-load  shown  in  Table  33.  and 

'nte  average  earning  per  ->-iie<,r  British  raih»aysha^e^^^^^^^ 
since  ,8,4,  having  been  $..36  in  1874.  $..^  '"  ""^i^if  .^"usVks  great,  so  that  the 
in  working  expenses  has  been  almost  as  ««"  "■  ^"„^„  "t. wSn  L^  afd  6,.36  cents  pe, 
Srr  Tro-  r^:  r^::^  S^r  rs„T"i™t  -  ^penses  hav.  bee.  in  cen» 

per  train-mile : 

1879.  1880. 

126  24  125 -^a 

66  00  64.74 


1877. 

, 130  50 

69  38 

Profit 6*" 


Receipts 
Cost.... 


1881. 

123.48 
64  56 


1882. 

123.80 
64.94 


1883. 

iai.76 
64 -34 


1884. 
119.13 
63.18 


60.34 


60  68 


58.92 


58.86 


57  43 


5S-9# 


.>,  more  uniform  than  would  be  shown  in  this  country,  even  in 

.,r^tr.::::^"^r::^^^  ^.«  ^  -  -  «^-ion  me^penses  o. 


CHAP,    v.— OPERATING  EXPENSES. 


117 


.the  British  railways  has  been  in  the  cost  of  maintenance  of  road.  This  has  fallen  from 
15.70  cents  per  train-mile  in  1874  to  12.76  in  1879  and  11.64  cents  in  1884.  Per  mile  0} 
road  expenses  ranjjed,  for  the  five  years  from  1874  to  1878  inclusive,  from  $1,865  to 
$2,020  for  maintenance  of  road,  and  averaged  $1,965.  Then  they  fell  off  suddenly  to 
$1,690,  and  have  never  been  so  low  since,  ranging  thence  to  $1,800  in  1883  and  $1,750  in 
1884,  and  averaging  $1,751  from  1879  to  1884. 

The  total  expenses  per  mile  of  road  have  ranged  from  $9,665  in  1875  and  $9,625  in 
1883  to  $8,775  in  1S79,  and  the  gross  earnings  averaged  $17,690  for  the  five  years  from 
1874  to  1878,  reaching  the  maximum,  $18,255,  in  1885. 


will  probably  be  greater  than  those  of  the  last  ten,  and  all  that 
we  can  be  sure  of  is  that  the  cost  per  ton-mile  (not  probably  per 
train-mile)  will  continue  to  fall  rapidly,  although  it  hardly  seems 
possible  that  it  can  fall  quite  so  rapidly  as  in  the  last  ten  years. 
Table  38  and  others  will  show  the  recent  changes  in  the  cost 
per  ton-mile,  and  Table  39  the  changes  in  the  cost  per  train-mile. 

106.  Nevertheless,  it  fortunately  happens  that  those  items  of 

expenditure  with  which  we  are  more  immediately  concerned 

those  which  are  affected  by  the  location  of  the  line — mav  be 
anticipated  with  reasonable  certainty  from  known  facts  and 
tendencies,  although  it  is  not  expedient  to  rely  too  much  on 
existing  statistics  of  the  iminediate  past  of  railways  in  respect 
to  some  items,  as  notably  steel  rails;  since  it  would  tend  to  the 
dangerous  error  of  overestimating  the  probable  expenses. 

107.  The  operating  expenses  of  railways  divide,  naturalh% 
for  the  purpose  which  we  have  immediately  in  view,  and  in  the 
main  for  all  purposes,  into  the  three  great  classes  below  : 

1.  Maintenance  and  Renewal  of  Way  and  Works,  in- 
cluding all  permanent  structures  and  buildings,  except  engine 
and  car-shops. 

This  has  until  recently  averaged  very  uniformly  25  per  cent 
of  the  total  expenses  on  all  American  railways.  It  is  now 
•decreasing  both  relatively  and  absolutely,  but  far  less  rapidly 
than  might  be  expected,  because  of  both  temporary  and  per- 
manent causes  below  mentioned. 

2.  Train  Expenses,  including  all  expenses  of  every  nature 
and  kind  connected  with  the  running,  handling,  maintenance 
and  renewal  of  motive-power  and  rolling-stock,  but  not  includ- 


Il8  CHAP,   v.— OPERATING  EXPENSES-RAILS. 

ing  any  station  or  terminal  expenses,  except  switching.  These 
expenses  have  heretofore  averaged  very  close  to  4^  per  cent 
of  the  total  operating  expenses,  and  cost  from  30  to  50  cents 
per  train-mile.  They  have  decreased  considerably  per  train- 
Lie  for  the  same  class  of  engines,  but  the  introduction  of 
heavier  engines  will  have  a  tendency  to  keep  them  more  nearly 
constant.  Relatively  to  the  other  operating  expenses  they  are 
crowing  continually  more  important. 

,    Station,  Terminal,  and  General  Expenses  and  Taxes. 
With  these  we  are  very  little   concerned.     Most  of   them  vary 
more    or  less    (for    the    most   part,    less)   with   the    tonnage   or 
volume  of  business;  but  all  of  them  are  independent  of,  or  in- 
appreciably affected  by,  any  of  the  details  of  hues  and  grades, 
and  therefore,  for  our  present    purpose,    may    be    ■"'^'"^^'l  J"" 
eether  and  neglected,  except  as  to  their  aggregate.     Taxes  at 
first  sight  appear  to  be  affected  by   the  alignment,  in   so  far  as 
thev  might  increase  with  the  length  of  the  road  ;  but  taxes  are 
based    upon    value    and    not    on    cost,    and   hence,    although 
nominally  based  upon  distance,  are  in  reality  much  ^^r^JJ^'^ 
based  upon  low  grades,  large  traffic,  and  good  rates      They  are, 
moreover,  too  small  and  variable  an  item  to  justify  their  consid- 
"a  ion  a    one  of  the  expenses  affected  by  any  of  the  details  of 
Xnment.     Station  expenses  also,  and  all   the   other  expenses 
me' tioned,  are  the  same  for  the  same  business,  whatever  c.uinges 
in  the  alignment  may  be  made,  except  as  such  change  bungs 
Idditionalway  business  ;  but  even  then   the  change  will  rarely 
be   sufficient  to  appreciably  modify  tiie  station  expenses      Fo 
its  indirect  value  in  such  cases  and  others,  and  as  a  n^at^r  of 
general  information.  Tables  75  to  80  give  what  the   cos    of  the 
virions  items  of  station   and   general  expenses  amount  to  on 
various  roads  and  in  various  sections. 

maintenance  of  way. 


CHAP.   V.—OPERATIN-G  EXPENSES— RAILS. 


119 


the  most  culpable  carelessness  as  to  the  quality  of  rails  purchased  ;  but 
the  difficulty  existed,  and  was  only  partially  remediable  at  best.  The 
cost  of  rail  wear  alone  per  train-mile  was  from  7  to  9  cents,  and  their  life 
on  important  lines  was  measured  by  months  rather  than  years. 

Under  these  circumstances  the  track  was  constantly  disturbed,  the 
ties  cut  full  of  spike-holes,  the  joints  imperfect  and  irregularly  spaced, 
owing  to  the  constant  cutting  of  rails,  the  line  and  surface  difficult  to 
maintain  correctly,  and  anything  like  a  permanent  rock  ballast  well-nigh 
out  of  the  question,  although  it  was  occasionally  used.  As  a  further  and 
very  natural  consequence  all  maintenance  expenses  for  the  above  items 
varied  to  a  very  remarkable  degree,  in  almost  exact  ratio  with  the  ton- 
nage and  rail  wear— as  indeed  they  still  do,  but  to  a  less  noticeable  ex- 
tent. Some  evidence  of  the  former  conditions  is  still  preserved  in  Table 
40.  but  further  space  need  not  be  devoted  to  the  discussion  of  conditions 
which  no  longer  exist  to  any  extent. 

110.  The  superiority  of  the  steel  rail  lies  not  so  much  in  its  greater 
strength  and  toughness  (although  it  is  stronger  by  20  to  30  per  cent)  as 
in  its  greater  homogeneousness  and  absolute  freedom  from  grain.  In 
other  words,  when  of  good  quality  it  is  tough  enough  to  last  until  it  is 
worn  out,  whereas  the  iron  rail  splits  into  pieces  long  before  it  has  lost 
any  serious  amount  by  wear.  The  wearing  properties  proper  of  iron  and 
steel  rails — their  resistance  to  abrasion— are  not  materially  different. 

111.  The  average  life  of  good  steel  rails  properly  manufactured  and 
inspected  so  as  to  eliminate  all  imperfections  arising  from  a  lack  of  ordi- 
nary care  and  skill,  and  weighing  60  to  80  lbs.  per  yard,  according  to 
the  weight  of  engine,  has  now  been  determined  with  a  considerable 
approach  to  certainty  to  be  about  150,000,000  to  200.000,000  tons,  or 
(what  is  probably  a  more  correct  way  of  putting  it)  from  300,000  to 
500,000  trains.  From  10  to  15  lbs.  or  three  eighths  to  five  eighths  of  an 
inch  in  height  of  the  head  of  such  a  rail  is  available  for  wear,  and  abrasion 
takes  place  at  the  rate  of  about  i  lb.  per  10,000,000  tons,  or  one  sixteenth 
inch  per  14,000,000  to  15,000,000  tons.  This  durability  may  be  regarded 
as  nearly  a  minimum  for  strictly  first-class  rails,  as  many  recorded  obser- 
vations indicate  a  much  higher  durability. 

112.  Unfortunately,  it  may  be  said  to  be  the  rule  rather  than  the  ex- 
ception, that  American  railways  now  buy  their  steel  rails,  as  they  for- 
merly bought  their  iron  rails,  without  any  effective  inspection  as  to  quality ; 
the  so-called  inspections,  when  there  is  any  even  in  form,  being  confined  to 
the  exterior  qualities  of  the  rail.  Unfortunately,  also,  a  few  years  since  the 
result  of  an  investigation  on  the  Pennsylvania  Railroad  into  the  wearing 


120 


CHAP.   V.-OPERA  TING  EXPENSES-TRAILS. 


CHAP,   v.— OPERA  TING  EXPENSES— RAILS. 


121 


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qualities  of  steel  rails,  which  showed,  or  seemed  to  show,  that  very  hard 
rails  did  not  wear  so  well  as  softer  and  tougher  rails,  was  taken  to  indi- 
cate that  softness  in  itself  was  a  desirable  quality  in  a  rail ;  and  the  pains- 
taking character  of  the  investigation  and  high  reputation  of  the  road 
having  given  these  conclusions  wide  dissemination,  manufacturers  for 
many  years  took  them  as  a  guide,  and  between  1880  and  1885  produced 
rails  which  have  deformed  readily  under  the  impacts  of  service,  espec- 
ially at  the  joints,  and  have  also  worn  away  very  rapidly,  so  that  their  life 
has  often  been  only  a  year  or  two  under  very  moderate  trunk-line  traffic. 
In  instances  it  has  been  only  a  few  months. 

113.  The  particular  cause  for  this  deterioration  of  quality,  whether  it 
is  chemical  or  mechanical,  or  both,  is  as  yet  obscure.  It  is  probable  that 
as  there  has  been  no  adequate  inspection  to  enforce  sound  practice  the 
chemical  composition  has  suffered  by  the  use  of  cheaper  ores,  cheaper 
men  to  supervise  manufacture,  and  less  care  in  all  the  processes.  But  a 
chief  cause  is  probably  mechanical— that  the  "  bloom,"  or  first  rough  cast- 
ing of  the  steel  from  the  converter,  out  of  which  the  finished  rails  are  fash- 
ioned, is,  in  tlie  first  place,  heated  unduly  hot  for  passing  through  the 
rolls,  and,  in  the  second  place,  is  passed  through  them  a  less  number  of 
times,  or  too  rapidly,  or  both.  In  order  to  roll  a  rail  very  rapidly  and 
with  few  passes  it  must  necessarily  be  very  hot,  both  to  begin  with  and 
when  it  finally  leaves  the  rolls.  Its  molecular  structure  might  be  expected 
to  be  disadvantageously  affected  by  this  lack  of  surface  compression,  inde* 
pendentiy  of  the  fact  that,  being  left  to  cool  slowly  after  it  leaves  the 
rolls,  it  is  thoroughly  annealed  by  the  same  process  as  makes  the  finest 
tool  steel  soft  enough  to  readily  suffer  deformation  from  dies.  The 
rapid  motion  of  the  rolls,  moreover,  may  not  give  the  molecules  suffi- 
cient time  to  flow  upon  each  other  properly,  and  a  spongy,  unhomogene- 
ous  metal  is  the  result. 

114.  Whether  or  not  this  is  the  true  explanation,  it  cannot  be  ques- 
tioned that  there  is  some  equally  simple  and  easily  remedied  expla- 
nation, because  certain  makers  do  produce  rails  of  excellent  quality 
which  are  sold  at  the  same  price  as  the  inferior  ones.  The  remedy, 
therefore,  lies  simply  in  more  thorough  tests,  especially  for  ability  to 
resist  deformation  ;  and  it  would  be  erroneous  to  conclude  from  this  ad- 
mitted but,  it  may  reasonably  be  hoped,  temporary  evil  that  the  estimate 
of  cost  of  rail  service  should  be  permanently  increased.  The  reasonable 
cost  per  train-mile  of  rail  wear  may,  on  the  basis  of  the  facts  above 
given  as  to  the  life  of  rails,  be  estimated  at  from  0.3  to  0.5  cents,  as  fol- 
lows: 


122 


CHAP,   v.— OPERATING  EXPENSES-RAILS. 


.  $2,850 
.     1.350 


Cost  of  one  mile  of  steel  rails,  95  long  tons,  at  $30, 
Less  scrap  value  of  unworn  steel,  say  nearly  half,    . 

Leaving  as  net  cost  of  wearable  portion,  per  mile,  .     .     .  $1,500 

Divided  by  total  life  of  300.0C30  to  500,000  trains,  this  gives  0.3  to  0.5 
cents  per  train-mile  ;  but.  in  view  of  the  present  difficulty  of  getting  good 
rails  and  tendency  to  increase  the  weight  of  trains,  we  may  assume  the 
even  figure  of  i.o  cents  per  train-mile  as  a  maximum  which  there  is  na 
need  of  ever  exceeding. 

No  allowance  for  interest  or  discount  to  represent  the  present  value  of  the 
scrap  is  made  in  this  estimate,  nor  should  there  be.  although  at  first  s^ht  an 
argument  to  the  contrary  seems  plausible.  The  whole  original  cost  of  the  steel 
is  a  permanent  part  of  the  cost  of  the  property  on  which  interest  must  be  paid, 
like  the  cost  of  the  ties  and  structures.  The  renewals  for  each  year  simply 
represent,  in  the  long-run.  the  rail  wear  for  that  year,  and  no  question  of  inter- 
est is  involved  in  the  cost  of  simply  using  the  steel  to  run  trains  over. 

115.  The  locomotive  alone  causes  by  far  the  greater  portion  of  this- 
wear-how  much  is  not  positively  known.    Freycinet.  a  French  engineer 
writer,  and  politician  of  much  prominence,  recently  Min>ster  of  Public 
Works,  estimates  that  the  locomotive  does  three  fourths  of  the  damage 
and  the  train  itself  only  one  fourth.     Launhardt.  a  German  writer  on  the 
subject,  after  noting  the  fact  that  the  locomotive  and  tender  together 
constitute  onlv  one  fifth  of  the  total  weight  of  train  on  the  Prussian  Stat^ 
railways  (it  would  be  considerably  less  in  this  country),  considers  that  half 
the  wear  is  due  to  the  locomotive  and  tender  and  half  to  the  train.     This 
in  all  probability  is  a  very  moderate  estimate.    Experience  on  the  gravity 
railwavs  in  Eastern  Pennsylvania,  worked  solely  by  "^^^^^d.  Pj^l^f^^-^"^ 
carrving  a  heavy  coal  traffic  with  the  ordinary  vehicles,  and  with  all  other 
usual  conditions  except  that  no  locomotives  run  over  the  ra-ls.  shows 
that  the  rail  wear  even  of  iron  rails  is  very  slight  indeed  under  heavy  ton- 
nacre.  but  with  light  loads  per  wheel ;  but  exact  figures  of  the  wear  cannot 
beVesented.     Mr.  O.  Chanute  investigated  this  question  somewhat  by 
placing  impression  paper  between  the  rails  and  wheels  and  determming 
The  arfas  of  the  surfaces  in  contact.     He  points  out  that  the  pressure  of 
the   drivers   approximate,   to  the   ultimate   crushmg   '^lf^''''\?^'^^ 
metal,  and  that  the  pressure  per  unit  of  area  is  very  much  less  with  ordi- 
nary car-wheels.     He  therefore  reaches  substantially  the  above  conclu- 
sions-that  from  one  half  to  three  fourths  of  the  total  wear  of  the  rails 
originates  from  the  engine  alone. 


CHAP,   v.— OPERATING  EXPENSES— TRAGIC  LABOR.      125 

116.  We  may  assume,  therefore,  the  cost  of  maintaining  fairly  good 
steel  rail  at  0.5  to  i.o  cent  per  train-mile;  the  cost  of  additional  engine- 
mileage,  the  car-tonnage  remaining  constant,  being  only  half  as  great. 
These  values,  although  in  round  figures,  probably  approximate  very 
closely  to  the  facts,  and  the  very  best  quality  of  rail  might  reduce  them 
one  half;  but  the  poorer  qualities  which  have  been  so  generally  sold 
of  late  years  greatly  increase  it,  when  so  poor  that  the  rail  speedily 
mashes  out  of  shape,  and  from  this  cause  and  renewals  of  the  still  re- 
maining iron  rails  combined.  2  cents  is  nearer  the  present  average  (see 
Tables  75-80).  Much  of  the  rapid  wear  of  rails  results  from  the  imper- 
fections of  the  fish-plate  type  of  joint  which  is  now  universal.  Its  de- 
fects of  principle  are  such  that  it  seems  quite  certain  to  be  supplanted 
within  a  decade  by  something  better — probably  by  something  closely  re- 
sembling in  principle  the  Fisher  "  bridge"  joint,  if  not  identical  with  it. 

TRACK    LABOR. 

117.  This  item  includes  all  the  considerable  elements  of  cost  in  main- 
tenance of  way  proper  outside  of  rails,  ties,  and  frogs  and  switches.  It 
has  been  unmistakably  falling  in  the  last  ten  years,  the  decrease  on  many 
roads  having  been  as  much  as  fifty  per  cent.  About  one  fourth  to  one 
third  of  this  decrease  is  accounted  for  by  the  decrease  in  the  rate  of 
wages  to  what  bids  fair  to  be  a  permanent  average  of  about  $1.25.  The 
remainder  is  almost  wholly  due  to  the  advent  of  the  steel  rail.  Except 
that  the  joints  are  still  so  weak  and  imperfect  a  detail,  it  would  unques- 
tionably fall  very  much  more. 

This  decrease  is  destined  to  continue,  but  less  rapidly,  for  some  time 
in  the  future  ;  and  in  making  estimates  of  operating  expenses  for  the  next 
few  years — if  not  for  a  long  period  ahead — the  apparent  indications  of 
the  statistics  of  other  roads  must  be  accepted  with  much  caution.  All 
the  roads  now  laid  with  steel — with  hardly  an  exception — are,  instead  of 
reducing  track  expenses  to  the  lowest  limit  possible,  maintaining  for  the 
time  being  something  like  the  old  rate  of  expenditure  and  perfecting  the 
condition  of  their  road  by  adding  better  ballast,  dressing  up  the  road-bed 
and  right  of  way,  improving  their  yards  and  switches,  etc..  etc.  This 
wise  procedure  is  in  reality  an  addition  to  the  capital  account,  but  for 
obvious  reasons  of  expediency  it  is  still  called  and  charged  to  mainte- 
nance of  way. 

118.  It  is  also  very  evident  that  the  larger  the  business  of  a  road,  i.e., 
the  more  prosperous  it  is.  the  more  likely  will  it  be  to  continue  this 
process  extensively.  For  example,  the  Pennsylvania  Railroad,  although 
laid  with  steel  and  ballasted  with  stone  throughout,  still  includes  a  very 
heavy  charge  per  mile  of  road  (although  not  per  train-mile)  in  its  annual 


124         CHAP.   V.-OPERATmC  EXPENSES-CROSS-  TIES. 


CHAP,   v.— OPERATING  EXPENSES— CROSS-TIES.         12$ 


accounts  (or  "  maintenance  of  way,"  the  reason  being  simply  that  it  is 
encaeed  in  giving  the  last  degree  of  finish  to  its  road-bed.  track,  and 
rightof  way!and  the  same  is  true  in  a  less  degree  of  many  other  ra.l- 

"^  n9   It  is  even  possible  that  this  practice  will  be  continued  indefinitely 
as  a  matter  of  permanent  policy ;  and  when  it  comes  to  dressing  up  the 
edge^o   rock  ballast  with  u  string,  sodding  and  planting  slopes,  etc   etc 
the^e  is  hardly  any  end  to  the  labor  which  may  be  kept  busily  employed 
'■  maintenance  of  way,"  nor  can  it  be  doubted  that  such  expenditure 
would  be  returned  in  part,  perhaps  many-fold,  by  its  value  to  the    me 
7or  its  value  lies  not  alone  in  the  direct  economy  of  such  fine  condition 
but  n  Its  value  as  an  advertisement,  by  making  travel  over  the  line  more 
attract  te  and  likewise  in  its  eflect  to  instil  habits  of  caution,  neatness 
Tnd  watchfulness  into  the  entire  force  of  employes.    Nevertheless,  such 
trcts  should  not  lead  us  to  confound  advertising  and  landscape  gardening 
with  ••  maintenance  of  way."  nor  blind  us  to  the  fact  concealed  from  sight 
in  the  current  statistics-and  likely  to  be  for  some  years  yet-that  the 
cost  of  r^aintaining  steel-rail  track  is  no  longer  greatly  affected  by  the  ton- 
nat      U  will  for  some  time  appear  to  be  the  case-as  it  came  very  nea 
to  bein»  actually  the  case  during  the  iron-rail  period-that  the  total  cost 
o°  mamtaining  'rack  varies  very  nearly  with  the  tonnage,  and  that  it  has 
not  blen  so  verv  largely  diminished  by  the  steel  rail  as  was  expected. 
Perhaps  therris' more- that  is  permanent  in  this  appearance  than  is  ex- 
acted a    cer,,in,y  there  is  unless  the  current  carelessness  in  buying  bad 
raiTs  ;;  good  prices  is  reformed;  but  the  following  estimates  (par.  ..4) 
seem  reasonable  and  sufficient.  . 

120   Crossties  alone  cost  from  S.20  to  S225  per  mile  of  mam  track 
«hout   vo  per  year  (one  eighth  of  the  total  number)  being  required  per 
■I  of  main  track  at  an  average  cost  of.  say.  5°  cents  per  tie  (it  is  often 
mile  of  mam  track,  at  an  a        =  ^^^.^  ^i.^^^s  as  many. 

rlr  '^:^;Tt:^:^^^  side-track  ties  Will  hardlv  aver- 
lie  in  CO  t,  however,  more  than  half  as  much  per  mile  per  year  as  mam- 
track  ties,  being  largely  "culls."  or  of  otherwise  inferior  quality. 

T     Fnol^nd  and  Europe  generally  the  number  used  per  mile  is  less-ordi- 
In  England  and  E"'°P    ^  >■  dimensions  being  in  England  some- 

r.ye'r:s::u;;rvrx -Hesinstead.^^^ 

r  •"  Tiin-gif h°;  a":  °'r  '^nz::^^.....  u 

sleepers  is  longer  Dy  aooui  ^yj y  nprhaos  mainly— to  greater 

'- :  CeV;:;::  :^:^:::^::^^^^ .-  (;-  ^-p- 

r:;rch Tmerrcrn  ro:ds  are  very  careless),  and  in  part  to  the  use  of  cast-iron 


Chairs  on  English  tracks  to  carry  the  rail  and  protect  the  sleepers  from  "cutting."* 
The  differences  of  practice  in  England  and  America  result,  for  the  most  part, 
from  differences  of  conditions,  and  not  from  mistakes  of  judgment  on  either 
side.     Where  wood  of  any  kind  is  dear,  hard  wood  out  of  the  question,  and 
labor  and  rails  cheap,  the  English  and  Continental  plan  of  widely  spaced  ties,, 
with  the  rail  carried  in  chairs,  is  at  least  defensible,  although  it  may  be  ques- 
tioned if  there  is  any  real  economy  in  spacing  ties  so  widely.     Where  good 
haru-wood  tics  are  cheap  it  would  be  folly  to  space  ties  farther  than  two  feet 
apart,  or  to  use  a  rail  requiring  chairs.     One  effect  of  the  English  plan  is  that, 
for  equal  stability  and  strength,  very  much  heavier  rails  must  be  used  than 
with  the  ties  nearer  together,  which  is  the  chief  explanation  of  the  fact  that  they 
are  heavier. 

121.  The  expense  of  cross-ties  will  probably  be  considerably  reduced 
within  the  next  ten  years  by  the  more  general  introduction  of  burnettizing- 
or  other  equivalent  processes,  and  it  will  then  be  almost  wholly  true,  as 
it  is  now  in  part,  that  the  life  of  ties  is  independent  of  the  tonnage.  The 
only  way  in  which  tonnage  seriously  affects  the  life  of  a  tie,  under  a  steel 
rail,  is  by  helping  on  that  process  of  local  rotting  which  is  popularly  and 
erroneously  known  as  *•  cutting"  into  ties.  The  difference  in  this  respect 
between  main-track  ties  (especially  if  of  soft  wood)  and  side-track  ties,  is- 
very  considerable :  but,  given  three  or  four  trains  a  day  over  the  tracks 
the  effect  of  even  twenty  or  thirty  more  trains  a  day  is  much  less  impor- 
tant, and  the  "cutting"  does  not  take  place  noticeably  faster.  This  re- 
sults from  the  fact  that  the  only  real  assistance  which  the  train  gives  to 
the  "cutting"  is  to  wear  away  the  rotted  surface,  so  as  to  leave  a  fresh 
surface  exposed  to  decay.  It  is  physically  impossible  for  the  rail  to  cut 
into  a  sound  tie  under  existing  loads,  except  as  assisted  by  the  greater 
rapidity  of  rotting  under  the  rail  than  alongside  of  it.  That  this  is  true 
is  conclusively  proved  by  the  fact  that  creosoted  or  similarly  preserved 
ties  do  not  cut  to  any  important  extent,  even  when  the  wood  is  soft. 

The  importance  of  this  distinction  as  to  the  cause  of  "  cutting"  is 
obvious;  since  it  follows  from  it  that  the  wear  will  not  be  verv  g-reatlv 
increased  by  an  increase  in  number  of  trains,  beyond  four  or  five  per  day, 
whereas  otherwise  the  wear  of  ties  would  be  directly  as  the  train-mileage. 

122.  Putting  ties  into  the  track  costs  about  one  third  as  much  as  the 
tie  itself,  including  all  labor  incident  thereto,  or  about  15  cents  per  tie, 
or  $50  to  $75  per  year.  Including  with  this  the  maintenance  of  ballast 
and  ditches  and  ordinary  track-walking,  but  not  including  policing  the 
right  of  way  and  road-bed,  special  watchmen,  removing  snow  and  ice, 
care  of  structures,  or  extraordinary  repairs — the  total  COST  OF  track 
Labor,  as  thus  defined,  properly  and  necessarily  chargeable  to  the  main- 


,26       CHAP.   V.-OPERATING  EXPENSES-MAINT.^Ay^ 


TT^I^aiUrack  once  reasonably  well  ballasted  and  in  good 

tenance  of  steel-ra  1  t""="^'  "  ^ji^  ^f  single-track  mam  Ime 

general  condition.  ,s  not «"  '-™  «300  pe  ^^^^^^  .^  ^^,y  ,^  ^ 

peryear.  or  say  hye  -"   -  eve,^  s,x  m,  e^  ^^  ^^^^^  .^  ^^^  ^^^„^^^,  „, 

very  Imuted  ^-^^^^^^^J'' I  ,„es  not  now  appear  probable  that  ,t 
maintenance  -  "°  ";™  d  to  advantage,  since  it  is  necessary  to  have 
can  ever  be  materially  reaucea  lo  °  ,      nrudential  reasons; 

..at  number  of  men  ava.  e  o;--^--J- .^..^r  the  track  has 
and  work  can  and  w.U  be  easily  to  ,^^^^j  ^^^     ^^^^^  ^^<.,,. 

been  brought  ,n  the  course  «' /[^^  '°  ^^^j  ^^e  present  rate  of  expen- 
se" nV^t'Tr  l-rf rt^e  r  rank^nl.  ^by  aimin.  at  absolute 

^Xtion.  permanently  i.-cur  -«"  "J::-^;,,,,,,  ,„  ,or  track- 
123.  About  $;o  per  n^ileoitne  above  t  ^^^^^^^^^  ^^^^  ^.^^ 

talking  which  -  about  -^    '^Tng  only  three  or  four  trains  per  day 

usually  be  ">-"f  °^"^^t  /o'd  that,  the  usual  expense  per  annum  is 
each  way.     For  a  tramc  oeyo  ^^^  fourths  of 

ahout  $5  p-.-''^':;„t;f;:aTa  3 1  o-^^^^ 

a  cent  per  tra.n-m.  e)  up  ^^-^"ZL     Snow  and  ice  is  another  source  of 
which  this  account  very  rarely  runs  ^         amounts  to  about  $5° 

irregular  expense  for  " --menance  o    w^       It  am  ^.^^  ^^ 

per  mile  of  main  line.  -"g'^^.  ;^^^j  P^^  ^Te  egions-™.-ing  much  high- 
doubie-track  ^-^^ ^^^^^l^f^.^  shallot  cuttings  are  the  greatest 
rLroTaro^r  a^rpLe  m  Lpect  to  snow  and  ice_a  consid- 
eration often  forgotten  in  fixmg  gradients.  ^j     „.„ack  railways  of 

"*•  ^''^r'ra;\1'"satre:  -trL'^Uo-  for  those  items 
ri;::;^cr:feVa«icaUy^^:/pendent  of  volume  of  traf^c  : 


...  $150  to  $225  >j 

Cross-ties lo  to      40 

Do.  for  sides, ,  en  to     200 


jjo.  lor  siucs, ICO  to 

Labor  on  track ^ 


Track-walking, 

Snow  and  ice 

Ballast,    .     .    .•     •     •     •     • 
Fences  and  miscellaneous. 


50  to 

o  to 

50  to 

25  to 


200 
100 

100 
50 


Per  mile  of  main  track, 
.not  including  mileage  of 
'sidings.    Common  track 
labor  $1.25  per  day. 


To  which  must  be  added  for 
cattle-guards,  open  culverts, 
and  crossings,  about 


$43S  to  $765 


Total,    .     . 
Steel  rails,  say . 


25  to      50 

$460  to  $8 1 5 
20  to     100 


CHAP,   v.— OPERATING  EXPENSES— MAINT.    WAY.      12/ 

To  this  estimate  must  be  added  certain  allowances  for  maintenance  of 
•structures,  for  the  maintenance  of  large  yards  and  terminal  facilities,  and 
for  extraordinary  damages  and  repairs,  and  also  for  the  wear  of  steel,  and 
other  expenses,  according  to  traffic.  The  amount  of  necessary  expendi- 
ture which  can  with  any  propriety  be  assumed  to  vary  directly  with  the 
tonnage  will  be — 

Steel  rails,  i  ct.  per  train-mile,  or  $20  per  1,000,000  gross  tons 
(including  all  expenses  for  relay- 
ing, spike,  etc.,  connected  there- 
with). 
Track    labor,    etc.,   \\  cts.  p.  t.  m.,  25    "  "  " 

Track  watchmen,      i    "       "  15    ".  "  " 


« 


M 


Total, 


$60    " 


(« 


«( 


This  amount  will  vary  almost  exactly  with  the  number  of  trains,  inde- 
pendent of  their  weight  and  length.  As  will  be  seen  from  Table  41, 
the  present  rate  of  expenditure  for  rail  renewal.s,  in  all  pnrts  of  the 
United  States,  is  much  higher  than  the  above,  or  about  $200  per  mile, 
but  this  can  hardly  continue  to  be  permanently  the  case. 

125.  Yet  it  must  be  admitted  that  there  are  some  strange  anomalies  in 
the  records  of  maintenance  of  way  expenses  which  seem  to  indicate  that 
such  expenditures  will  continue  to  bear  a  nearly  constant  ratio  to  the  train 
expenses  proper,  as  they  have  in  the  past.  For  example,  if  Table  41  be 
examined,  it  will  be  seen  that  in  every  item  of  maintenance  of  way — even 
those  which  seem  most  nearly  independent  of  the  number  of  trains,  like 
ties,  bridges  and  buildings,  repairs  of  road-bed  and  track — it  is  the  cost 
per  mile  of  road  which  varies,  and  that  the  cost  per  train-mile  or  the 
percentage  of  the  total  remains  far  more  nearly  constant.  In  fact,  the 
cost  of  rails,  which  one  might  expect  to  be  almost  precisely  so  much  per 
train-mile,  comes  much  the  nearest  of  all  to  being  uniform  per  mile  of 
road.  Beginning  with  the  section  of  heaviest  traffic, — the  Middle  States 
group,  which  includes  Ohio,  Indiana,  and  Michigan, — the  cost  of  rail  re- 
newals, in  cents  per  train-mile,  is 

3.50,    4.08,    5.03,  6.08,  6.72,  3.66,  averaging  4.43  ; 

while  that  of  road  and  track  labor  is 

9.2,    ii.o,    ii.o,    Z.l,  16.5,   8.3,    averaging  10.2. 

Individual  roads  may  be  compared  almost  at  random  with  similar  in- 
•dications.     The  following  two  roads,  not  selected  in  any  way  except  as 


•I 


128        CHAP,    V.-OPERATING  EXPENSESr^MAJNT,  WAY.. 


CH.   V,^OPER'G  EXP.—MAINT,   WAY  AND  ROLLG-STOCK.     1 29 


^^^pi^^^ng  extremes  of  traffic,  may  serve    as  illustrations,  the  years 
given  being  fairly  representative  : 


Penn. 
R.  R. 

1883. 


Char., 
Col.  &  Aug. 

1883. 

34 


Av.  U.  S. 

1880. 

6.1 


Trains  per  day  each  way  (main  line) 64. 5 

Repairs  road  bed  and  track  (cts.  per  train.    ^^^  ^^      ^^^^^^      ^^^^^ 

TotaTcostoi-trai>;-m"iie;;:::.:: 86.0     ••      87.5      ••      9.-o" 

Table  41. 
Maint;pnance  of  Way  Details. 

Deduced  from  U.  S.  Census  of  x88o.    See  also  preceding  table^ 


Groups  of  States. 


Trains 
each  Way 
Per  Day. 


New  England 

Middle 

Southern 

Northwestern. 
Southwestern, 
Far  Western 


Totnl  Cost 

Per 
Train -Mile 


Cost  Repairs  Road-bed  and 
Track. 


Average  U.  S 


*EsumateI~The  report  of  one  road  in  this  sm 
error  which  vitiates  the  total 


all  group  contains  an  obvious  and  largfr 


Repairs  road-bed  and 
track,  p 

Per  mile 

Tie  renewals,  p.  c. .  . 

Per  mile 

Bridges.        buildings, 
knd  fences,  p.  c. . 

Per  mile 

Rail  renewals,  p.  c. .. 

Per  mile 

Total,  p.  c 

Per  mile 

Cost  per  train-mile. . 


10.51 

$374 
2  64 

$144 

6.64 
$360 
4.20 
$220 

19.79 
$1,081 

$1.05 


$621 

2.78 
$i6S 

4-44 
$268 

3-47 
$236 

17-35 
$1,051 

%o . 906 


$273 
4- 30 
$97 

5-80 

$131  I 
6.16 

$210 
22.42 

$501 
$0,715 


12.45 
$361 

3-07 

$88 

6.0S 
$176 
«^.o3 
$166 

2 1 .  60 
$625 

$0.88 


13-59 
$480 

4.21 

$148 

3-45 
$121 
3.66 

$213 
21.25 

$749 
$0,608 


13.63 

$382 

3-48 
$98 

4-95 
$139 
6.8T 

$158 
22.06 

$619 
$1.21 


11.23 

$450 

3 -04 
$121 

5-14 
$207 
4.40 
$196 

19-41 

$778 

$0.91 


Table  42t 

Trunk-Line   Maintenance  Expenses  in  Cents  per  Train-Mile  by 

Decades  for  34  Years. 


N.Y.C&H.R 

i860 

1870 

i83o 

1884 , 

Erie. 

i860 

1870 

1880 

1834 

Penna.* 

1S60 

1870 

l83o 

1SS4 

Bah.  &  Ohio.j 

i860 

1S70 

i83o 

Phil.  &  Read. 

i860 

1870 

looO.  ..••.• 
1883 


Miles 
Run, 
Thou- 
sands. 


4-493 
11.430 
16.654 

16,453 

3-475 

9.326 

11.452 

11,305 

3633 
10.185 

17.241 
21,491 

3831 

7941 

12,768 

1.853 
5.100 

7.799 
12,347 


Expenses  Per  Train-Mile. 
Maintenance  of — 


Way. 


CtS. 
19.8 

39-8 
18.9 
24. 8 

24.1 

39-6 
20.7 
18.2 

21.4 
30.1 
14-5 
15.8 

15-9 
26.3 

18.3 

II. 2 
22.6 
26.3 
19. 1 


En- 
gines. 


CtS. 

9.0 

9.8 

5.8 
5-3 

9.0 

14. 1 

5-1 

4.4 

7.7 
9.1 
7.2 
7.0 

6.8 
6.9 
9-4 

8.6 
8.6 
7-8 
7-9 


Cars. 


cts. 
8.9 

15-4 
1-1.4 
10.3 

II. 7 

12.0 

8.0 

8.9 

8.2 
II. 7 
10.5 
II. 4 

8.7 

5-5 
20.6 

8.9 

13.5 
12. 1 
14. 1 


Total 

Rolling 

Stock. 


Cts. 

17.9 
25.2 

20.  *2 
15.6 

20.7 
26.1 
I3-I 
13-3 

15-9 
20.8 

17-7 
18.4 

15-5 
12.4 
30.0 

17-5 
22.1 

19.9 
22.0 


Total 
Ex- 
penses 

Per 
Train- 
Mile. 


CIS. 

95-2 
122.2 

107.5 
108.6 

94.6 

129.5 
108.5 
106.8 

99-3 

no. 6 

81.8 

81.8 

51.8 
68. 8 
82.0 

78.6 
108.2 

117-5 
117. 2 


Percentages. 


Track. 


20.8 
32.6 
17.6 
22.8 

25.5 

30.5 
19.0 

17.0 

21.5 
27.2 
17-7 
19-3 

30-7 

38.3 
22.3 

16  5 

19-3 
22.4 
16.3 


En- 
gines. 


9-5 
8.1 

5-4 
4.8 

9-5 
10.9 

4.7 
4.1 


,8 

2 

,8 

.6 


I3-I 
10. 1 

II. 5 

10.9 

7.4 
6.7 
6.8 


Car*. 


9-4 
12.6 

13.4 

9-5 

12.4 
9-2 

7.4 

8.3 
8.5 

10.6 
12.91 

13-9 

16.7 

8.0 

25.1 

11-3 
II. 9 

10.5 
12.0 


*  Pennsylvania  Division  only. 


t  Main  stem  and  branches. 


In  Table  42  is  given  a  record  of  expenses  for  maintenance  of  way  on 
five  trunk  lines  for  the  past  34  \^ears.  In  this  table,  it  will  be  noted,  an 
enormous  expansion  of  train-niileage  has  occurred,  ranoing  from  four-  to 
seven-fold,  while  yet  the  cost  of  maintaining  track  has,  on  the  whole, 
decreased  less  rapidly  than  other  maintenance  expenses.  There  has 
been,  on  each  of  these  lines,  a  considerable  expansion  of  track-mileage 
as  well  as  train  mileage,  but  this  increase  has  been  of  branches  only,  not 
of  main  line.  Therefore,  while  due  allowance  for  the  effect  of  this  greater 
9 


•srt?'-^ 


'^MMj^ 


,30    C^.   V.-O.E^C  ....-MAJ^^T^^^AV^f^^^O^^ 

i; -rri  7::;^^^.  ^y  --p--"  -''>  -^^^ '-  ^° 

lit^l^-  ,  -^^o^  of  thpPennsvlvaina  Railroad 

In  the  following  table  (43)  »f  "P"'  ^t  ,e  very^eg  n'-g  of  its  o„cr- 
only  is  carried  back  ten  years  f"rthcr-to  t  e  ve  y   J  avera:,ed 

ation.  and  every  year's  experience  .s  '"^l"''"'' *  ■^^^^^;f„„,  and  shorten 
together  by  half-decades  to  eUmmate  acc.denta  var  at-n  ^^^^  ^^ 

the  table.     In  this  table,  but  not  ,n  tl^  P--^"^";,;"^;^..,  ,,  u>e  single 
gine-wages  are  included  wiih  repairs  of  engines  ana 
item  •'  motive-power  and  cars :" 

Table  43. 

OP.a.x,KO  S....SX.CS  OK  .„.  '----rtrr^oi!^.--"     ^ 
Branches)  averaged  by   Half  Dlcades  from 

Operation. 


Years 
avekaged. 


Averajje  Miles 
Run. 

I    =    ICX30. 


Train  Load 

E.  only. 

Tons. 


Peu  Cent  of  Total 
EXPENDnURB. 


Molive-powcr 
and  Cars. 


1851-55.. 
1856-60. . 

1861-65.. 

1866-70. . 

1871-75. • 
1876-80. . 

1881-84. . 


1. 416 

2,934 

5- 530 

8.766 

14368 

16.182 

20.808 


101.6 
110. 6 

146.24 

158. 88 

187.76 
251.32 
298.45 


42.3 
42.9 
48.1 

41.4 
38.2 

39-4 

41.7 


Maintrnance 
of  Way. 

13.4 

23.7 
22.8 

27.2 

23  4 
i3.4 
20.0 


Per  Cent  of 
MiHhienancc 

(,f  Way  10 

Molive-|)ower 

and  Cars. 

317 

55-4 

47  5 
63.6 

61.3 

44-3 
48.0 


both  directions  see  Table  33. 

The  drop  in  the  last  two  half-decades  is  th^eflect  of  .he  introduaion 
o,  steel  rails  :  but  both  in  the  -or^^^J^';^  'Z^^Z^e  is  to  in- 

brings  this  tendency  out  still  more  clearly  : 


CH,   V.—OPER'G  EXP.—MAINT.    WAY  AND  ROLLG-STOCK.     131 

Table  44. 
Comparative  Cost  of  Maintenance  of  Way  to  Repairs  of  Engines  anc 
Cars  on  Each   of  the   Five  Lines  in  Table  42,  Cost  of  Repairs  of 
Engines  and  Cars  being  $1.00. 


N.  Y.  Cent. 

Erie. 

Penna. 

B.  &0. 

P.  &R. 

Average. 

i860 

1S70 

IS80 

iS34 

I. II 

1.58 

0.945 
1-59 

1. 16 

1. 51 
1.58 

1.37 

1.33 
1.45 
0.82 

0.86 

1.025 

2.12 

0.615 

»    •    • 

0.64 
1.02 
1.32 

0.87 

I.C53 
1.536 
1.056 
1. 172 

Average. 

1.306 

1.405 

I.II5 

1.915 

0.962 

1. 199 

The  contrast  in  the  proportionate  cost  of  maintenance  on  the  various  roads  is  in  part 
genuine,  but  in  part  no  doubt  results  from  considerable  difference  in  what  items  are  in- 
cluded in  "  maintenance  of  way"  or  of  cars  or  engines.  Less  pains  were  taken  in  this 
respect  than  to  have  the  comparison  of  one  year  with  another  correct  for  each  road  sepa- 
rately. 

The  last  column  of  this  table  is  the  most  instructive.  With  the  ex- 
ception of  1870,  which  was  an  abnormal  year,  it  will  be  seen  that  the 
tendency  of  maintenance  of  way  to  mcrease  in  relative  importance,  in 
spite  of  an  immense  growth  of  traffic,  seems  marked  and  clear. 

Table  45. 

Growth  of  English  Train-Mileage  and  Coal  Consumption  of  Engines 

Per  Mile. 


Train-miles  (i  =  1000) -j  ^g^ 

Increase  per  cent 

Engine-miles |  J^73 

Increase  per  cent 

Coal  burned,  lbs., per  train- j  1873 

mile \  1883 

Increase  per  cent 

Coal  burned,  lbs.,  per  en- j  1873 

gine-mile /  18S3 

Increase  per  cent 


Great 

Eastern. 


8.932 

13.679 
52.0 

10,819 

17.077 
57.8 

41.65 
4596 
10.35 

34.39 
36.81 

7.05 


Great 
Western. 


19.717 

31.128 

58.0 

22,778 

36.465 
60.3 

41-73 
37.69 

—  9.8 

36.12 
32.17 

-  10.8 


London,  B. 
&  So.  Coast 


5.300 

7.9S6 

50.8 

6.208 

9.630 

55.2 

43.33 
37.07 
16.9 

36.99 
30.74 
20.3 


Midland. 


ig.8ii 

330S7 

67.1 


57.18 
49.00 

14.3 


II 


The  mileage  represented  above  is  5,221  miles,  or  only  a  trifle  less  than  one  third  of 


^•i 


H'.    V.-OPIiKATING  EXPENSES-FUEL. 


132  ai 

and  train-load  is  given  only  for  the  Great  Eastern, 


The  change  in  engine- 


F.kst-Class  Gooo^^_^_^^_^^, 


Engine,  Great  Eastern 


Diameter  of  driving-wheels 

Cylinders 

Total  workin?  weight,  lbs 

Working  pressure 

Coal  Train: 

Consumption  per  mile 

Speed,  miles  per  hour 


1873 

5  ft.  3  in. 

16V6  X  74 

70,700 

X40  lbs. 

43.75  lbs. 

17-4 

398  tons. 

43.97  lbs. 


1883 

4  ft.  10  in. 

17^  "  24 
84,000 

X40  lbs. 

46.68  lbs. 

30 

438H  tons. 

4^.58  lbs. 


Per  cent 
increase. 


8.6* 


xa-4 

31.6 


6.78 
15.0 
X0.3 
D.  3  »7 


. fHrivers    The /«»^a/ increase  in  power  of  tbe- 

♦  Increase  per  cent  in  /.«^.''.  due  to  d«reasc jj  d  •  ^^^^^^  ^^^^  becomes  x08.6xXx.xa4  - 

engine,  due  both  to  decrease  of  dnvers  -^J^l^^^^^.^..^  ,,  ,he  increase  of  we.ght. 

,..x,or«.xpercent.ncrease.,almoste,acty    ^  .  a^st-class  goods- 

The  high  average  speed  of  English  -^^^J^^'^:Z^':^Z^  traffic,  are  noticeable. 

prevail  quite  as  strongly  in  England  as  ^^^^^^  ^^  j^„,  ^3,  1885,  which  paper,  how- 

ever,  makes  some  vc  y  writer. 

the  Railroad  Gazette  of  Sept.  n,  i»5,  ^7 

Train  Expenses. 

,„.  T>,e  COS.  of  fue,  per  .ross  -  ^  A-tt^l^^^^  IC 

a  minimum  of  $1.20  to  ^^r"  To  tl  at  the  least  favored  points 
r  ^f  ^Misr-ve:;  a^t  To^ ^ses  to  S^.^  or  more  at  points 

nHir:;n,ption  of  fuensas^an  average  a.^^^^^^ 

run  for  heavy  passenger  "a-ns.  J""'^-  passenger  engine  running 

30  lbs.  per  mile  for  light  P='==«"S^',"^'"';„^h  L  this,  or  from  20  to  30 
ight,  without  any  train,  burns  nearly      -"^^"^j^he"  American"  eight- 
,bs.  per  mile.     A  heavily  loaded  « -  ght  eng  ne  o  ^^^^ ,. 

wheel  type  will  burn  almost  75  'bs- P"         •  j^„^  ,^  t„  .^olbs.   The 


C//^/'.    v.— OPERATING  EXPENSES— FUEL. 


133 


JCI.;  and  from  data  given  there,  in  connection  with  the  above,  it  appears 
that  the  average  consumption  of  fuel  increases  considerably  less  rapidly 
than  the  power  of  the  engine,  as  might  be  expected. 


Table  46, 
Motive-Power  Expenses  Per  Train-Mile  on  Various  English  Railways. 


MOTIVE-FOWER  EXPENSES  IN  DeTAIU 


Engine  repairs — labor. . . . 
•'  **      — materials 

Total  engine  repairs. 

Wages,  engine  crew 

Fuel 

Water 

Oil  and  stores 

Repairs  shops,  etc 

Gas 

Office  and  general 

Total  motive-power.. 


16.74 


Great 

Western 

Railway, 

1869-76. 

Great 

Southern  and 

Western, 

X875. 

Midland 

Great 
Western, 

1875. 

cts. 
3.76 
2.46 

cts. 
2.82 
3.80 

cts. 
3-42 
2.78 

6.22 

6.64 

6.18 

4.66 

4-34 

4.32 
6.61 

3.84 
6.50 

0.42 
0.48 

0.50 
0.66 

0.32 
0.82 

0.12 

•    •    •    • 

•   •  •  • 

O.IO 

0.32 

•   «  •   • 

0.40 

0.66 

0.20 

19.76 


17.90 


The  above  is  from  a  paper  in  the  Transactions  of  the  Institution  of  Civil  Engineers, 
the  reference  to  which  the  writer  has  lost. 

127i  Several  newly  invented  types  of  compound  locomotive  engine,  having 
separate  high-pressure  and  low-pressure  cylinders,  are  being  extensively  intro- 
duced in  Europe  with,  it  is  said,  very  satisfactory  results.  If  we  may  judge 
from  what  has  already  taken  place  in  marine  engines,  it  is  probable  that  they 
will  eventually  come  into  general  use,  and  they  promise  a  considerable  reduc- 
tion of  fuel  consumption,  but  there  are  several  practical  disadvantages  wiih  the 
type  which  have  not  yet  been  fully  overcome — notably  a  difficulty  in  starling. 
The  burden  of  evidence  seems  to  be  that  the  coal  consumption  is  reduced  at 
the  rate  of  about  20  to  25  per  cent. 

The  consumption  of  fuel  on  English  railways  in  general,  however,  is  lower 
than  prevails  in  the  United  States,  although  very  much  less  so  than  commonly 
supposed.  It  was  reported  by  the  late  Howard  Fry,  in  a  paper  before  the 
Master  Mechanics*  Association,  at  from  26  to  35  lbs.  per  mile  run,  for  passenger 
service,  and  from  35  to  45  lbs.  per  mile  run,  for  freight  service  ;  but  the  follow- 
ing statistics,  which  have   been   compiled  by  the  writer  from  later  and  more 


^ 


134  CHAP.    V.^OrERA  TING  EXPENSES-FUEL. 

■    .       /T  Kioc  AC    A-*A^   SO)   show  that  the  actual  difference  bc- 
dcfiniie  statistics  (Tables  45.  4/-    43.  49;-  =»"" 

En      sh  ana  rreHcL  fu.,  consu.pUon.      The  ^^^^^^^^  ^^^^ 
«Dlamable  by  a  difference  in  the  average  tra.n-load;  .n  part  also,  d"""''"';  'J* 
befi    road  bed  and  alignn,ents.  use  of  copper  fire-boxes,  and   more  espec.ally 
^reater"km  and  care  in  firing.    The  longer  average  tr.ps  of  Amcr.can  eng.nes 
o  her  thn       being  equal,  should  reduce  the  average  fuel  ""su.-npuon.     The 
oiner  inin5,b  uciu^    ^  u^ku,  that  fuel  economy   s  subordinated  m 

ZtiTaririlnrHlvriXtu  C:  trbl."  herea^s  in  England  heavy 
St  uls,  or  what  would  pass  for  such  in  America,  are  the  excepuon. 

Table  48. 

PASSENGER  TRAIN   CoAL  CONSUMPTION.    PENNSYLVANIA   RAILROAD. 

~~1 


Year. 


1874- 
1875- 
1S76. 

1S77- 
1S78 

1879- 
i8ao. 
1881. 
1882. 
18S3. 
18S4. 


Cars  Per 

Train. 


Coal  Per  Mile. 


5- 

5 

5- 

3 

5- 

6 

5. 

10 

5 

13 

5 

29 

5 

.27 

5 

.01 

5 

.14 

4  95 

5 

02 

Per  Car. 


9.0 

8.5 
8.3 
8.72 

8.43 

8.40 

8.76 

10.78 

9.61 

10.84 

10.67 


Total. 


49-5 

45-1 

46-5 

44-5 
43.2 

44.4 
46.2 
54-0 
49.4 

53-7 
53.6 


The  last  column  is  not  given  in  the  reports,  but  is  obtained  by  multiplying  together 

*-';i:  ^:^^i^  cen.  m  the  coal  ^^:^:-^j:^:^^, 

t^ZC^^Z^ZrZ:'^^^  .ileakand  the  much 
-Thir^irr^a  has  been  selected  ^;;^^^::--:^::^ftX^  ^^l 

accessible.  It 'v--^:-o::rrro7t::::rd  began o„  -^-  sho« 

&  Mrhl^rsotu  :rn   for  example,  several  years  before  it  began  on  *e  Peansy.van.. 
The  I'hLelphia  &  Reading  runs  about  58  lbs.  per  passenger  tram-mde. 


.  Table  „  »a,  misplaced  i.  maV.ng  up  this  Pan.  and  i.  give  at  the  end  of  the  volume. 


CHMP.    v.— OPERA  TING  EXPENSES— FUEL. 


135 


Table  49. 
Average  Freight-Train  Coal  Consumption,  Pennsylvania  Railroad. 


Coal 

BuR.NEO  Per 

MiLB. 

No.  Cars. 

Train -load 
Totis  Fr't 

Approx. 
Toul  W't 

Year. 

Per  Cur. 

of  Irani; 

Per  Ton 

Per  Car- 

Per  Train- 

Tons. 

Freiglit. 

Mile. 

Mile. 

1874.- 

21. 1 

(6.5) 

327 

(.646) 

4.2 

88.5 

1875- . 

21-5 

(6.7) 

•    •    •    • 

(.627) 

4.2 

90.2 

1876. . 

22.2 

(6.9) 

•    •   •    • 

(.609) 

4.2 

93.1 

1S77.. 

22.92 

(7-1) 

•   •    •   • 

(.585) 

4.15 

95.0 

1878.. 

25.06 

(7.3) 

«    •    •    • 

(-497) 

3-63 

91 .0 

1879.. 

25.60 

7-55 

436 

.490 

370 

116. 7 

i83o. . 

25.77 

8.18 

•    •    •   • 

•477 

390 

112. 0 

i83i.. 

24.40 

8.68 

«    •    •    • 

.492 

4.27 

109.3 

1882.. 

24-55 

9.01 

•   •    •   • 

.494 

4-45 

104.3 

1883. . 

23-97 

10.28 

•    •    •    • 

.454 

4.67 

100.5 

1884.. 

25.66 

10.58 

566 

•430 

4.55 

99.2 

The  tons  freight  per  car  was  obtained  by  dividing  the  coal  consumption  per  car  given 
by  that  per  ton  ;  the  approximate  total  weight  by  assuming  the  average  car  to  have 
weighed  18,000  lbs.  (9.0  tons)  in  1874,  19,000  lbs.  (9.5  tons)  in  1879,  and  23,000  lbs.  (11.5 
tons)  in  1884 ;  the  coal  burned  per  train  by  multiplying  the  number  of  cars  by  the  coal 
per  car.     The  remaining  figures  are  direct  from  the  report. 

The  figures  in  parentlieses  above  are  estimated,  not  being  given  in  nor  deducible  from 
the  reports  ;  but  they  are  not  far  from  the  truth,  a  gradual  increase  of  average  car-load 
having,  as  is  well  known,  been  going  on  even  in  the  years  1874-9,  v.-hich  has  jrone  on 
much  more  rapidly  since.  One  of  the  chief  reasons  why  the  average  car-load  has  been  so 
small,  on  all  the  American  east  and  west  trunk  lines,  has  been  the  enormous  dispropor- 
tion (more  than  3  to  i)  in  east-bound  to  west-bound  traffic.  The  increasing  coal  ship- 
ments westward,  to  a  considerable  extent  in  cars  coming  east  with  grain,  has  in  recent 
years  helped  much  to  decrease  this  disproportion  on  some  roads  ;  so  that  the  increasing 
average  car-load  is  not  due  solely  to  increased  capacity  of  cars,  although  that  is  the  chief 
cause. 

The  proportion  of  switching  is  very  heavy  on  English  railways,  the  ratio  of 
engine-miles  to  train-miles  being  almost  uniformly  as  high  as  125  to  100,  and 
in  some  cases,  as  high  as  177  to  100. 

On  German  railways  the  average  consumption  is  about  50  lbs.  per  revenue 
mile,  costing  about  six  cents. 

128.  The  cost  of  fuel  per  mile  run  can  be  calculated  from  the  above 
data  for  any  particular  line.  In  absolute  cost,  it  is  by  far  the  most 
variable  element  in  the  running  expenses  of  railways,  but  its  percentage 
to  the  other  expenses  is  considerably  less  variable,  owing  to  the  fact  that 


II 


,36  C/fAP.    V.-OPEKA  TJNC  EXPENSES-FVEL. 

.,e  san,e  causes  which  n,aUe  Cue,  --^^^:;^:r;::t^^ 
expenses  to  a  considerable  extent.     The  total  avera  e  cos    P 

..^.ains,  according  " -'^^^p^slania  r'  ^ad  .  to  about  :o  cents 

5  cents  as  a  minimum  (on  the  Penns>  '^n  (g„ 

n  Massachusetts  and  ,.  cents  on  the  P^<=^^,^.      ^^^f;     J.^ed  cost  runs 

roads  in  the  Rocky  Mountam  res.o"  on  winch  the  repo  ^  ^^^^^_ 

still  higher  than  this-up  to  as  mud>  ^^'"Trthecttuns  still  lower- 
there  are  a  few  specially  favored  -^^^  -*''-'     ::r„a  are  n.ostly  due  to 

r^r,:;  ::rac\::rt:airmS':ith  a^ctious  .lowances. 

Table  50. 

EFFECT   OF   LENGTH   OF   TRA.K   ON   COAL  CONSUMPTION. 

J  ij»o««  Pa««enper  Trains— Michigan  Central 
tCoo.pa«U,=  Coa,  Con.u.p.ion  with  L.^.-^Hea„  Passenger 

Light  Tkains. 


CHAP,    v.— OPERATING  EXPENSES— FUEL. 


137 


No.  of 
Round 
Trips. 


Av  No. 

Cars 
Handled. 


Coal  Consumption,  Per  Mile. 


Av.  Temp. 


Per  Cent 

Correction 

for  Temp. 


Corrected 
Lbs.  Coal 
Per  Mile. 


3 
1 
7 

2 

3 
I 


16 


7i 

74 

8 

•  • 

8i 

71 

9 

81 

9^ 

73 

Hi 

•  • 

8.78 


,8 
.6 
.6 


75-4 


87 
87 
79 


84-4 


79-3 
78.6 

79-4 
85.4 
77-3 
75.0 


79-3 


33  ^ 

29.5 

36-3° 

44.2: 

27.0 

32.4° 

-3-55 

+  1.55 

—  0.25 

4-3-15 
4-7.10 

-  1.50 
4-1.20 


77  07 

79.82 
79.20 
88.10 
82.80 
73  88 

80.25 


The  correction  for  temperature  is  by  a  rule  deduced  by  the  writer  from  records  cover- 
ing many  millions  of  train-miles,  that  the  effect  of  differences  of  temperature  alone^ 
length  0/  train  and  all  other  conditions  being  equals  is  to  increase  or  diminish  coal  con- 
sumption at  the  rate  o/onE  per  cent  /or  each  two  degrees  Fahrenheit  (and  a  small  frac- 
tion more)  difference  of  external  temperature :  a  rule  easily  remembered  and  one  which 
appears  to  apply  fairly  well  to  both  passenger  and  freight  service,  and  to  be  practically 
invariable  whenever  the  effect  of  all  other  causes  for  variation  can  be  eliminated. 

Since  the  effect  of  increasing  the  average  length  of  train  from  5.56  to  8.78  cars,  or  3.23 

cars,  is  shown  above  to  increase  coal  consumption  from  58.56  to  80.25  lbs.  per  mile  run, 

21.69  lbs. 

or  21.69  lbs.,  or  at  the  rate  of =  6.736  lbs.  per  mile  per  car,  we  have, 

3*^2  Ccirs 

Lbs.  coal 

per  mile. 

For  the  long  train,  burning, , 80.25 

Consumption  due  to  cars,  8. 78  x  6. 736  = 59-14 

Leaving  as  due  to  the  engine  alone,  without  cars, 21. 11 

For  the  short  train,  burning, " 58.56 

Coal  consumption  due  to  cars,  5.56  X  6.736, 37-45 

Leaving  as  due  to  engine  alone,  without  cars,  as  above,      ,    ,    21. 11 

This  result  agrees  closely  with  what  direct  expjeriment  has  shown  to  be  the  consump- 
tion of  heavy  passenger  engines  running  light.  Mr.  Reuben  Wells  some  years  ago  made 
a  test  of  a  liglit  passenger  engine,  14  x  22  cylinders,  running  108  miles  with  six  stops  at 
22  miles  per  hour,  and  losing  about  one  sixth  of  its  time  only  in  stops,  with  a  consump- 
tion of  only  18^  lbs.  per  mile,  and  this  test  was  in  warm  weather.  Allowing  for  the  dif- 
ferences of  weather,  size,  and  number  of  stops,  the  correspondence  is  close,  and  other 
tests,  which  need  not  be  referred  to  in  detail,  have  shown  from  20  to  30  lbs.  Mr,  Wil- 
liam Stroudley,  Mechanical  Superintendent  of  the  London,  Brighton  &  South  Coast  Rail- 
way, alleges  in  a  paper  before  the  Institution  of  Civil  Engineers  (1885),  that  a  heavy  pas- 
senger engine  was  run  light  between  London  and  Dover  with  a  consumption  of  only  7  lbs. 
per  mile.  As  the  distance  is  only  a  little  over  50  miles,  however,  and  the  quantity  stated 
would  amount  to  only  a  few  inches  over  the  bottom  of  the  fire-box  of  20  square  feet,  or 
barely  as  much  as  the  same  record  shows  was  habitually  used  to  get  up  steam,  there  is 
probably  some  error  in  this  estimate. 

The  best  existing  direc  t  evidence  on  the  effect  of  length  of  train  on  coal  con- 
sumption is  given  in  Table  50.  There  is  considerable  difficulty  in  obtaining 
records  of  this  kind,  in  which  a  series  of  trains  of  widely  varying  lengths  are 
run  with  all  other  conditions  approximately  identical.  The  correctness  of  the 
result  reached  in  Table  50  may  be  tested  by  grouping  the  various  single  records 
differently — a  test  which  should  never  be  omitted  in  computations  of  this  kind, 
since  it  will  often  be  found  that,  when  grouped  in  one  way,  the  records  will 
appear  to  lead  to  one  conclusion,  while  if  grouped  in  another  way  they  will 
indicate  something  quite  different. 

Tested  in  this  way,  the  correctness  of  the  preceding  conclusions  is  confirmed. 
If,  instead  of  averaging  the  single  tests  together  in  only  two  classes,  of  "light" 


JilB 


I  38  CHAP.  V.^OPERA  TING  EXPENSES-FUEL. 


CHAP,    v.— OPERATING  EXPENSES— REP' KS  ENGINES.      1 39 


"  ~      ,.   -A    ♦!,•  oc  rp«;ts  as  tabulated  above  into  four  equal 

and  -heavy"  trains,  we  div.de  the  25  tests  as  tal.  ^^^^  ^^^^^ 

.roups  of  six  tests  each,  as  nearly  as  may  be,  and  see  how  ^^^^ 

Lned  beneath  the  table  (lbs.  coal  ^^^ ^^r.^^ ^oll^^^^^^     as  follows: 
with  the  actual  coal  consumption,  we  find  a  close  corresp  


No.  of 

Roun.l  Trips 

Averaged. 


Cars  her  Train 


Pounds  Coau  Per  Milk. 


~" r^^TTfiZr^^eciinc  for  difference  of  temperature. 

•  Actual  consumpuon  afier  corrccimt  »"i  «  

.  f  rh.  rP.nlts  under  this  entirely  different  grouping  is 

The  correspondence  of  the  results  ""^^J  ^  \    j^  dearlv  conform 

surprisingly  close,  '^^f^^^^^^^^^^^^^^  the  fuel'consump. 

r  •:  -^^ct^yri^::^:^::  -  ^^^^^^  -  -  --  ^^  ^--  -  ^^ 

-nt^lietermined^awfor^^ 

by  records  on  a  large  ^f ;;;';;^'^  ^^^^  ,  R,,road.  alone  among  American  rail- 
determining  the  ^-;^  J^^^  ^^f .^  ,,,  consumption  per  carmile  and  per 
ways,  publishes  a  ^^^^^^^^^'"frs  oer  train  for  every  month  in  the  year.  As 
^-^"■"^^"e:fthe"  :::e"rAs?-^':h^  passenger  tram  and  passenger 

:a^Z^c\nlm;tio:on  each  of  its  three^ramic^ 

Pounds  of  Coal— 


Penn«5ylvania  RR.  Div 

U.  RR-  N.  J.  Div 

Phila.  &Erie  Div 

:  rirZir^the  coal  c^sumption  per  mile  according  to  the 


Computed  Coal  Cons.mition. 
Pounds  per  Train-Mile. 


Actual. 

Pounds 
per 

Train- 
Mile. 


Ekkok  in  Fokmula. 

+  or-. 


Penna.  RR.  Div. 
U.  RR-  N.  J.  Div 
Phila.  &  Erie  Div 


The  correspondence  here  is  close,  if  we  remember  that  the  Pennsylvaaia 
Division,  while  making  fewer  slops  than  the  Michigan  Central  train,  whose 
record  was  used  in  table,  has  a  large  proportion  of  heavy  sleeping-cars,  while 
the  New  Jersey  Division  not  only  has  a  large  proporiion  of  parlor-  and  sleeping- 
cars  on  through  trains,  but  makes  an  enormous  number  of  stops  on  way  trains, 
boih  into  New  Jersey  and  into  Philadelphia. 

129.  The  conclusion  is,  therefore,  not  unfair,  that  something  like  6^ 
to  6|  lbs.  of  coal  per  mile  is  added  to  the  consumption  for  each  passenger 
car  of  20  tons  or  more  moved  at  way-train  speed,  and  for  each  sleeping- 
car  of  30  tons  or  more  moved  in  tlirougli  trains  making  few  stops,  and 
that  the  locomotive  alone  is  to  be  charged  with  rather  more  coal  than 
that  due  to  three  cars. 

This  leads  to  the  conclusion  that  dead  weight  to  the  amount  of  30  tons  added 
to  a  train  of,  say,  five  cars,  will  certainly  not  increase  coal  consumption  as  much 
as  to  add  another  car,  both  because  it  does  not  increase  air  resistance,  and  be- 
cause the  added  load  decreiises  somewhat  the  rolling  resistance  per  ton.  If  we 
assume  it  to  add  5  lbs.  per  mile  to  the  coal  consun)piion,  we  are  certainly  not 
underestimating  it  proportionally.  Adding  6  tons  per  car,  therefore,  to  the 
average  weight  of  a  train  of  five  passenger  cars  means  no  more  than  an  in- 
crease from  55  to  60  lbs.  per  train-mile.  If  we  assume  this  5  lbs.  of  coal  to  be 
worth  one  cent  (at  the  rate  of  $4  per  ton  of  20C0  lbs.  for  coai),  if  an  extra  pas- 
senger at  3  cenis  per  mile  be  attracted  to  the  train  every  third  trip  he  will  pay 
for  the  loss  of  fuel  due  to  adding  6  tons  to  the  weight  of  every  passenger  car — 
which  goes  a  little  way  toward  explaining  the  tentiency  to  increase  weight  for 
the  sake  of  luxury,  which  seems  so  reckless.  This  appears  to  neglect  the  efifect 
of  the  extra  weight  on  grade  resistance,  and  so  in  a  sense  it  does  as  well  as 
many  other  effects,  but  not  50  much  as  it  appears  to.  since  the  effect  of  gradients 
is  included  in  the  records  which  we  have  used. 

The  use  of  wood  for  fuel  is  rapidly  passing  out  of  date  in  all  parts  oif  the 
United  States.  About  i^  cords  of  good  hard  wood  (a  cord  being  4X4X8  feet, 
or  12S  cubic  feet,  and  weighing  from  3200  to  3600  lbs.  when  well  seasoned)  is  usu- 
ally taken  as  equal  to  one  long  ton  of  coal.  Inferior  woods  will  average  from 
two  down  to  even  three  cords  of  wood  equal  to  one  ton  of  good  coal,  but  some 
of  the  poorer  Western  coals  will  evaporate  only  half  or  two  thirds  as  much  as 
good  bituminous  or  anthracite. 

REPAIRS  OF  ENGINES. 

130.  The  fall  in  the  cost  of  this  item,  of  late  years,  has  been  very  rapid, 
but  it  is  probably  now  at  about  its  minimum,  unless  and  until  some  new 
process  of  manufacturing  steel  and  iron  shall  materially  reduce  the  cost 


81^ 


140     CHAP 


V -OPERATING  EXPENSES-REF RS  ENGINES. 


a/A  P.    v.— OPERATING  EXPENSES— REP' RS  ENGINES.     M^ 


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,42     CHAP.   V.-OPERA  TING  KXPENSES-REP  KS_EKC1NES^___ 

•  1  ^'^iK,  in  QViflnf»s      For  this  purpose  solid  steel 

"'Tfe'"b!e"";)on  pp.  .40  and  ,4:  shows  the  cost  of  engine  repairs  per 
en  J  e-, nil    0"  the  Pennsylvania  Ra.lroad  for  a  long  senes  c^  yea.  and 
sufficiently  ilU.strates  the  general  tendency  of  the  cost  of  th.s  .tern,    he 
ablX  wing  however,  it  nmst  be  ren.embered.  nothnvg  '"ore  than  the 
cos  o    abo.-  and  n.aterials  directly  applied  to  repairs  and  renewals  proper 
wi  ho'     including  any  allowances  or  charges  for  -P-s.  and  renewals  o^ 
Tools   shops   machinery,  and  oiher  items,  for  which  see     ..ble  57  and 
othe,;      n     figures  given  are  h.  all  cases  for  what  is  now  known  a   the 
Pennsylvania  Railro.rd  Division,  excluding  the  la.er  acqu.s.t.or.s  of  the 
Philadelphia  &  Erie  Railroad,  and  United  Railroads  of  New  Jersey. 

m  F  om  the  above  table  it  appears  that  the  cost  per  m.  e  on  the 
Penn  ylvlnia  Railroad,  at  the  present  time,  is  from  5  to  6  <;ents  for  engme 
feoa^rl  proper,  and  this  may  be  consulered  the  mnunmm  under  the  mos 
avor'b  e  cLun,stances,  on  roads  having  a  heavy  traffic  and  convement 
o  the  great  iron  and  coal  centres.  Many  roads-perhaps  n.ost  roads- 
.how  a  lower  average  tha..  this;  but  such  a  result,  when  .t  contnmes  for 
more  Ua^  two  or  three  years,  is  very  apt  to  be  one  of  the  before  men- 
Zed  .niracles  of  booklLping,  based  upon  running  an  unusually  large 

"Mr  ;Ve'Sch!.s°e«rroads  average  about  5*  cents_a  surprisingly 
low  nv'e^aie  for  that  region  of  the  country,  but  doubtless  very  nearly 
correT  U  may  be  explained  largely  bv  the  greater  proportion  o  pas- 
Tr  tr,  ns  (more  than  one  half  the  whole,  as  against  about  one  fourth 
::r  r:  :  Tn^e-f  the  country),  and  also  by  the  fact  that  a  v^y  exces 

^i  tViA  frpio-ht  iraflfic.  as  compared  with  the  lest  oi  me 
:o:^r;°rn;::ely  blT:ess  with  hght  load^.  a  denser  settW  region 
country.  'S  mere       y  t^ain-load  heavily  in  th.s  way. 


CHAP,    v.— OPERATING  EXPENSES— REF RS  ENGINES.     143 

all  classes  of  engines,  on  roads  with  sufficient  traffic  to  have  proper  facili- 
ties for  economy  in  shop  work.  Wagesdo  not  vary  widely  in  any  part  of 
the  United  States,  and  no  causes  exist  for  very  wide  fluctuations  in  this 
item. 

Table  52. 
Cost  of  Locomotive  Repairs  in  Detail. 

Performance  and  Cost  of  Three  Passeng^er  Engines  for  Five  Years,  New  York  Central  & 

Hudson  River  Railroad  (Hudson  River  Div.). 


Per- 
cent- 
ages. 


Machinery  (and  ^  machin 
ihi  lubur) 

Drivers  and   tires  (and  ^ 
muchinisi  labor) 

Trucks     (and     blacksmith 
labor) 

Boilers  and  flues 

Wood-work  and  flttings, 

Painting 

Totals,  cents,  per  mile 

Percentages 


Engine  O 

NLV. 

Tendef 

t. 

•       Engink  and 
Tendek. 

Mat. 

lab. 

Total 

Mat. 

Lab. 

Total 

Mat. 

Lab. 
cts. 

Total 

CIS. 

cts. 

CIS. 

CIS. 

cts. 

CIS. 

CU. 

CIS. 

.214 

.465 

.679 

— 

•  •  •  • 



.214 

.465 

.679 

.063 

•155 

.218 

•  «  •  • 

.018 

.018 

.063 

•173 

.236 

.114 

.082 

.196 

.150 

.020 

.170 

.364 

.102 

.366 

.361 

.224 

.48s' 

.021 

.017 

.038 

.282 

.241 

•523 

.014 

.056 

.070 

.008 

•OI.S 

.023 

.022 

.071 

.093 

.024 

.049 

•073 
1.721 

.012 

.010 

.031 

.036 

.068 

.104 

.690 

1. 031 

.191 

.089 

.280 
14.0 

.881 

1.120 

2  001 

34-5 

51  5 

86.0' 

95 

4-5 

44  0 

56.0 

100. 0 

% 

33-9 
XI. 8 

18.3 
26.1 

4-7 

100. o 
100. o 


u 

M 


«( 


Average  mileage  per  engine  for  the  five  years  included, .        .        .  416,163 

"        year 83,232 

•♦             "                "        month, 6,936 

••             *•                "        day  in  service,  ....  278 

per  cent  of  time  »dle  for  repairs  or  otherwise,    .        .        .  t-i-"^ 
"       for  all  enjrines  of  Pennsylvania  Railroad  from 

the  beginning  of  its  history  (see  Table  51),       ....  i7-9}( 

The  above  table  represents  the  very  lowest  cost  at  which  locomotives  can  be  operated 
in  actual  service  : 

First,  Because  the  eng:ines  were  entirely  new  at  the  beginning;  of  the  record,  and 
although  the  record  covers  something  over  half  the  average  mileage-life  of  a  locomotive 
(which  may  be  taken  as  600,000  to  800,000  miles),  yet  the  latter  half  of  its  mileage-life 
(including  cost  of  renewal)  would  average  three  to  four  times  as  high  as  the  first  half ; 

Secondly,  and  equally  important.  Because  of  the  very  heavy  mileage  duty,  which  is  at 
least  three  times  the  average  of  American  f>assenger  engines,  and  four  to  six  times  the 
average  of  European  engines.  This  heavily  reduces  the  expenses  arising  from  frequent 
<X)oIing-off  of  the  engine.     Compare  the  following  Table  53. 


■' 


ill 


■ 


,44     UIAP.    V.-OPEKATmC   EXPENSE^REFR^^^^CT^ 


Table  53. 

Engine  Repairs  Per  Mile  Run.  in  Detail.  .86S-.875. 

/.     rt   c;n  &  W   Ry.  of  Ireland  (1866-75). 
Including  both  Repairs  and  Renewals.    Gt.  So.  &  W.  Ky. 


Engine  anu 
Tbndrk. 


icx>  o> 


Machinery 

Drivers  and  lires  (and  1 

frames) f 

Trucks  ' 

Boilers  and  flues. 
Wood-work  and  fillings. 
Pajnttn{j 

Totals,  cents  per  mile 

Percentages. 

and  renewals  separately. 

,34.  Rep.,  o.  cou.e  ^-^^^:^£x^i:^z:t^ 

with  a  very  considerable  decree  "  «"^'f  J'^^.^"  "^  V^pairs  of  tender. 
About  one  eigl.tl.  of  the  cost  of  eng.ne    ^pa-^  '=  ^r  repa  ^^^^ 

which  is  of  course  substantial  y  the  --«  /«    ^'J  ^^J^^J,  \^^  „bor,  as 
remaining  cost  is  almost  equally  d'vded  between  ma  e  ^^^ 

will  appear  from  Tables  5^:53-55-56.     ^he  cost  of     -  >  ^,. 

slightly  afiected  by  the  we.ght  of  ''-  ^"g';;^ ^'J^j  „,,erial  will  be 
though  it  is  so  affected  to  some  exten     Jhe  cost  ^^^^ 

nearlv  In  accordance  with  the  we.ght,  but  not '"  X  ^°'  ""^  ^  therefore, 
fpensive  parts  being  substantially  the  same  on  aU  "«  -  '  '  .  _th  ^^^^^^^ 
we  say  that  half  the  total  cost  of  engine  J/'"  (';;7^^„.,„  bably 
varies  with  the  weight,  and  half  .s  •"''^P«"^'="' \*'^7°^'^e\ervle,  and 
L  very  nearly  exact,  for  engines  engaged    „     he  same    se^  ^^  ^^._ 

and  tear  from  their  difference  in  proportion  and  des.gn. 


CHAP,    v.— OPERATING  EXPENSES— REFRS  ENGINES.     HS 


Table  54. 

Details  as  to  Cost  of  Locomotive  Repairs. 

Cost  Per  Train-Mile  of  Labor  and  Material 


English  Railways, 
Average,  1868-75. 


London  &  Northwestern 

Midland  

Great  Northern 

Great  Western 

Lancashire  &  Yorkshire 

Gt.  Southern  &  W.  of  Ireland. 

Average 

French. 

Paris  &  Orleans.  1875 

Paris,  Lyons  &  Med.,  1865-74. . 

Prussian  Railways,  1874. 

State  Railways 

State  Control  Railways 

Private  Railways 


Increase 
per  cent 
in  No.  of 
Engines. 


Labor. 


32.  a 

73-6 
8.1 
42.3 
47-2 
15.0 


36.4 


cts. 
3.04 

6s 

12 

86 
05 


Mate- 
rial. 


3.08 


cts, 

3 
3 
3 
3 
3 


TO 
ID 
29 
58 

34 


382 


313 


1.70 
2.00 


Labor. 


R'd  H'se.l  General. 


3-21 


Total. 


cts. 
6.14 

5-75 
6.41 
6.44 
6-39 
6.90 


Per  cent 

of 
Labor. 


6.34 


3.32 
3.83 


0.58 

1-33 
0.80 


1. 10 
1. 16 
1.03 


American  Railways. 

Phila  &  R'g  (1869-75).  repairs  only 

"    (1876-80),        "         ♦'     

(1869-75),  renewals  only 

(1876-80),        "         (approx.). 
total  rep'rsand  ren'ls  ('69-75). 

('76-8I). 


390 
2.38 
81 
60 


7^ 
98 


1.70 
1.98 
0.97 


2  94 

1-93 
1.22 
0.90 

4.16 
3.83 


4.03 
483 


% 

49.6 
46.0 
48.7 
60.1 

47.6 
44.6 


Av.  Total 
Cost  Re- 
pairs for 

31  preced- 
ing yrs., 
1849-69. 


49-3 


424 
41.6 


6.90 

713 
5.87 
6.73 
536 


.40 


3.38 
4.47 

3. 80 


6.84 

431 
2.03 

1-5 

8.87 

6.81 


50.0 

55-5 
654 


I 


6.7 

55.) 
(40.) 
(40) 
(53.) 
(58.4) 


For  further  notes  as  to  ratio  of  cost  of  labor  to  material,  see  Index. 

None  of  these  figures  include  shop  and  general  charges,  maintenance  of  machinery, 
clerks,  draughtsmen,  policing  shops,  etc.,  which  run  about  50  per  cent  or  over  of  labor 
account  on  nearly  all  railways. 

These  statistics  are  supix)sed  to  be  all  per  train-mile.  The  ratio  of  engine-miles  to 
train-miles  on  English  railways  is  about  as  135  to  100— sometimes  even  177  to  100.  The 
same  holds  substantially  true  of  American  railways,  reported  statistics  being  generally 
computed  per  engine-mile.  A  deduction  of  15  to  20  percent  from  the  total  cost  of  engine 
repairs  per  train-mile  will  give  the  cost  excluding  switching-engines,  which  cost  much  less 
per  mile  for  repairs  than  others,  on  most  roads. 
zo 


"S^r- 


Table  55. 


Cents  Per  Train-Mile. 


Itkms. 


Boiler 

Smoke-box,  etc 
Wheels,  frame,  etc 

Machinery 

Mountings 

Painting 
ToUl  Engine 

Tenders 

Total 
Percentages 

•*c    to  264  cent-  on  renewals,  to  .19* 
credits  for  old  material  (7°»"«"f •  °"  "^^.^^  U^lTfor  net  cost,  probably  about 

*"' t:"«  «;-t;  constitute  over  thirty  per  cent  of  the  labor  on  repairs  proper,  or 
.616  cent  per  mile. ^ 

Unaer  these  assun,ptio„s we  are  'f -^^"^.t^'r'pef^Urrt""^ 

the  eight-wheel  "  ^"^"'^^^JZ^^'^Z^Z^s  proper.  Heavy  Mogul 
favorable  circumstances  f° "fP^'^'^f "^^;,\b„„t  one  tenth  to  one  eighth 
or  ten-wheel  engines.  ^!""'^;  ^l  J'"  „'^3°',  ^^  ,uh  the  as  yet  fragmentary 
„ore.    This  estimate  .s  l^^^^^^^Z  latter  do  not  exist  in  suffi- 

"  .0  T.Bt..  S,  --  ..^^r  ^stuJ  t.  -  tbe  En.lUb,  sbow  tbe  cost 

^r.LTtrli'nlne'Ir  .U  en^nes.  i.,c,uain.  swUcbin,. 


C^AP.    v.— OPERATING  EXPENSES— MOTJVE.POWER,     I47 


Table  66. 
Engine  Repairs  and  Renewals,  Paris  &  Orleans  Railway  of  France 
(1865-75). 


Labor. 

Materials. 

Total. 

Grand 
Total. 

Re- 

newals. 

Re- 
pairs. 

Re- 
newals. 

Re- 
pairs. 

Re- 
newals. 

Re- 
pairs. 

Engines 

.130 
.040 

.842 
•370 

.342 
.106 

1-238 
.540 

.472 
.146 

2.080 
.910 

Tenders 

2.552 

1.056 

Total  repairs  proper 

.170 

I. 212 

.448 

1.778 

.6x8 

2.990 

3.608 

Tools  and  machinery 

Clerks  and  general 

.074 
.248 

.094 

•    •    •    • 

.168 
.248 

.168 

.248 

Total  all  repair  expenses. . 

1.704 

2.320 

4.024 

4.024 

The  proportion  of  renewals  to  repairs  in  this  table,  and  in  less  degree  the  cost  of 
pairs  only,  is  stated  to  be  unduly  low,  as  appears  certain  from  the  figures. 

Table  57. 
Total  Cost,  by  Items,  of  Motive-Power. 

Cents  Per  Train-Mile. 


re- 


Engine  Wages. 


American. 


Penna. 
R.R. 

1879-83. 


L  S.& 
M.S.Ry 
1872-81. 


Fuel        J  Co*'  •  • 
^''-  "I  Wood 


Maint. 
Locs. 


Repairs  Prober 

Mt.  shops  

'*  tools  and  mach'y 
Clean'g  and  polic'g 
Watchmen 


5-450 


4  705 
.223 


fOil 

I  Tallow , 

<^tores. .  -J  Waste 

Other  stores. 
tLoc.  fixtures. 

'^ater   J  Expenses 

Supply  \  Maintenance. 


5.910 
.612 
•435 

1-715 
•133 


5.787 


[s.ss 


Mass. 
RRs. 

1878-81, 


Av.  of 

U.S. 
Census. 

1880. 


English. 


Gt.  W.  Ry 

1869-76. 


7.0 


5015 


•255 
•259 
.123 
.052 
•358 


„  (Taxes  

^'«V....^  Stationery. 
(  Incidentals 


'J'otal  Motive-Power. 


.602 
.368 


•35 


\- 


22 
xo 


10.94 


S-02 


8.4 


^5-6 


4.66 


4-34 


Lab.  3.76 

Mat  2.46 

0.22 

0.40 


Gt.  So. 
&W. 

i875^ 


4-32 


6.6z 


iMidl. 
Gt.  W. 

1875. 


-I. II 


l. 


•215 
.098 

•415 


21.928 


0.6 


0.48 


2.82 
380 
0.32 

0.66 


2?i 
6.50 


342 
2.78 


0.20 


0.42 


22.6 


16.74 


0.66 


0.82 


0.50 


0.32 


1976  1 17-90 


'i 


I 


„8   »..  ..-or^^^r^^^^J^^^^^s^^:^^ 


Table  68. 

^xT  TwPNTY  English  Railways, 

COST   OF   MOTIVE^POWER^^ND_CAK^^ 


CHAP,    v.— OPERATING  EXPENSES— MOTIVE.POWER.     I49 


«.Lareest     I      4  ^-a^'ff^*^ 
CrrpoXns.     Corporations. 


Mass. 
1878-81. 


11,005 

No.  of  locomotives i        33.203 

No.  of  carriages '  * '       335.158 

No.  of  wagons * ' ',^;«*e*  *  *    .         17.064 

Av.  mileage  per  yearjpe^ejigine^^^^ J_ 

12.46  cts. 
6.17  ** 


Cost  of  working...... 

engine  repairs. 

..,  18.63  cts. 
Total  motive-power . 

2.58  cts. 
Cost  of  carriage  repairs ••••j     ^  gg  .. 

•  •       wagon 

1  2«;.OQ  cts. 
Total  cost  Iocs,  and  cars^_^._^^^j^    ^5 

$1,086 

133 
23.41 


Cost  per  engine..  \     pg^     \ 

carriage  v    ^^^^   \ 

it         wagon..  )  V 


6.118 
14.902 

171.431 
16,520 

12.94  cts. 

6.90  •' 

19.84  CIS. 

2.28  cts. 
J-98J_ 

26.10  cts. 

$1,148 

160 
20.80 


$1,108 

370 
55.40 


considered,  without  important  error,  to  have 


tialf  the  weight,  capacuy,  *" 


.w  ».n--.  „   .,_oad   the  writer  was 

on  the  Pennsylvania  RaUroaa,  m 

"xVconlolid'atYon  locomotives  are  not 


and  practice  with  Consolidation  cn^ 
informed  as  follows  by 


In  answer  to  inquiry  as  to  experience  ana 
SrT."N.lly:Supt.M  Motive-Power:         ^^^^  ^^^^^^  ^^  curves  than  other 


locomotives,  we  think.  hundred  miles  between  a  Class  I 

..  2.  The  comparative  cost  of  ^^J^^^ ^^J p^en-wheel)  locomotive  is  about 
locomotive  (Consolidation  type)  and  a  Class  U  K 

as  follows:  4.87 

♦'  Class  I ...  4-5*^ 

•'Class  D, ■ 

.     .     .  0.37 
Difference,      •*•„'*' 

„  .,.,.,  «M  ^  ■"■  X™ '.'.""i  l...«"'  "  "«'  ""'"""■  "" 

ai  rule  cost  about  twenty  per  cent  less 

most  favorable  conditions. 


Table 
Minor  Details  as  to 


59-60. 

Locomotive  Repairs. 


Deiaif  items.  Gt.   S 
&  W.  Ry..  Ireland 

Cents  Per  Train-Mile. 

Detail  items.  Gt.  S. 
&  W.  Ky.,  Ireland. 

j  (Condensed  in  pre- 
ceding Uble.) 

Cents  Per  Train-Mile. 

(Condensed  in  Ta 
ble  55  ) 

Rep'rs. 

RenMs. 

Total. 

Rep'rs. 

Ren'ls. 

Total. 

Copper  plates  

.052 
.020 
.062 

.128 
.028 

.162 

•034 
.200 

[•.260 

.214 

•054 
.262 

.416 

Mountings 

.118 

•  154 

stays 

.272 

tubes 

Fire-bars  and   brick 

arch 

Boiler  sundries 

Clothings   painting, 
etc  

.060 

.058 

.118 

Total  Engine 

I  542 

I  724 

3.266 

Toul  Boiler 

.290 

.656 

.946 

\Tender 

.280 

.292 

•  572 

Smoke-box  and  plat- 
form.   

.052 

.092 

.144 

1 

Engine  and  tender.. 

1.822 

1.870 

3.838 

Wheels 

Axles 

.114 

.198 
.138 
.068 

.164 
.128 
.128 
.062 
.092 

.164 

.326 
.200 
.160 

Less  credits 

.264 

.192 

•456 

Tires  

Spririps 

Sundries 

Labor  acct.,  as  distributed  in  detail  to  gen- 
eral items  in  Table  55: 

Total  Running GW 

.518 

•574 

1.092     j 

Labor,  r'd-h'se  rep*r. 
"      shop 
"       tender       " 

.616 
.976 
.286 

j-  .704 
.098 

Cylinders  

.048 
.078 
.052 
.010 

•034 
.04a 

•034 
.054 

.080 
.070 

.058 
■  .132 

.I02 
•590 

2.296 

Axle-boxes 

■384 

Axle-brasses 

Big-end  brasses 

Pistons,  etc     

Glands  and  bushes. . 

Toul  Labor  

1.878 

.802 

2.680 

Slide-valve  castings, 
brass 

Eccentric  liners 

White  metal 

Machinery  sundries. 

Proportion  of  round-house  repairs,  Phila. 
&  Erie  R.R.,  about  the  same,  viz.:  26  per  cent 

Total  Machinery.. 

.504 

.190 

.694 

1 

of  labor. 

See  also  Table  I3€ 

i. 

Table  61. 
Cost  of  Maintenance  of  Tires  in  Detail,  Gt.  S.  &  W.  Ry. 

Cents  Per  Train-Mile. 


Date. 

Engines. 

Tenders. 

Pass. 

Freight. 

All. 

Total. 

1860-64. . . 
1865-69. . , 
1870-74... 

.33 
.44 

.22 

.57 
.46 

.44 

.42 

•45 
.30 

.24 

.15 
.23 

.66 
.60 

•53 

Average . . 

•33 

•49 

•39 

.21 

.60 

Mileage  of  Tires, 
Iron, 
Steel, 


4'  6"     &  6" 

52,300   114,500 

105,700   196,600 


,50    CHAP.    V.-OFEnATWG  EXPENSE^-MOTIVE^FOWER^ 


CHAP,    v.— OPERATING  EXPENSES— MOTIVE-POWER.      I51 


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152     CHAP.    V. 


-OPERATING  EXPENSES-MO TIVE-PO WER, 


Table  64. 

COST  OP  A  PENNSYLVANIA  RAaKOAD  "CLASS    I"  (CoNSOUPAT.ON)  ENO.NE. 


%% 


Boiler 

Machinery 

Running  gear 

Frames 

Fittings 

Painting 


Total  engine. 
Tender 


Material. 

$1,877 

935 

1.456 

200 

652 

47 


Labor. 


Tot.  engine  and  tender. 


$5,167 

845 


Toul. 


$6,012 


$3,968 


Phila.  &  Reading.  1881,  average  of  18  engines. 


$9,980 


$10,370 


See  also  Table  134. 


Table  65. 


R.X,0    OF    COST    O.    MATKKUX.S    TO    TOTAL    CoST   .Oa   BOTH    NEW   ENO.NBS 

^  AND  Repairs. 


On  New  Engines  (or  Renewals). 


Chicago,  B.&Q.RR-,  Class  A.... 

Pennsylvania  "  "      C... 

"       I.  • 


English  (R.  Price  Williams) 

Gt.  So.  &  W.  of  Ireland 

41  »*  "      renewals.. 


Paris  &  Orleans. 


64.6^ 

66.7 

60.3 

78.1 

72.9 

69.5 

71.8 


On  Repairs  Only  (,ex  Renewals). 


New  York  Cent.  &  H.  R.  RR 

Philadelphia  &  Reading 

Av.  of  U.  S.,  repairs  only 

ii  »»       repairs  and  renewals . . 

Gt.  So.  &W.  of  Ireland 

"  "    av.  repairs  and  renewals 

Paris  &Orl.,"        "        " 


43-3 
Abt.,  44 
"      50 

45-3 
55-8 
58.0 


CHAP,    v.— OPERATING  EXPENSES— MOTIVE.POWER.     153 

135.  The  apparent  cost  of  repairs  has  been  kept  down  on  all  our  rail- 
ways for  the  time  being  by  the  constant  additions  of  new  stock,  thus 
greatly  reducing  the  percentage  of  renewals  and  heavy  repairs.  Table  51 
will  show  to  what  a  very  important  effect  this  cause  must  have  contrib- 
uted to  reduce  the  apparent  average,  especially  during  the  rapid  growth 
of  traffic  of  the  last  ten  years. 

136.  The  distribution  of  the  cost  of  repairs  to  the  various  parts  of  the 
locomotive  concerns  us  quite  as  much  as  its  total  amount.  Information 
on  this  head  is  somewhat  difficult  to  procure,  as,  so  far  as  the  writer 
knows,  no  American  railways  publish  such  statistics  in  a  complete  form, 
and  few  take  much  trouble  to  collect  the  information.  Tables  53  to  67, 
however,  give  the  cost  of  new  "  American"  engines  in  detail,  and  also 
very  full  statistics  of  the  cost  of  engine  repairs  and  renewals  on  English 
railways,  which  latter  are  undoubtedly  substantially  accurate,  and  (with 
proper  allowances)  of  general  application  to  all  railways. 

137.  From  these  data  we  may  conclude  that,  with  no  very  great  fluc- 
tuations, the  total  cost  chargeable  to  repairs  of  engines,  including  renew- 
als, may  be  distributed  about  as  follows : 

The  boiler  and  its  attachments  require  about 20  per  cent 

The  running  gear  and  frame  (of  which  the  frame  consumes 

very  little,  say  2  per  cent), 20  per  cent 

The  machinery  proper 30       " 

The  mountings,  fittings,  and  painting, 12       " 

The  smoke-box  and  attachments 5       " 

Total  of  engine 87  per  cent 

The  running  gear  of  tender 9 

Tank  and  body  of  tender,    .    , 4       « 

Total 100  per  cent 

138.  Maintenance  of  shops,  tools  and  machinery,  and  other  miscella- 
neous motive-power  expenses  do  not  usually  appear,  as  before  stated,  in 
statements  of  the  cost  of  repairs  or  of  running  engines,  although  they  con- 
stitute a  legitimate  addition  thereto.  On  the  Pennsylvania  (Table  57) 
these  items,  including  stationery,  incidentals,  and  watchmen,  but  not  in- 
cluding the  item  of  "  laborers," — the  latter  doubtless  largely  for  clean ino- 
engines, — amount  to  twenty-five  per  cent  of  the  cost  of  engine  repairs,  or 
about  \\  cents  per  train-mile,  and  the  item  of  "  laborers"  to  as  much  more. 
This  is  higher  than  is  usual,  or  perhaps  it  would  be  more  proper  to  say 


tW^K 


t1> 


154     ClfAP.    V.-OFE,ATWG  EXPENSES-MOl^yf^^^ 


that  it  is  based  upon  a  closer  apportionment  than  is  -^^1;  --V  jj"^^ 

^•^Tarri^re-noXr^'r:!^;:^^ 

an^Lirect  motive-power  expen^s^^^^^^^^ 

r  aK^h^rs^ieSs!  U  aU  the  e.^nses  are  apportioned 

"'^Thist  an "xpense  whicl,  is  affected  but  slightly  by  very  considerable 

.ir:re?.^-.n....dben.^ 

engine  repairs  proper,  but  rareiy  ib.     it  la  «        v 

-r .;  :r  r;r..« ....  ■-- — rr  ;2,%s 

one  cent  per  mile,  .but  often  run  as  low  as  half  a  cent,  or  even 

Table  66. 
^r^r.  rn^T  OF  Labor  and  of  Material,  and  of  the. 

P.KCENTACES  0;;^-J-;-   ';rNBW   LOCOMOTWBS. 

,SHop  ana  .ne.,  e.^nses  no.  -udea,  — in,  .0  a.u.  .  per  cen.  o.  U^r 


Items. 

(For  amounts  see  Tables  6i. 

6a,  etc.) 


C,  B.  &  Q.  RR. 

(ClassH). 
St'd  FreiRhi. 


Penna.RR./'C." 
St'd  Passenger. 


Penna.  RR.,  "  I.'" 

St'd  Freight. 


Lab'r  Mat'l  Toul 


Boiler  and  braces 

Machinery 

Running-gear 

Frame  and  bed-casting 

Fittings  and  pump,  cab,  etc 

Painting 

Total  engine 
Tender 


Total  engine  and  tender. 


Reported  cost  labor  and  mai'ls. 


Cylinders  and  weight  (long  fns) 


C//AP.    v.— OPERATING  EXPENSES— MOTIVE-POWER.     I55 


Table  67. 
Percentages  of  Cost  of  Various  Parts  for  Various  Foreign  Locomo^ 

TIVES. 
^ (For  American,  see  preceding  table.    See  also  Table  131.) 


Itrms. 


Paris  &  Orleans 

(France). 

St'd  Freight. 


Boiler^  smoke-box,  chim- 
ney, stays 

Ask-/>an,  foot-plate,  cab, 
sand-box 

Wheels,  bearings,  frames, 
springs 

Machinery,  pumps,  re- 
verse-gear   

Cocks,  safety- valves 

Fainting,  brass  sheathing. 


Total,   both  engine  and 
tender 


Lab'r  Mat'l  Total 


8.3 
2-3 
5  7 

10. 1 
0.9 
i.o 


35-2 

2.9 

18.2 

10.6 
2.2 
2.6 


Reported  cost,  labor  and 
materials 


Cylinders     and     weight 
(long  tons) 


Approx.      increase     per 
cent  in  cost,  due  to 


28.3 


43-5 

5-2 

239 

20.7 

31 
3-6 


Items. 


Boiler 

Smoke-box,  etc.... 
Wheels,  frame,  etc. 


Gt.  So.  &  W. 

(Ireland). 
St'd  Freight. 


Lab'r  Mat'l  iTotal 


71.7 


100. o 


$9,650 


(17X24)— 29.5  tons 


r  \  brass  in  b'r  i6.oj( 
.(  f  wr't-i.  wh's  ii.65< 


Machinery. 
Mountings. 
Painting... 


5-6 

3-9 

3-3 

9-5 
1-7 
I.I 


Total  engine  and  tender 


25.1 


27.6 

4-3 
27.5 

8.7 
4.6 
2.2 


33  •« 

S.a- 

30.8 

18.3 

6.3 
3-3 


74-9 


100.  o 


$9,424 


17X24 — 30.0  tons. 


.10.0^ 
.i2.8)C 


Items. 


Boiler        

Wheels,  frame,  etc. 

Machinery 

Smoke-box 

Mountings 

Painting 


Gt.  So.  &  W. 

(Ireland). 

Heavy  Passenger. 


Lab'r 


5.0 

4.5 
10.4 

51 
1.9 
1.6 


Total  engine. 


Tender. 


Total  engine  and  tender. 


Mat'l 


23-3 
28  5 

7-4 
3-8 
6.0 

2-5 


Total 


28.3 

330 

17.8 

8.9 

7-9 
41 


Great  Western  Railway  (England). 


Heavy  Passenger. 


Reported  cost,  labor  and  mat'ls 


Cylinders  and  weight  (long  t'ns) 


Approx.   increase  per  cent    in 
cost,  due  to 


28.5     71,5    100.0 


$9,072 


Lab'r 


3-8 
5-6 
4.9 

■9-4 


23 -7 


17X24 — 31  tons. 


(17X22)— 30.3  tons. 

jbrassinb'r    %.o%   5  ojS 

{  wr't-i.  wh's  13.3d  10. o^ 


5-8 


Mat'l 


25.0 
19.4 

3  4 
II. o 


Total 


58.8 


29.5 


II. 7 


70-5 


28.8 
25.0 

8.3 
20.4 


82.5 


175 


100. o 


$7,432 


St'd  Freight. 


Lab' 


4-1 

5.7 
4  9 

•9.6 


Mat'l 

24.6 

16.0 

3-2 

12.4 


243 


6.5 


30.8 


56  2 


13.0 


Total 


28.7 

21  7 

8.1 

22. 0' 


80.5 


69.2 


19.5 


100.  o 


$6, 


709 


17X24—30.5  tons. 


.  5  o< 
.lo.ojt 


The  distribution  to  items  is  not  precisely  identical  in  these  tables,  as  will  be  apparent 
'rom  the  percentages.  Multiplying  any  percentage  by  the  total  cost  gives  the  absolute 
expenditure  for  the  item. 


1 56     CHAP. 


V.^OPERA  TING  EXPENSES-MO  TIVE^PO  WER. 


CHAP,    v.— OPERATING  EXPENSES— MOTIVE-PO  WER.      I  5/ 


■li 


larger  roads,  especially  where  there  is  an  independent  account  kept  with 

"'hi"  Wa'ter-supply  costs  about  half  a  cent  pertrain-mileas  an  average, 
son  ^tnlunning  below  that  on  roads  of  very  heavy  traffic,  but  ofter.er 
runningnearer  to  one  cent  per  mile.     On  all  but  roads  of  very  cons.der- 
ab"  trfffic  one  cent  is  the  safer  estimate.    The  quantity  used  ,s  very  con- 
siderable     About  six  or  six  and  a  half  pounds  of  water,  as  an  average,  .s 
evaporated  per  pound  of  coal,  and  a  freight  engine  burnmg  a  hundred 
;Zds  of  coal  p'er  mile  will  use  some  eighty  gallons  o   ---  - ;;^-- 
The  refilling  of  a  2400-gallon  tank  within  t  nrty  m.les  ^''^e  "Wnost  as  an 
averac^e.     Practically  the  consumption  of  water,  as  of  coal,  is  '"-egular, 
aid  afull  tank  may  In  cases  be  used  up  within  fifteen  mdes;  requ.rmg. 
for  pr  ctical  convenience,  tanks  every  ten  miles  which  -  th-verag^ - 
roads  of  thin  or  average   traffic.     On  lines  of  heavy  traffic  tanks  a  e 
Jaced  at  average  intervals  of  hardly  more  than  five  or  s.x  m.les.    Table 
57  gives  considerable  data  as  to  these  mmor  items. 

142.  Switching  engines  constitute  an  enormous  proportion  of  the  total 
numberTr  service  on  most  roads,  the  average  of  the  whole  State  of  New 
Yo?k  be"n/twenty-eight  per  cent  of  the  whole  number  m  service,  or 
Larly  fo";  switchLg Engines  for  every  hundred  in  through  servceearn- 
"„g  money      Tl.eir  "mileage"  is  fixed  by  an  allowance  (usually  s.x  m>  e 
"^  Tour,  but  sometimes  eight),  so  as  to  bring  their  expenses  per  "mne 
Tr,  some  reasonable  or  desired  ratio  to  that  of  through  c.g.nes.     The 
Ireat  expense  of  this  service  does  not  tend  to  decrease,  but  rather  to  m- 
freLe  w^th  growth  of  traffic,  and  is  with  reason  felt  to  be  largely  due  to 
removable    and  hence   discreditable,  defects   of   admm.stratK,n.      The 
buTden  i    ;omewhat  relieved  at  the  larger  terminals  by  fixed  te-^ 
<:har<.es  allotted  out  of  the  through  rates  before  d.v.dmg  >t  (at  New  Yo  k 
four  to  five  cents  per  hundred  pounds  out  of  through  rates  of  twenty  to 
hirtv  cents,  or  even  less).     It  is  a  charge  but  little  affected  by  any  of  the 
details  o"a  ignment.  so  that  we  need  not  discuss  it  in  detaU.  but  m  cer- 
t!in  computftions  it  is  an  element  which  needs  to  be  ■•e^embered-nota- 
w"  in  computations  of  the  value  of  reducing  grades  on  old  -ads  whereby 
this  portion  of  the  motive-power  expenses  is  not  ser.ously  reduced. 

The  diagram  given  in  Fig.  4  illustrates  very  fairly  the  .P«""f-<=y  ;' 
I  „,!„,  %xoenses      Alone   of  all  the  items,  wages,  it  will  be  seen,  have 

rlldprlcti  ally  uniform.  There  was  a  slight  tendency  to  decrease  during 
ZZU^^  of  .877-79.  but  they  recovered  later,  and  remain  at  the  end  sub- 
ctantiallv  what  they  were  in  the  beginning. 

The  cost  of  fuel  declined  sharply  aher  .872,  but  since  1876  has  been  nearly 


Fig.  4.— Locomotive  Expenses,  C,  B.  &  Q.  R  R. 

I 


158     CffAP.   V.-OPERA TING  EXPENSE^MOTIVE-POWeR. 

uniform  Tvtq  possible  causes  for  this  are  indicated  on  the  diagram  both  of 
rhich  p  obably  had  their  effect.  One  was  the  increase  in  miles  operated  wh.ch 
Irobabrgave  better  access  to  coal-mines,  but  another  and  probably  very 
Tportant  contributing  cause  was  the  increase  in  miles  run  per  engme  per  year 
Zch  likewise  began  simultaneously,  and  ceased  to  advance  sharply  after  the 

rn«!t  of  fuel  ceased  to  decrease. 

The  course  of  cost  of  repairs  is  very  instructive.     It  will  be  seen  tha    the 
decrease  has  been  enormous,  and  it  is,  doubtless,  in  great  part  d^'"  "-'"/='' 
Z  permanent  causes,  such  as  the  decrease  in  cost  of  matenals  and  better  shop 
facilities.     But  it  needs  but  a  brief  glance  at  the  line  showmg     Number  of 
Ses  on   road,"  in  connection  with  the  cost  of  repairs,  to  detect  anothe 
explanation,  of  vast  importance  in  its  effect  on  operating  expenses,  wh.ch  .s 
too  little  re;embered  in  studying  ma.ntenance  charges,  viz.,  the  enormous  and 
continuous   infusion  of  "new  blood"  into   the  locomofve  stock,  gmng  at  all 
*imes  a  very  large  number  of  new  locomotives  in  the  stock  ,n  addtUon  to  the 
portion  natufally  required  to  replace  old  engines  worn  out.    As  new  eng.nes 
cosHomparatively  little  for  repairs,  it  is  inevitable  that  this  abnormal  propo - 
^n  of  ne'w  engines  should  greatly  affect  the  average  -«;' ;;=P-^^^;^;'„; 
verv  clear  that  it  did  so.    The  very  small  expense  for  repairs  m  1875-9  "^s  not 
rhollyd"e  to  economies  enforced  by  hard  times,  although  no  doubt  largely  so 
Tut  in  great  part  to  the  fact  that  there  was  a  greater  proportion  of  new  engmes 
Ts  rvl  e  than  at  any  time  before  or  since.     Afterwards  the  mevtab  e  .ncrease 

the  continual  additions  of  new  stocK  cease,  u  is  v     ;r  ..^.^oir*" 

tne  conu  remembered  also  that  these  nommal     repairs 

rr  i^lirm^V  i'dl"  -  -  maintenance  of  s-PS  etc.  which  a„ 
reallv  a  part  of  the  cost  of  repairs,  but  not  ordmanly  included  m  .t  A  ch.et 
reason  for  th^  heavy  decline  since  .866  is  undoubtedly  the  contmued  .mprove- 
m'tin  the  character  of  the  roadbed  and  in  the  quality  of  the  workmanship  and 

""Xhe'ln^rete  in  the  average  miles  run  per  engine  shows  an  unusually  favor- 
able record  and  one  not  likefy  to  be  much  further  improved  on,  since  an  av.r^, 
of  near  V  a  hundred  miles  per  day  for  every  day  in  the  year  and  lor  all  engme. 
nearlv  reaches  the  possible  limit.  It  implies  that  single  engines  have  more 
than  doubed  this  The  decrease  in  miles  run  and  simultaneous  increase  m  cost 
If'paTrs  per  mile  run  in  x88,  can  hardly  be  an  entirely  accidental  come 

'""able  68  shows  the  average  miles  run  per  year  and  the  -e«ge  cos.  per 
vear  of  "locomotive  power"  (repairs,  stores,  wages,  and  fuel)  on  ten  repre- 
len  ative  English  and  American  lines.  The  latter  by  no  means  represent  the 
Us  Amerlan  practice,  as  will  be  evident  from  Fig.  4,  but  are  those  Imes  (for 


CHAP,    v.— OPERATING  EXPENSES— MOTIVE-POWER.     1 59 


the  most  part)  which  are  operated  under  the  most  fairly  comparable  conditions 
with  the  English  lines.  Could  the  ton-miles  and  passenger-miles  per  year  per 
engine  be  compared,  the  contrast  in  work  done  per  engine  would  be  astounding 
<over  three  to  one),  but  the  English  railway  statistics,  alone  of  those  of  civilized 
countries,  do  not  give  these  facts.  In  part  the  difference  in  work  done  is 
explicable  by  difference  of  conditions,  but  by  no  means  wholly  so. 

Table  69  gives  the  work  done  per  year  per  engine  and  the  number  of 
engines  in  all  countries,  from  which  it  appears  that,  far  as  American  practice 
is  ahead  of  English,  the  latter  surpasses  that  of  all  other  countries. 


Table  68. 

-Annual  Average  Expenditure  Per  Locomotive  for  Locomotive  Power 
ON  Ten  Leading  Lines  in  the  United  Kingdom  and  in  the  United 
States,  with  the  Average  Annual  Number  of  Train-Miles  Run  Per 
Engine. 

^Abstracted  and  recomputed  from  "  Railway  Problems,"  by  J.  S.  Jeans,  Secretary  British  Iron 

and  Steel  Association.] 


English  Locomotives. 

American  Locomotives. 

Per  Locomotive. 

Road. 

Per  Locomotive. 

Road. 

Average 
Annual 
Expendi- 
ture. 

Average 
Train- 
Miles. 

Average 
Annual 
Expendi- 
ture. 

Average 
Train- 
Miles. 

'Great  Northern 

$3,320 
3,540 
3,040 

2,455 
3,000 
3,720 
2,980 
2,610 
4.370 
3.610 

21,518 
16,240 
19,600 
15,422 
19,313 
21,456 
18,101 

19.959 
22,323 

19.844 

Boston  &  Albany 

Boston  &  Lowell 

Boston  &  Maine 

Boston  &  Providence  . . . 

Old  Colony.  

N.  Y.,  New  Haven  &  H. 
N.  Y.,  Lake  Erie  &  W'n. 
N.  Y.  Cent.  &  Hudson  R. 
Pennsylvania— Pa,  Div.. 
Baltimore  &  Ohio ... 

Average 

$7,240 
8,600 
6,640 
6,840 
6,440 
8,610 
4,260 
7,720 
5,880 
2,700 

North-Eastem 

20,000 

Midland 

25,000 

London  &  North- Western 
Great  Western 

21,000 
18,000 

Great  Eastern    

20,000 

Caledonian 

31,000 

North  Britiih 

London  &  South-Western 
Lood.,  Bright.  &  So.  C'st 

14,000 
25,000 
26,000 
27,000 

Average 

$3,080 

17.539 

$5,590 

23,928 

,  Average  earnings  per  year  per  locomotive, 


j  American, 
•J  English, 


Average  rate  per  ton-mile \  American, 

\  English,    . 

J  American, 


.    $14,860 
•    $10,940 

1.057  cts. 
2  to  2.4  cts. 

2.198  cts. 


Average  rate  per  passenger-mile, •{  t" ,"•  r"/V   '     .-*vo«.i.». 

1  English  (about  the  same). 

All  the  above  is  for  1883,  except  the  rates,  which  are  for  1885.     The  earnings  and 
rates  given  are  for  the  national  aggregates,  and  not  merely  for  the  ten  roads  above. 


l6o     CHAP. 


v.— OPERA  TING  EXPENSES-REPAIRS  OF  CARS. 


CHAP.    V.-OPERATING  EXPENSES-REPAIRS  OF  CARS.     l6l 


Table  69. 
Total  Number  of   Locomotives  in  Different  Countries.  Number   of 

TRArMlLES  WHICH   THEV  HAVE  ACCOMPUSHED.  AND   THE  AVERAGE  MiLES 

Per  Day  and  Per  Year  Per  Locomotive. 
[Abstracted  from  •«  Railway  Problems,"  by  J.  S.  Jeans,  Secn^tan.  British  Iron  and  Steel  Asso. 
'•'^  ciation,  with  some  modihcations.] 


CoxmTRiES. 


United  States 

United  Kingdom 

Germany 

Austria 

Belgium 

France •  •  • 

Italy 

Luxembourg 

Norway 

Netherlands 

Roumania 

Russia • 

Finland 

Switzerland 

India 


Number 

of 
Locomo- 
tives. 


Train- 
Miles. 
X  :?  1,000. 


Average 

Miles 

Per  Loco- 

tnotive 

Per  Annum. 


23,823 

14.827 

11,330 

3.671 

1,790 

8,088 

1,630 

34 
III 

519 
211 

5.844 

98 

595 

1,730 


538,011 
272.803 

134.489 

47.144 

23,870 

135.860 

24,642 

433 

1,557 

11.435 

2,207 

61.940 
1,177 
7,674 

33.919 


22.583 

18,395 
11.870 
12,842 

13.335 
16.798 
15.I18 

12.735 
14.027 
22.033 
10,460 

10.599 
12.010 

12,897 
19,606 


Average 
Miles 

Per  Loco- 
motive 

Per  Day. 


62 
50 
33 
35 
37 
46 

41 

35 
38 
60 

29 
29 

33 
35 
54 


' T~.  "t     ,8«,  fnr  the  United  States  and  Great  Britain,  and  for  1882- 

The  above  statistics  are  for  1883  for  the  ^m*^^^^^  ^  ^  f^r  large 

for  the  other  countries.     Some  American  roads  (see  Fig.  4)  run  up  to  an         <^ 
numbers  of  engines  of  100  miles  per  day. 

,43.  REPAIRS  OF  CARS  Can  be  estimated  with  most  ^o^ectness  per 
car  mUe  and  not  per  train-mile.  They  may  be  roughly  placed,  with  a 
verv™!;  degree  o^orrectness,  at  \  cent  per  freight  car-m,le  and  .4 
::iprpt'engercar.mi.e.  on  the  larger  roads      On  -all -ads  i  cen 

per  car-mile  for  freight-car  repairs  is  more  ^^'^X^'XliJ.TZTtL 
^ting  much  less  than  this  require  allowances.  This.  .h°«^^;:' ;\'"  ^^ 
case  of  engine  repairs,  includes  only  labor  and  material  d'>-«f 'V^PP''^ 
Tthe  cars  themselves,  and  there  is  a  considerable  amount  of  >nc,d.ntal 
expendrre,  which  is  really  a  part  of  the  actual  cost  of  "-"'-"'"^  ^"^t 
ca^s  but  which  is  yet.  for  very  proper  reasons,  already  suted.  not  gen 
erally  included  in  the  reported  cost  of  car  repairs.  „  ,„  ,.  .,  ogr 

Such  general  and  incidental  expenses  amount  to  from  .o  to  25  per 
cent  of  the  total  cost  of  car  repairs  proper. 


Table  70. 

Average  Cost  of  Car  Repairs  on  Western  &  Atlantic  Railroad  fo« 

Different  Kinds  of  Cars. 

Cost  Per  Car  Per  Year. 


Passenger. 

Local  Box. 

Stock. 

Coal  and 

Flat. 

Line. 

Running  gear 

Interior  fittings 

Misceilans  material.. 

$64.80 

23-45 
41.75 

$6.78 
12.10 

$7.46 
8.50 

$6.76 
6.50 

$19.09 
13. 49 

Total  material 

Labor 

$130.00 
111.50 

$t8.88 
II. 12 

$15.96 
9-35 

$13.26 
4.48 

$32.58 

10.62 

Total 

$241.50 

$30.00 

$25.31 

$17.74 

$43.20 

Miles  per  car 

No.  of  cars  in  use.. . . 

36.480 
138 

7.780 
194 

5,601 
40 

5,420 
489 

10,045 
648 

The  above  includes,  whether  by  chance  or  otherwise,  no  charges  whatever  for  seats  or 
upholstery  of  passenK:er  cars.  Otherwise  it  includes  all  work  done  in  the  car  department 
for  maintenance  of  cars,  both  repairs  and  renewals.  The  cost  per  passenger  car  is  very 
low. 

Tables  70.  71,  72,  73  were  computed  from  data  given  in  a  very  careful  paper 
on  car  mileage  and  repairs  by  E.  C.  Spalding,  Car  Accountant  W.  &  A.  R.  R., 
and  afford  about  the  most  trustworthy  data  on  the  details  of  car  repairs  which  is 
extant.  Such  information  is  very  difficult  to  obtain,  and  even  this  affords  no 
means  of  distributing  expenses  to  different  parts  of  the  car  body.  Making  a 
proper  allowance  for  labor,  it  will  be  seen  that  somewhat  over  40  per  cent  of 
car  repairs  arises  from  running-gear  maintenance,  and  nearly  75  per  cent  from 
truck  repairs.  By  far  the  larger  part  of  the  remainder  is  for  draw-gear  re- 
pairs.    Other  repairs  of  body  are  a  very  small  expense. 

These  statistics  give  the  true  average  cost  of  car  repairs  for  a  stock  which 
II 


„*■, 
t 


■w*r- 


,62     CH.^P_V^^0PERA^^ 

~  '  ".        ~ZZ^A     Thev  are  almost  the  only  records  of 

is  being  neither  increased  nor  decreased,     l  ney  arc 

mileage  per  year,  so  ihat  the  rottn.g  a  ^_^  ^__^  ^  ^^_^^. 

what  higher  cost  per  mile  run  for  such  cars, 

for  running  gear  only  and  for  the  aggregate  of  »»   '^-^^  ^^^^        s„„,,„„ 

Table  74  giv«  'he  cost  of  car  repa.rs  on  the  Lake  Shore  «.  g        ^__^  ^^^^ 

car  maintenance  is  clear  from  the  note  to  the  table. 

Table  71. 
i>-t,AT„<;  Pfr   Mile  Run  by  Items  for  Cars  of 


Cast-iron 
Wrought-iron 
Lumber 
Springs 
Bolts 
Paint 
Labor 

Nails,  chains,  and  metal- 
lic sundries. 


Av,  miles  run  per  year 
Av.  total  cost  per  year 


C//.-iP.    v.— OPERATING  EXPENSES-REPAIRS  OF  CARS.     163 


Table  72. 
Cost  of  New  Box  Car  in  Detail,  1883. 

[Deduced  from  data  given  in  a  paper  by  E.  C.  Spalding.  Car  Accountant.  Western  &  Atlantic 

Railroad.] 


Material. 


Lumber 3,987  ft. 

Wrought-iron...704  lbs. 

Cast-iron 606   " 

Nails,  etc 

Draw-springs. . .  .46  lbs. 

Tin  roof 

Painting 


Total  body 

P.  c.  of  total  cost.., 


$79-74 

35  20 

18.18 

5.21 

414 

12. 60 
3-28 


f«58.35 
31.2 


Labor. 


}  20  days  carpenter. 


$45  00 


4  days  tinner 

I'y^  days  painter. 


4.00 
3.00 


Total. 


$52.00 
10.2 


$183.33 

4-14 
x6.6o 

6.28 


$210.35 
414 


Per  Cent. 


36.  z 

0.8 
3  3 

X.3 


41-4 


Truck. 


Wheels........  4,200  lbs. 

Axles 1,400    " 

Brasses 64    " 

Springs 184    " 

Lumber 487  ft 

Wroughi-iron.  1,000  lbs 

Cast-iron 1,306    " 

Painting 


\  $ 


Total  truck . 


160.00 

14.08 
16.56 

9-74 
50.00 
39.18 

■79 


$290.35 


Total  car $448.70 

Percent 88.5 


$x6o.oo 

24. 08 
16.56 

J04-57 
1.29 

315 
3.8 

[■Carpenter 

Painter 

$5.65 
•50 

3-3 
20.7 

•3 

$6.15 

$296.50 

58.6 

$58.15 
"5 

$506  85 
100.00 

100. 0 

The  weight  of  metal  in  a  standard  New  York  Central  40,000-lb.  box-car  is  dven  as 
follows :  t,  «» 


Wrought-iron  in  car  body 2,552    lbs 

Ca.st-iron  in 
Steel  in 


797 

104      *' 

Malleable  iron  in      "         i^U  •* 


-iron  in  trucks,  includ'g  axles,  3,144 


Cast-iron  in  trucks,  includ'gwheels,  5,366  lbs. 

Malleable  iron  in  trucks 48   " 

Journal-bearings 80  " 

Wheels,  each 


525 


Axles  (M.  C.  B.  SUndard; 347   •• 


The  total  cost  per  tratn-mile  of  passenger-car  repairs  and  freight- 
car  repairs  is  very  nearly  the  same  in  the  aggregate,  as  may  be  seen  from 
Tables  75-80.  although  the  proportion  of  the  constituent  elements  differs 
considerably.     (See  par.  1 50.) 


«! 


Table  73. 

AVERAGE  COST  IN  DETAIL  OF  KEEP.KG  .N  REPAIR  TWCKS  AH»  BODIES 

Separately  of  Box  Cars. 
Age  of  cars  three  years.     Built  at  cost  of  $5.5.00  each.     (Compare  Table  87.) 


Trucks. 
Original  Cost,  ta^S- 


Items. 


Cost  Per 
Year. 


Axles... 

Brasses 

Wheels. 


Running  gear. 


$3  04 

12.44 

6.06 


Per  Cent    j 
of  Total. 


Body. 
Original  Cost,  $200. 


6.3 
25.8 

13.6 


Springs 

Labor  

Cast-iron 

Wrought-iron. 

Bolts 

Lumber 

Nuts 

Paint 


$21-54 


Total 


$4-97 

a. 7a 

a. 66 

3.10 

.67 

.11 

.03 

.03 


Items. 


Cost  Per 
Year. 


Per  Cent 
of  Total. 


44-7 


$34.81 


10.3 
5.6 
5  5 
4.4 


x-7 


Labor 

Cast-iron 

Wrought-iron 

Bolts 

Lumber 

Springs 

Chains,  nails,  nuts 
paint,  screws,  sol 
der,  tin 


73.3 


$5-45 

x-33 
1.40 

X.II 

1.70 
1.36 


X.X9 


3.6 

2-9 

a. 3 
3-5 
a. 6 


<.6 


Total  cost  per  car. 


$13.44 


37.8 


$48.25 


lOO.O 


all  the  Western  &  Atlantic  records. 


per  car-m>le.  tl  ,s   ra  e  havmg  ^^  ^^^^  ^^  ^^^  ^^^^^^  _.^^^_ 

1:Z  ct"nrrn:trvice.  U  not  ^ ^^^  ^:'^ 

„3e.  ^^^'^Z:^T^^^::ii^lL  ...  road 
is  sufficient  to  do  tins,  espec.ai  y  expense,  any 

using  foreign  cars  is  ''^''^^^^^^^ 
deterioration  which  parts  of  the  car  otner  inan 


CHAP.    V.-OPERATING  EXPENSES-REPAIRS   OF  CARS      1 65 


suffer  while  on  its  lines.  Nevertheless,  whenever  business  is  brisk  and 
cars  are  scarce,  which  may  be  one  half  to  two  thirds  of  the  time,  the  price 
fixed  is  not  sufficient  to  cause  cars  to  be  sent  home,  and  earnest  efforts 
are  now  making  to  bring  about  a  change. 

145.  This  effort  is  more  particularly  directed  to  the  fixing  of  some  per-diem 
rate,  to  cure  the  great  present  evil,  that  when  cars  are  kept  on  hand,  on  a  side- 
track, instead  of  being  sent  home,  sometimes  for  weeks,  the  offending  road  loses 
nothing,  since  it  pays  nothing  for  the  car  except  wnen  it  is  in  motion.  The 
most  favored  plan  is  a  change  to  a  mixed  per-diem  and  mileage  rate,  approxi- 
mating to  25  cents  per  day  +  i  cent  per  mile.  If  the  car  were  kept  faithfully  in 
service,  there  would  probably  be  no  dispute  that  f  cent  per  car-mile  is  sufficient 
to  cover  (i)  maintenance  and  renewal  charges,  (2)  interest  on  the  value  of  the 
car,  and  (3)  a  fair  business  and  punitory  profit  in  addition. 

Table  74. 

Cost  of  Freight-Car  Repairs  Per  Car  Per  Year,  on  Lake  Shore  & 
Michigan  Southern  Railway,  for  Six  Years. 
(Average  mileage  of  cars  per  year,  about  12,500  miles.) 


Tbar. 


1880 

1881 

18S2 

1883 

1884 

1885 

Total,  6  years 
Av.  per  year. 


Cost  Car  Per  Year. 


Repairs  only. 


I47.S0 
43-46 
38.90 
30.64 
21.24 
35-30 


New  cars  built 

for  acct. 

"  repairs." 


$217.34 
36.22 


I4.OO 
2.74 

1-59 

5.56 

3.17 
1-05 


Total  repairs 
and  ren'ls 


No.  OF  Cars 


1x8. II 
3.02 


$51.80 
46.20 
40.49 
36.20 
24.41 

36.35 


Total  in  use. 


Built  new 

for 
renewals. 


$235.45 
39-24 


12.107 
14.663 
16.796 
16.649 

16.355 
16.629 


107 
66 

58 

197 
108 

38 


15,520 


574 
95.7 


For  the  ten  years  1870-7C  preceding  this  table,  the  Lake  Shore  built  in  all  2,233  care 
entirely  new  on  renewal  account,  making  the  total  number  rebuilt  entirely  new  in  sixteen 
years,  2,807.  The  stock  of  cars,  beginning  with  6,077  in  1870,  was  increased  to  10,185  in 
1874,  and  then  remained  practically  stationary  until  the  middle  of  1879,  when  the  increase 
be^an  to  the  figures  above.  Except  that  a  large  majority  of  cars  are  rebuilt  piecemeal, 
and  mamtam  a  kind  of  continuous  existence,  at  least  10,000  cars  should  liave  been  rebuilt 
durmg  this  period  instead  of  2,807.  It  is  probable  that  most  of  the  latter  were  broken 
op  entirely,  chiefly  because  they  had  become  of  too  antiquated  design  to  be  serviceable. 


Mi' 


1 66     aiAP.    V.-OPE RATING  EXPENSES-REPAIRS  OF  CAKS. 

146    The  repairs  »hich  the  road  using  foreign  cars  has  to  pay  for  in  addl- 

146.    1       repa  importance,  and  are  determined 

•'°:h!:  :r  M    vryH    "     n7oL  there  is  an  inspector,  usually  a  Joint  in- 

-:rio  aiits  ra!s  ov°r:rrvi::i^ra:ry;r.rKire:cfr:;::.de" 

determined  "^^  "'-- f -"y^ t  p     sed  oi  as  fuifiiiing  a.i  the  same 

-=ndir,::;^^^^^^^^^^^^^ 

rr:?:•mlaer^::a1du'^n1o.t•mrgr";ytents.     .--^vayaroad 
;"aVc:.^e::t'to  pay  for  repairs  due  to  gradua.  de.^^^^^^^^^^^ 

"°7  r  ti,:!:"  rpTprtc":;": ast  hi::;  "pL^  i..spectio^n,  it  does 

small  '°7-y/Xe    Lenh:  United  States  (or  theVt  twenty  years, 

'Z'::~Z^:iZ^^^^^^o.  but  be  greatly  affected.    Table  74 
the  appciretiL  cosu  v  ^         ^^^^^      ^ny 

Item.     Few  railways  keep.  F  enormous  a^^pjregate  of 

cost  of  the  vanous  .^..^  wh^^^^^  ^.^on 'which  appears  in  the  reports. 
"  repairs  o   cars,     ^hat  being  t  >  ^^^,^  ,^  determine  pre- 

or.  as  a  rule,  on  the  books.     It  is  ^ner^^^  Nevertlieless.  from 

cisely  the  ratio  of  the  vanou-te-  to  e^^^^^  other^^  N^  ^^^^   ^^^^^^^^^ 
the  information   given   m  Tables  70  to  73  ^^^ 

especallv  Table  87)  we  may  conclude  that  ^^e  actual  cost  P 

renewals  of  freight  cars  is  divided  very  nearly  as  follows . 


CHAP,    v.— OPERATING  EXPENSES-REPAIRS  OF  CARS     167 

Wheels 30  per  cent. 

Axles,  brasses,  and  axle-boxes, 30        " 

Springs jq 

Truck  frame  and  fittings, 5 

Total  truck, 70  ** 

Brakes, 5  <• 

Draw-bars, jq  «• 

Sills  and  attachments, 5  «« 

Car  body,  painting,  etc., t  «« 

Total, 100        " 

149.  Passenger-car  repairs  are,  for  wheels,  axles,  and  brasses,  but 
slightly  more  than  for  a  freight  car  per  mile.     Exact  information  as  to 
the  comparative  mileage  of  passenger  and  freight  wheels  is  difficult  to 
obtain,  owing  to  the  fact  that  as  soon  as  wheels  show  any  noticeable  de- 
fect, which  yet  does  not  make  them  unsafe,  they  are  withdrawn  from  pas- 
senger service  and  put  under  freight  cars,  often  making  a  large  mileage 
before  being  finally  scrapped.     The  general  tendency  of  the  available 
evidence  is  that  there  is  but  little  difference,  and  that  difference  in  favor 
of  passenger  cars,  the  effect  of  the  higher  speed  being  counterbalanced 
by  less  injurious  brakes  and  better  springs.   The  extra  cost  of  repairs  and 
renewals  of  passenger  cars  is  mainly  in  its  decorations,  better  painting, 
and  interior  fittings;  and  bearing  in  mind  that  passenger  cars  are  not 
exposed  to  anything  like  the  rough  service,  blows,  and  shocks  which 
come  upon  freight  cars,  we  may  say.  without  any  error  of  moment,  that 
the  average  cost  per  passenger  car-mile  is  about  as  follows : 

Frt.  Car.    Pass.  Car. 
Cts.  Per  Mile. 
o. 


Running  gear,  draw-bars,  etc 0.3 

Sills,  frames,  etc., o.i 

Painting  and  varnishing  car  body 

Interior  fittings  and  upholstery, 


Total. 


0.4 


0.2 
0.2 
0.5 

1-4 


tSO.  In  other  words,  the  cost  of  maintaining  a  passenger  car  for  those 
Items  or  parts  of  items  which  are  affected  by  differences  of  distance,  cur- 
vature, and  gradients  is  not  so  much  greater  than  for  freight  cars,  but 


l68     CHAP     V -OPERATING  EXPENSES^TRAm  WAGES. 

iBl    The  average  milea-e  of  freight  cars  per  year,  taking  the  wiioie 

miles  per  year,  or  even  le=s.     The  tende"cy  .  J  ^^^es  e..or- 

J        ^c«      ThP  mileao^e  made  by  dittereiu  cars,  nuwcvci, 

,       ••  W"  ^a  s  so  called,  belonging  to  the  independent  or  sem.- 

1   nUef^e   as'is  but  natural:  both  because  they  are  exclus.vc  y 

looked  after.     The  general  average  of  all  classes  ol  ^ 

70)  is  about  as  follows :  ^.^^^  ^^^  ^^^  ^.^^^  p,,  y,^,. 

,c  to    20  5,000  to    7.500 

Coal  and  flat  cars '^5^^   ^  9,000  to  .  5.000 

B"'"^?,'^ 7010100  25.000  to  35.000 

'■"'^MeV  : : : : '.  '•  35-45    -.000  to  .6.500 

The  average  ™ilea.o.  pas^.er  ca.  -^-^-,^1^.^. 
1!^:^:TrTl^^  than  this-up  to.   in  so.e  case. 

,.:t^C-,  are  less  dimcuu  ^^ -rtL1':o^rrr:hi^r; 

„ess.    The  following  are  a  close  ''PP^"'''"^^^*^^^  ^i,,^.     m  ,^■,^^^ 
prevail  in  this  country  for  average  runs  of  a  hundred  ^^ 

^hey  were  naturally  higher  than  ^^'S.  say    5  Per  ^^^^^^^  «^„^  [,,„,, 

^hey^;^;"c"oLSy  iM^^l'U  of  the  country,  but  less  than 
any  other  item  of  train  expenses :      ^^^^^^  ^^^^^^ 

^     ■          „  ftv5oto$3.75  ♦sso'o*^^ 

E"g'"«"='" ,\.x.o     loo  .75  to     2  oo 

1''^'="'^" 275  to     300  375  to     500 

Conductor ■=•'>  ^  ,  co  to     %V> 

Braken,an  (each.  $..75).     3-50  to     S-^S  3.5°  to     3  5^ 

Baggage-men,    .    •    •    •     •  •  •       ___J_11        - — 

$11.50  to  $14.00         $14.50  to  $16.50 


CHAP,    v.— OPERATING  EXPENSES-STRAIN  WAGES.     169 


153.  The  system  by  which  train  wages  are  fixed  varies  materially.  It 
is  sometimes  strictly  by  the  month  or  day,  especially  in  passenger  ser- 
vice—a certain  run  being  called  a  day's  work,  independent  of  the  time 
actually  employed.  These  runs  may  vary  anywhere  from  75  to  no  or 
120  miles;  but  if  it  constitutes  ^/^/^r/^  a  day's  work,  it  is  rated  a  day, 
independent  both  of  time  and  distance  run. 

This  system  was  formerly  universal,  and  is  still  very  common  for  pas- 
senger service  ;  but  with  increase  of  traffic,  and  especially  with  the  con- 
solidation of  lines  into  great  systems,  with  runs  of  widely  var>'ing  length, 
the  practice  is  coming  more  and  more  into  vog^e  of  paying  strictly  ac- 
cording to  mileage,  in  the  manner  specified  in  par.  191.  The  chances 
are  that  the  tendency  to  pay  in  close  accordance  with  mileage  will  be- 
come stronger  and  stronger  with  the  great  organizations,  especially  in 
freight  service,  while  the  former  plan  will  always  prevail  with  the  smaller 
independent  lines,  and  even  on  many  of  the  larger  lines  for  passenger 
service. 

154.  A  compromise  plan,  intermediate  between  these  two  extremes, 
is  at  present  more  usual  than  any  other.  The  runs  over  various  divisions 
are  graduated  as  i  day,  i^  day,  \-^^  day,  sometimes,  though  rarely,  \  day, 
etc.,  etc.,  so  as  to  have  a  close  correspondence  with  the  real  distance,  but 
not  to  be  in  exact  ratio  thereto ;  other  circumstances,  such  as  number  of 
stops,  etc.,  being  often  taken  into  account.  This  appears  to  be  not  only 
fairer  than  an  exact  mileap:e  basis,  but  more  acceptable  to  employes.  The 
present  system  of  handling  traffic,  by  which  the  freight  crews  not  only 
know  no  distinction  of  night  or  day  or  week-day  and  Sunday,  but  do  not 
even  recognize  the  day  of  twenty-four  hours,  tends  to  facilitate  this  basis 
of  payment;  the  crews  being  "on"  or  "off "  at  intervals  determined  by 
the  pressure  of  traffic,  and  not  at  all  by  the  number  of  hours  in  the  day 
or  days  in  the  week.  In  passenger  service,  or  wherever  the  freight  ser- 
vice is  tolerably  regular  in  its  character,  the  deference  paid  to  an  exact 
mileage  basis  is  much  less  marked.     (See  also  par.  191.) 

155.  The  tendency  is  strong  to  increase  the  length  both  of  locomotive 
runs  and  of  divisions.  Locomotive  runs  were  formerly  from  80  to  100 
miles.  At  present  they  range  by  preference  from  120  to  150  miles,  the 
gradients  being  often,  of  course,  a  controlling  condition.  The  prevailing 
tendency  is  well  illustrated  by  the  locomotive  divisions  on  the  Canada 
Pacific,  of  which  there  are  19  on  the  2445  miles  between  Montreal  and 
the  Pacific,  an  average  run  per  locomotive  of  I28f  miles.  The  shortest 
^nd  longest  mns  are :     (See  page  178.) 


I70 


CHAP. 


v.— OPERATING  EXPENSES— SUMMARY. 


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176         CHAP.    V.-OPERATING  EXPENSES-SUMMAKY. 


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178         CHAP. 


V.-OPERA  TING  EXPF.KSES-SUMMARY. 


6  f M2  . . 3.  . .4.  n6.  and  two  of  ..8  miles)  under  .20  miles. 
\  lo  12^  .25  and  .26  miles)  between  .20  and  .30  m.les. 
\  I'.lo,  ;;;:  Z.  U3.  .3..  .34  -.es)  between  .3°  and  .40  n-les. 

1  (145  miles)  between  140  and  150  miles. 

2  (150   152  miles)  over  150  miles. 

Thus  the  minimum  is  n2  and  the  maximum  .5^  miles.    This  practice 
tends  strongly  to  economy.  „^„^„-_„  ,„  tut  sliehtly  affected  by 

156.  GENERAL  AND   Sr..TION   EXPENSES  are  bUSUg      J 
any  probable  variations  in  the  line  and  g'^'^'^^- ^°   f'ns  con^.ected  with 
to'consider  then,  in  detail.  a>tboughJ°r  many  J    -^  ^^  ^„,     ^hey 

the  operations  of  railways.  ="=''   ^"^f'',' „[^„e  total  operating  ex- 
amount  altogether  to  about  "j.rty  per  ce"t  o     '^  P^ 
penses,  ranging  from  twenty  to  forty  per  «"'  '"  ^'^'^        ^  ,„  „pendi- 

^    167.  In  Tables  75-  76.  77.  78  "^%f' "^"/"'""'fd     '  several  interior 
tures  for  the  railways  of  the  entire  Un.ted  Sta  e   and  the  sev  ^^^^ 

groups  thereof,  for  the  four  great  trunk  ""-•   °^  '°"J,^'^,,  „,  ,„n,p„ted 
Ldforthe  six  '-ding  Chi«go  ln.s.     T^^^^^^^^  „^^^  ,„ 

riat  sT:  f:r=ii  -rrrtlticon  an  approximate,  si.- 

Table  79. 
Operating  Expenses  of  British  Railways.  1884-85. 


Onts  per 
Train-mile. 


Maintenance  of  way 

Locomotive  power 

Rolling  stock 

Traffic  expenses 

General  charges 

Rates  and  taxes 

Government  duty 

Compensation: 

Personal  injuries 

Damage  to  goods 

Legal  and  parliamentary  expenses.. . 
Miscellaneous 


Totals, 


11.32 

16.55 

6  05 

19-77 

2.87 

3-45 

0.6S 

0.27 

0.34 

0.51 

0.79 

62.60 


Per  Cent. 

18. 1 
26.4 

9-7 
31.6 

4.6 

5.5 
I.I 

0.4 

0.5 
0.8 

13 


100. o 


penses  has  taken  place  since 


,^=?.r?;.^:='.=tr„:riT„"..»~.. 


CHAP.  V.-OPERA  rmc  expenses-summar y,       i  79 


Table  80. 

Approximate  Estimate  of  the  Details  of  Operating  Expenses  for  an 

Average  American  Road. 

[Liable  to  considerable  variations  in  individual  instances,  especially  when  the  traffic  is 
very  ^reat  or  very  small,  but  to  much  less  extensive  variations  than  might  be  imagined 
even  ,n  extreme  cases.     The  average  total  cost  per  revenue  train-mile  is  still  not  ven^ 
much  below  $i.oo.  and  by  taking  it  at  that  even  figure  the  following  become  either 
percentages  or  cents  per  train-mile,  which  we  shall  hereafter  assume  them 

XO   B  C  J 


Train  Expenses. 
47.0  p.  <;. 


Engines. 
18.0  p.  c. 


Road 

engines. 

14-4  P-c. 


Fuel 7.6  p.  c. 

Water 0.4    '* 

Oil         and 

waste 0.8     ** 

^     Repairs —  cn- 
l      gines 5.6 


«( 


Maintenance  of  Way. 
23.0  p.  c. 


Train 

Wages  and 

Supplies. 

17.0  p.  c. 


Cars. 
12.0  p.  c. 

Track 

between 

Stations. 

8.0  p.  c. 

Road  BED. 
7.0  p.  c. 


^  Switching  engines 3.6  p.  c. 

Switching  engine  wages 1.6    " 


Train 

wages  and 

supplies. 

15.4  p.  c. 


Engine  w'ges.6. 4  p.  c. 
Car  wages. .  .8.5 
Car  supplies. 0.5 


<4 


Repairs  and  renewals..    ..lo.o  p.  c. 
Mileage  (a  practical  equiv- 
alent for  repairs) 2.0 


<( 


Renewals  of  rails 2.0  p.  c. 

Adjusting  track 6.0    " 


(  Renewing  ties 3.0  p.  c. 

\  Ei  "'        


I 


Yards  and 
Structures.  - 
8.0  p.  c. 


i)arihwork,  ballasting,  etc.. 4.0 

'  Switches,    frogs,    and    sid- 

p'."P  •••• 2.5P.C 

nruJges  and  masonry 3.5 

^  Station  and  other  buildings. 2.0 


(t 


Total  *'  Line"  or  Transportation  Expenses -o  o  p  c 

Station,  Terminal,  and  General  Expenses  and  Taxes...*.*..' .*.*.' .30.0    "  * 

Total  Operating  Expenses ioq.o 


p.  c. 


See  Table  81  for  similar  estimate  from  former  edition. 


,80         CHAP.    V.-OPEKATINGJXPENSES-SUR^^ 

curred  in  making  oyer  ^^^^^^^^^^ I'^^.l^^,  of  comparison  than 

the  result  is  more  ''''^'y^^fj,";',^;,^"'^ -''''>-'"  ^''"'^^'"• 

any  individual  attempts  to  do  ^he  same  it.    .  _^  ^^^^^ 

'u  Table  78  are  '"'ew.se  repeat  dU-  ^       ^^^^  ^^^^  ^^^^^„^^    , 
which  the  writer  computed  (or  ^^J°J^  ^,.^^  ,„  ^en  years.     It 

seventeen  different  roads,  ^^'^'^^avejaged  for  ho  ^^^^.^^.^^  .^ 

will  be  seen  that  the  <^°"«^P°"''^*"'f/Xd  a  pretty  accurate  basis  for 
singularly  close-quite  euou.h  ^°;°  i„  Table  79 -e  given  some  corr<^ 
estimating  the  expenses  of  any  roaa. 

sponding  statistics  for  English  radways. 

,i,»  o-round  eone  over,  we  may  estimate 
168.  Summanzmg  the  g'°""'l  S°  ^'    ^^  Central  States, 

0,e  operating  expenses  of  a  '-'-^y  •^;';^^^^"    „„,acter,  about 
laid  throughout  wiU>  steel,  and  of  good  ave  age  ^^_^      ^^,^ 

as  in  Table  80,  on  the  P'-ous  pag  •     W  ^^^^^     ^^^^ 

tnble  will  applv  to  railways  in  any  pait  ot  tiie 
;  "'c,   ..  c!!«  «.  v.™>i.~  being  V.  ™e  .    »m.  _^  ^_^ 

Table  81- 

Ct.ss,.c.Tto.o.OP...T,«o  EXP.WS.S  A.OPX.O  -N  THE  Fo.M.a  E.mo. 
CLASsiFicAii  ^^  ^^^^  Treatise. 


Train  Expenses. 
43  P  c- 


Maintenance  of  Way. 
ay  p.c. 


Engines 


.21  p.  e. 


Cars 

Train  wages. 


.lO 


12 


M 


lO    p.  C. 

2 


9 
.  lO 

.  6 
.  6 


Track  — 
Road  bed 


•«^ 


Yards  and  structures  7 

TRANSPORTATtON    EXPENSES     ^^ 


I 


iFuel.   

■{Oil,  waste,  etc 

I  Repairs •• 

Repairs,  inspection,  etc 

(  Enirineman  and  firemen 

I  Conductor  and  brakemen 

Renewal  of  rails 

.  Adjusting  track,  etc 

i  Renewal  of  ties  

1  Eariliwork,  ballast,  etc    .^. 
Switches,  frofis  and  s.d.ngs 
Bridgesand  bridge  masonry.  2.5  „ 
Elation  and  other  buildings...  i-S 


7 
6 

3 

4 
3 


»t 
tt 
t» 
t* 
•t 
It 
It- 


J^I5^T;S■a.,■'an7£S^ETcns^  ana  T.x«. 


....70   p.^c. 

« ■•  •  •  3^ 


Sution, 
Total  Operating  Expenses^ 


100   p. 


C//AP.    v.— OPERATING  EXPENSES— SUMMARY,  I8I 


of  the  facts  on  neighboring  roads.  This  table  gives  merely  a 
rude  average  for  use  in  the  remainder  of  this  volume  for  com- 
puting examples. 


Table  82. 

Percentage  of  Total  Revenue-Mileage  (assumed  as  ioo.)  of  Revenue- 
Passenger  Trains,  Revenue  Freight  Trains,  "Switching  Trains,"  and 
"Other"  (mostly  Work)  Trains  in  the  United  States  and' Each 
Group  of  States. 

[Camputed  from  the  Statistics  of  the  Census  of  1880.    For  Census  Groups  see  Table  75] 


Group  of  States. 

Miles 
Oper- 
aied. 

Revenue  Train-Mile- 
age. 

Other  Mileage. 
(Per  Cent  of  Rev.  Miles.) 

Pas- 
senger, 

Freig't. 

Total. 

Switch- 
ing. 

Other. 

TotaL 

New  England   

5,887 
28,693 

14.243 
25,038 

877 
13044 

51.8 
35.6 
34-3 
31-2 
16.9 

34-8 

482 
64.4 
6.V7 
68.8 
83.1 
65.2 

100.0 
100. 0 
100. 0 
100. 0 
100. 0 

lOO.O 

12.6 

16.5 

7.2 

16. 1 

4-4 
10.8 

3-5 
45 
5-6 

5-9 
1.9 

9.0 

Middle,  Ind.,  and  Mich 

16.1 

Soutliern  

21.0 

111.,  la.,  Wis.,  Mo.,  Minn 

La.,  Ark.,  Ind.  T  

12.8 
22.0 

Far  West  and  Pacific 

6.3 

19.8 

United  States 

87,782 

35-5 

645 

100  0 

14.4 

51 

«9-5 

It  is  quite  certain  from  the  statistics  that  the  actual  proportion  of  switching  mileage 
is  larger  than  the  above,  both  because  fully  one  third  of  the  roads  do  not  report  switching 
at  all,  and  because  many  include  switching  with  train-mileage.  The  per  cent  of  switching 
to  revenue-mileage  of  a  few  single  roads  runs  as  follows  : 


Eastern. 


Boston  &  Albany... 
Boston  &  Lowell... 

Cent.  Vermont 

Ras-ern 

Fitchburg  

M.iine  Central 

Nas'iiia  &  Lowell.., 

Old  Colony 

Prov.  &  Worcester. 


Per  Cent. 


12   9 

18. 

13-8 

29. 

21. 

3' 

3-* 


4 
4 


14  8 
37-3 


Middle. 


.Allegheny  Valley   

Atl   &  Gf.  Western 

Rait.  &*  Ohi.' 

CI..  C'>1..  C.  &  Indianapolis 

CI.  &  Pittshurg  

Col..  Ch.  &  I"d   Central.... 
Del.,  Lack   &>  \V.--!t€rn    .. 

N.  Y.,  L.  Ene&  W 

N.  Y.  Centra!  &  H.  R 


Per  Cent. 


35-5 
21.8 


5 
25 
33 

3t 

4 
24 
33 


The  two  roads  given  in  italics  above  are  among  those  which  show  an  extraordinarily 
Jow  cost  per  train-mUe.     The  main  cause  therefor  is  clearly  indicated  in  the  above  figures. 


l82  CHAP.    V.-OP ERA  TING  EXPENSE^SUMMA R  Y. 


In  Table  80  o,u  fif"'  o(  the  total  cost  of  motive-power  has  been 
allotted  to  switching-engines.  In  most  cases  '"«=-  -^  '^  S" 
propom..„  than  this,  independent  of  the  switching  done  by  .eg- 
Zlr  trains  in  iransUu,  as  is  partly  indicated  by  the  following 

Table  82.  ..       ^     t*  i,  1^  ©^ 

In  Table  8.  is  given  the  table  corresponding  to  Table  80, 
which  was  used  in  the  former  edition  of  this  treatise  as  the  as- 
sumed average  distribution  of  expenses  for  computing  examples. 


PART  II. 


THE  MINOR  DETAILS  OF  ALIGNMENT 


"Despise  not  small  thing:s,  for  therefrom  comes  sorrow  and  disap- 
pointment.  Yet  remember  that  they  are  small,  and  fix  your  aims  and 
your  thoughts  chiefly  on  the  great  ends  of  life."— Horace  Mann. 


II 


PART  II. 

THE  MINOR  DETAILS  OF  ALIGNMENT. 

CHAPTER   VI. 

THE   NATURE    AND   RELATIVE    IMPORTANCE   OF  THE  MINOR  DETAILS 

OF    ALIGNMENT. 

159.  The  three  details  of  alignment  which  are  properly  to  be 
classed  as  minor  details  are  the  following: 

1.  Distance,  or  length  of  line. 

2.  Curvature,  not  sharp  or  so  ill-placed  as  to  limit  the  len«h 
or  necessary  speed  of  trains,  but  Only  to  increase  the  expense  of 
running  trains.  cApcuse  oi 

3.  Rise  and  Fall,  or  elevations  overcome  by  the  engine  on 
gradients  not  exceeding  in  resistance  the  maximum  of  the  road 
and  hence  not  limiting  the  length  of  the  train  ' 

160.  These  are  termed,  collectively,  the  minor  details  for  the 
reason  that  their  influence  is  comparatively  trifling  upon  he 
future  o  ,„e  property  in  comparison  with  two  other  details  of 
overwhelming  importance,  viz.:  ciaiis  oi 

I.  The  amount  of  traffic  which  the  line  has  been  or  mav  be 
adapted  to  secure  (often  very  largely  and  even  ruinously  aff  c.ed 
b>  tl«.  U.cat:on,for  reasons  discussed  in  Chapter  III  the  fol 
lowing  Chapter  VII.,  and  Chapter  XXI.),  and 
be  thlr.'"''"?  °«^°'^^TS  or  other  causes,  whatever  thev  may 
cl>'ef  part  in  fixing  the  cost  of  handling  the  traffic.  These  causes 
lead  of  "Limiting  Gradients  and  Curvature  " 

rise^a°ndTn""''' ""■"  """^  ^"''"^  '^  ^'^'''""">  "'"'^'"'■e,  and 

<lo  s  soml       '^  """'  ''^'^''''' ^""-  ^«=Pa.ately  or  collectively. 

some  violence  to  popular  impressions,  which  exist  even 


I86   CH,   VL-RELATIVE  IMPORTANCE  OF  MINOR  DETAILS. 

^one  engineers.  It  will  therefore  be  well  that  we  should  first 
see,  by  a  -  bird's-eye  view"  of  the  subject,  free  from  all  detail, 
why  the  designation  is  a  proper  one,  nevertheless. 

161.  The  ideal  line  for  a  railway  between  any  two  points  is 
popularly  felt  to  be  a  right  line  between  the  two  termini.     This 
may  even  be  found  stated  as  an  axiom  in  some  engineering  works, 
and  in  a  strictly  engineering  sense   it  is  true.     If  it  were  true  in 
everv  sense,  it  should  follow  that,  in  proportion  as  a  line  deviates 
therefrom,  it  is   bad  ;    and   since  the  three   details  classified   as 
"  minor"  include  every  possible  deviation  therefrom  in  either  of 
the  three  dimensions  of   space,~curvature   representing  lateral 
deviations;  rise  and  fall,  vertical  deviations;    and  distance,  lon- 
gitudinal deviations,-the  three   together,  far  from  being  minor 
details,  seem  naturally  to  represent  or  include  all  the  conditions 
which  make  a  line  good  or  bad.     This  view  is  so  far  plausible, 
tfiat  it  is  asserted  or  implied  to  be  the  true  one,  not  only  in  com- 
mon  talk,  but  in  technical  discussions  or  writings.     "A  short, 
straight  line  was  obtained,  with  few  curves  or  high  elevations, 
will  pass  very  generally  as  a  description  of  what  must  be  an  ex- 

cellent  line. 

Yet  as  a  matter  of  fact,  this  view  is  wholly  erroneoiis-so 
eravelv  erroneous  that  the  excellence  or  badness  of  the  line  in 
all  the'minor  details  put  together,  within  wide  limits,  has  com- 
paratively a  very  slight  influence  on  its  value  as  an  investment 
or  on  its  usefulness  to  the  public. 

162.  We  shall  see  why  this  is  true  of  each  detail  separately,  as 
we  come  to  consider  each  in  detail.  To  see  why  it  is  true  of  all 
three  put  together,  let  us  take  the  case  of  two  railways  be- 
tween the  same  points-one  a  little  shorter,  a  little  less  crooked, 
and  with  a  little  less  up  and  down  in  its  gradients;  but  suppose 
them  both  to  have  cost  the  same  money,  to  have  the  same  tribu- 
tary population,  to  be  able  to  haul  the  same  trains  with  the  ^''"^^ 
engines,  and  to  make  the  same  time  between  term.n.  These 
conditions  obtain  in  many  instances,  and  may  conceivably  in  a  U 
Nay  we  might  even  extend  our  parallel,  and  assume  that  there 
are  considerable  differences  in  one  or  the  other  of  the  minor 


CH.   VI.-RELATIVE  IMPORTANCE  OF  MINOR  DETAILS.    iS/ 

details  between  the  two  lines,  but  always  on  tlie  condition  that 
they  st.ll  remam  minor  details  as  already  defined,  in  that  they 
do  not  affect  the  sources  of  traffic  nor  the  amount  of  trafnc  which 
can  he  handled  by  one  train. 

163.  Which  of  these  two  lines  is  the  best  property  '  It  is  a 
matter  of  the  merest  chance-a  mere  question  of  management. 
or  of  business  shrewdness  in  effecting  connections.  The  difVer- 
ence  in  the  minor  details  will  beyond  doubt  be  of  large  absolute 
importance  but  will  have  so  trivial  an  effect  comparatively  that 
It  will  hardly  enter  into  the  question  at  all. 

164.  This  results  simply  from  the  broad  general  fact  that  those 
deta,  s  aftect  only  //,.  cost  per  trip  of  running  trains,  and  that  but 
thghty,  while  they   do  not  reduce,   nor  in   any   manner    affect 
(within  wide  limits),  either  the  work  done  or  the  revenue  earned 
by  each  train.     It  is  now  abundantly  established  bv  experience 
that  the  effect  of  those  details  on  the  <iirect  cost  per' trip  or  per 
mile  of  running  trains  is  an  exceedingly  small  percentage  of  The 
aggregate,  within   the  widest  limits  of  deviation  which  exist  in 
practice      As  for  distance  :  the  additional  cost  of  runni„<r  a  few 
more  miles  is  but  a  small  portion  of  the  average  cost,"and   is 
ahvays   counterbalanced    by   the    receipts    of    some   additional 
revenue-often  enough  to  make  the  advantage  greater  than  the 
disadvantage,  and  ahvays  enough   to  greatly  reduce  the  disad- 
vantage.    As  for  curvature,  and  rise  and  fall:    it  is  now  estab- 
lished beyond  all  question  that  no  considerable  difference  in  the 
aggregate  expenses  per  train-mile  on   different   railways,  or  on 
different  divisions  of  the  same  railway,  can  be  detected,  which  is 
clearly  due  to  differences  in  the  amount  of  curvature,  or  rise  and 
Wl   even  when  very  marked  differences  in  those  details  exist 
rabies  75  to  8o,  as  well  as  Table  83.  afford  cumulative  evidence 
Of  this  fact,  which  has  been  commented  on  at  intervals  from  the 
very  beginning  of  railroad  history.     One  of  the  eariiest  records 
Of  the  fact  IS  the  following  statement  of  the  eminent  En<^lish 
ngmeer  Mr^Cha.les  B.  Vignoles,  formerly  President  of  the  In- 
s Vs  "°P       ^'V  oE."Si"<="s,  as  quoted  with  approval  in  Demp- 
si^y  s     Practical  Railway  Engineer"  (p.  n). 


I 


I88   CH.   VI.-RELATIVE  IMPORTANCE  OF  MINOR  DETAILS. 

~"l65.  •' Mr.  Vignoles  stated  in  a  paper  before  the  British  Association 
for  the  Advancement  of  Science  that  he  had  analyzed  railway  expenses 
of  working,  and  the  average  expenses  of  a  train-m.le.  as  deduced  l.om 
several  years'  experience  and  observation  on  various  ra.lways  operaung 
uncL  dffferent  cLumstances  and  with  greatly  different  gradients.  The 
relit  was  that  on  passenger  and  light  traffic  lines  the  total  cost  of  a  train- 

Table  83 
AVERAGE  Cost  Per  Train-Mile   of   running   Engines  on  the  several 

DmSlONsTDIFFERING   VVID.LV    IN   THE   AMOUNT  OF   CUKV.TUKE   AND    KiS. 
rND^LL)  OF  THE  PENNSYLVANIA  AND  PHILADELPHIA  &  EkIE   RAILROADS. 

Averaged  on  the  Pennsylvania  Railroad  for  a  period  of  four  y^r.  (1859^70-73),  and 

on  the  Philadelphia  &  Erie  for  three  years  (1866-70-73). 

[Reproduced  from  first  edition  of  this  Treatise.] 

PENNSYLVANIA   RAILROAD. 


Divisions. 


Passenger  Engines. 


Re- 
pairs. 


Eastern 

Middle 

Av.  Eastern 
and  Middle 

Western 

Mountain  and 
Tyrone  ... 

AvWf  stern. 
M  o  u  n  tain 
and  Tyrone 

Av.  of  entire 
road 


6.3? 
10.08 


Fuel 

6.08 
6.33 


Stores 


Total 


1.03 
1.03 


8. 30 
7-97 

3.Q1 


5-94 
7.07 


6.20 
6.38 

6.70 
6  54 


X3  43 
1744 


Freight  Engines. 


Re- 
pairs. 


10: 
1. 17 

.73 


6-37 


•  95 


1543 
15-52 

"34 


13  43 


6-53 
7.67 


Fuel. 


7.78 
7.67 


Stores  Total 


•99 


14-43 


7.10 
10.54 

9-20 


7  72 
8.79 

7.38 


Average  op  Passenge« 

AND  Fkkight. 


Re- 
pairs. 


9.91 
8. 50 


8.09 


1.86 
1. 10 

1. 18 
1.61 

•93 


»5-56| 
16.44 


16.00 
20.94 

17.60 


6.43 
8.87 


Fuel.  Stores 


6-93 
7  00 


1.27 


7.91         1.23 


19.27 


17.63 


7. 65,       6.96 

9  251     7  59 
6.60'     7-04 


X.15 
1.07 

x.xi 
«^39 


•  83 


7-9a 
7.78 


7  3'' 
7-14 


1. 11 


1. 11 


Total 

14.50 

16.94 

15  7a 
18  33 

14  47 

if-3S 
16.03 


PHILADELPHIA  &   ERIE   RAILROAD. 


Divisions. 


Eastern 

Middle 

Western  . . 

Average 


Averagr  of  all 
Engi.nes. 

Re- 
pairs. 

10.64 
II. I 

10.49 

10.74 

Fuel. 

Stores 

Total 

9.91 
9-77 
9  92 

9.87 

1.19 
1. 19 
115 

21  74 
22.06 
21.56 

1.18 

21.79 

On  the  Philadelphia  &  Erie  the  expenses  of  en- 
gines are  not  kept  separate  for  the  different  classes. 
The  difference  m  the  cost  of  repairs  from  thai  on  the 
Pennsylvania  Railroad  is  due,  as  the  writer  learns, 
to  the  very  different  character  and  condition  of  en- 
gines. 


CH.   VI.-RELATIVE  IMPORTANCE   OF  MINOR  DETAILS.    1 89 

mile  averaged  3..  per  mile-2..  M.  being  tl,e  least,  and  3..  Ad.  the  Great- 
est; and  tl,atth,s average  seemed  to  hold  good  irrespccLofgradsZa 
curves  .n  .tal.cs  as  quotedj.  It  was  not  found  practicable  to  distituish 
the  add.t,o„al  expense,  if  any;  but  .-.s  three  fourths  of  railway  expen  es 
were  qu.te., .dependent  of  these  carves,  such  add,tio„s  must  be  ImaH '• 

66.  1  he  esseiuial  truth  of  this  statement  has  been  grou.in<r 
better  and  better  established  with  time  to  the  present  day,  an3 
we  shall  read.ly  find  evidence  that  it  even  understates  the  flcts 
when  we  come  to  consider  the  effect  of  these  details  in  the 
separate  .terns  of  railway  expenditure.  From  this  it  does  not 
follow  that  these  details  have  no  important  effect  on  expenses. 
They  do  have  an  important  effect,  which  increases  by  a  la>-.^e 
pccentage  certain  single  items  of  expenses,  and  is  .eadily  fac^d 
there.n.  But  they  always  add  only  a  trifling  pe,centage  to  the 
aggregate  expenses,  even  when  very  marked  diffcences  exist 

167.  And,    moreover,    the    important    further   fact    must    be 
remembered  that,  as  respects  any  one  line,  the,e  can  be  at  most 
as  we  began  by  assuming  (par.  162),  only  a  "little"  difference  in' 


Fig.  s. 

^he  minor  details  for  the  vastest  expenditure  cannot  effect  much 
mo  e.  No  possible  expenditure  can  eliminate  curvature  alto- 
gether  and  give  a  continuous  right  line  A£,  Fig.  5,  of  any  con- 


Fig.  6. 


s^derable  length,  m  place  of  the  curved  line  shown,  nor  make 
much  more  reduction  in  it  than  is  indicated  bv  the  dotted  line  in 
••■S.  5;  nor  can  we  make  moie  than  a  small  diffe.ence  in  distance 


I 


I90   CH.  VI.-RELATIVE  IMPORTANCE  OF  MINOR  DETAILS. 

ordinarily,  nor  have  we  more  than  the  choice  between  the  grade- 
lines  b  and  ..  Fig.  6  saving  a  mere  fraction  o  the  nse  and  fall. 
The  grade-line  „,  taking  out  all  the  rise  and  fall  between  A  and 
n  is  rarely  a  financial  or  physical  possibility. 

'  168.  For  these  reasons,  assuming  what  cannot  always  be 
assumed,  that  the  engineer  has  first  done  well  in  putting  h.s  line 
upon  the  ground  so  as  to  avoid  unnecessary  distance,  curvature 
and  rise  and  fall  (i.e..  that  which  might  have  been  eliminated 
.vi.hout  expense),  to  eliminate  altogether  even  '<  little  difieiences 
in  the  minor  details  will  ordinarily  involve  an  immense  expense. 
But  ftrant  them  all  to  have  been  eliminated,  without  expense, 
from  the  least  favored  of  the  two  lines  which  we  began  by  assum- 
in-  (par.  162),  and  let  us  see  with  somewhat  more  detail  to  what 
extent  it  will  be  benefited  thereby.     (For  a  more  exact  estimate 

^"it  wiU  not  reduce  the  interest  charge,  even  it  it  do  not  (as  it 
ordinarily  must)  increase  it,  and  that  takes,  say,  one  third  of  the 
receipts.  As  respects  the  remaining  two  thirds  of  the  receipts, 
which  includes  what  are  ordinarily  termed  "  operating  expenses: 
It  will  not  reduce  the  number  of  trains,  for  the  length  of  trains 
is  not  affected  by  them.     Consequently, 

It  will  not  reduce  train  wages  and  supplies,  which  are  (Table 
io\  some  17  per  cent  of  the  expenses  ;  .       ,  u  - 

It  will  not  reduce  station-agenfs  wages,  nor  station  labor, 
tior  the  salaries  of  the  general  officers  and  clerks,  nor  taxes  nor 
terminal  expenses,  and  these  constitute  some  30  per  cent  of  the 

expenses ;  .  •.  r  «i   «:i 

It  will  somewhat  affect  repairs  of  engines  and  cars,  fuel,  oil 

and  water,  and  maintenance  of  way,  aggregating  some   53   per 
cent  of  the  operating  expenses;  but  ,  r  ,„,  ^nd 

,69.  It  will  not  affect  that  portion  of  the  cost  of  fuel  and 
enoiue  and  car  repairs  which  is  due  to  yard  and  station  vvork 
sto^pping  and  starting,  wear  of  paint  and  rottingof  wood,  natura 
ruling  wear  over  the  rest  of  the  possible  line,  injury  to  boilers 
from  cooling  off,  care  and  maintenance  of  shops  (excep  .n  an 
indirect  and  trivial  way),  etc.,  etc.  These  causes  together  in- 
elude  an  immense  proportion  of  the  total  of  these  items. 


CH.   VI.-RELATIVE  IMPORTANCE  OF  MINOR  DETAILS.    I9I 

We  have  seen  (par.  142)  that  something  like  28  per  cent  of 
the  locomotives  of  New  York  State  are  used  for  vard  work  only 
besides  which  a  large  proportion  of  the  wear  and' tear  and  waste 
of  power  of  engines  in  regular  service  comes  from  yard  work 
and  stopping  and  starting.  Precisely  how  much,  we  will  not 
now  consider ;  but  it  will  be  plain  in  a  general  wav  that  only  a 
minute  percentage  of  even  the  cost  of  engine  and  ca'r  repairs  can 
be  saved  by  improvements  of  line  which  do  not  reduce  the  num- 
ber  of  trains  required. 

Then  as  to  maintenance  of  way:  All  that  degeneration  which 
comes  from  the  elements,  from  the  decay  of  ties,  from  the  growth 
of  weeds  ;  expenses  for  maintaining  frogs,  switches,  sidin-rs 
yards  stations,  bridges,  culverts,  crossings,  signals,  track-walkers 
(fdV  the  most  part),  track-watchmen,  hand-cars,  fences,  etc.,  are 
virtually  unaffected,  or  nearly  so,  by  any  modifications  of  line 
{except  distance)  which  are  within  the  power  of  the  engineer  to 
effect,  as  ,s  likewise  that  portion  of  the  wear  of  rails,  ties,  and 
surfacing  which  would  exist  on  the  best  possible  line,  and  which 
IS  on  any  long  line  (for  none  are  everywhere  unfavorable)  by  far 
the  larger  part  of  it. 

oK  "^'i^li^'f  '■^™^'"='  therefore,  only  a  very  small  fraction  of 
about  half  the  operating  expenses,  or  a  very  small  fraction  of 
one  third  of  the  revenue,  which  varies  directly  with  the  minor 
details  of  alignment,  whereas  a  full  half  (in  round  figures)  of  the 
operat.ng  expenses  or  a  full  third  of  the  revenue  varies  directly 
with  the  number  of  trains.  The  smaller  loss  is  still  enough  to 
justify  and  require  the  utmost  care  of  the  engineer  to  avoid   it, 

Zrll  11"^-  T"^''  '"  '"'"'"  "•  "--di"^"')'.  anything  but  the 
«or  t  of  b.d  judgment  to  sacrifice  the  securing  of  good  limiiing 
gradients,  or  the  reaching  of  more  traffic  points,  to  get  "a  shorf 
traight  and  level  line,"  which  may  or  may  not  mean'a  good  line! 
for  ve  shall  see  (Part  III.)  that,  although  a  tolerably  •'  level  "  line 
passing  over  low  summits  ordinarily  means  one  with  low  ruling 
guides,  yet  that  the   two  have  no  very  exact   relation  to  each 

171.  We  may  further  enforce  the  very  important  moral  of  the 


192    CH.   VI.-RELATIVE  IMPORTANCE  OF  MINOR  DETAILS. 

comparative  unimportance  of  the  minor  details  of  alignment  by 
what  is  reallv  a  close  parallel  from  ordinary  business  life : 

Let  us  assume  the  case  of  a  large  wholesale  house  which 
sends  out  its  "drummers"  to  all  parts  of  the  country  to  obtain 
business.  Every  time  it  sends  one  out  it  has  a  reasonable  cer- 
tainty of  sellin-  something  and  a  possibility  of  selling  a  good 
deal  Such  a  house  may  be  compared  to  a  railway  corporation, 
which  sends  out  its  trains  to  secure  a  certain  minimum  but 
varvins:  maximum  of  traffic. 

'       Now  in  the  conduct  of  such  a  business  there  are  three 

ends : 

1.  To  sell  all  the  goods  possible. 

2.  To  dispense  with  all  the  miles  of  travel  possible.  ^ 
-K    To  reduce  the  cost  of  travel  per  mile.                              ^ 

So  in  planning  a  railway  there  are  these  three  ends,  precisely 
analogous  to  the  former  in  their  nature,  and  as  nearly  as  may  be 

in  degree  : 

1  To  sell  all  the  transportation  possible. 

2  To  dispense  with  all  the  train  miles  possible. 

X   To  reduce  the  cost  of  running  trains  per  mile.  _ 

172.  Of  all  the  three  ends  sought  in  the  drumming  business, 
the  least  important-the  minor  detail  of  the  drumming  busi- 
ness-is to  leduce  the  direct  costof  travelling;  the  expenditures 
for  railway  and   sleeping-car  fares   and   to   "otels-     Not  tha 
they  are  unimportant,  for   the  firm  which  was  reckless  abou 
theL  might  readily  be  ruined  ;  but  they  are  a  minor  detail,  of 
smaTl"ffcc    upon  the  ultimate  result,  whether  they  be  large  or 
smal    W  the  business  as  a  whole  be  well  planned  and  well  con- 
ducted   Ind  the  firm  which  should  concentrate  its  attention 
upon  them,  giving  its   thought  to  selecting  -f-  where  te 
travelling  expenses  per  day  or  per  mile  were  small,  to  t^e  neglec 
of  the  more  important  question  of  securing  more  business^o 
reducing  the  amount  of  travel  required,  whether  its  cost  per  tn.le 
or  per  day  were  large  or  small,  would  be  justly  deemed  on  the 

'^NoTut  many  have  been  so  ruined,  for  the  petty  end  which 


CH.  VI.-RELATIVE  IMPORTANCE  OF  MINOR  DETAILS.    I93 

the  dullest  mind  cannot  fail  to  perceive  and  comprehend  may 
fill,  from  that  fact,  an  unduly  large  arc  in  the  mental  horizon  of 
many. 

173.  And  so  not    only  some  but  many  railways  may  be    as 
they  have  been,  ruined  as  productive  properties  by  the  undue 
importance  given  by  engineers  to  the  minor  details  of   align- 
ment :  those  details  which  do  not  add  at  all  to  the  traffic  of  the 
line,  and  which  do  not  reduce  at  all  the  number  of  trains  needed 
to  handle  it,  but  which  simply  effect  a  "picayune  "saving  in  the 
cost  per  mile  run  ;  a  saving  which  is  often  so  slight  as  to  be 
imperceptible,  which  still  more  often  adds  to  the  interest  charge 
more  than  it  saves,  and  not  infrequently,  as  we  shall  see,  results 
in  a  negative  saving,  or  absolute  loss  from  the  larger  expendi- 
ture. ^ 

As  a  matter  of  fact,  the  first  and  most  important  end  in  the 
conduct  of  the  drumming  business  is  to  get  all  the  business  possible  • 
everything  else-both  the  drummer's  time  and  his  expendil 
tures-is  subordinate  to  that,  because  if  the  end  is  not  secured 
the  means  must  necessarily  be  bad.  So  with  a  railway  corpora- 
tion  :  the  first  and  most  important  end,  when  there  is  any  great 
difference  between  routes,  is  to  put  the  line  where  there  will  most 
business  come  to  it. 

174.  And,  finally,  the  second  most  important  end  in  the  drum- 
ming business  is  to  obtain  the  most  business  with  the  least 
possible  aggregate   of   travel,  because   avoidable  travelling   is 
expensive,  not  only  from  its  direct  cost,  but  from  its  waste  of 
the  drummer's  time  and  possible  earnings  in  more  productive 
localities.     If  in  any  possible  way  one  drummer  can  be  made  to 
do  the  work  of  two,  or  two  drummers  the  work  of  three    the 
economy  is  so  great  that  any  probable  or  possible  difference  in 
the  drummer's  expenses  per  mile  will  hardly  affect  the  question 
at  all.    So  with  a  railway  corporation:  the  second  most  important 
end  is  to  do  their  business  with  the  least  number  of  trains  per 
rnile,  because  making  one  train  do  what  two  did  before  saves  all 
the  expense  of  the  extra  train,  whereas  cutting  out  some  curva- 
ture  or  distance  will  only  save  a  part  of  it— and  a  very  small 


:■  i. 


m 


,94  CH.   ,I.-HBLATIVEJA^^ 

'"T'T^il  all  has  been  done  which  can  be  done,  therefore,  to 
part.     Until  an  nds  L.CC  :,  u  Viardlvworth  while  to 

reduce  the  number  of  trains  required,  it  is  hardly  w  ort 

;t  a  thought  to  reducing  the  -P-^J-^J^thTl  tter^^^ 

Lrds  it  ^--^rSSrwTr  tlJct^^^^^        on  the  two 

iriS:"--rrtrg:"t  the  busmess  to  carry  and  to  maUe 

' 'T;;  The  stud^nt'can  do  no  more  profitable  thing  to  qualify 

Why  this  is  so  in  railway  business  appears  more  in  detail 
the  three  following  chapters. 


CHAPTER  VII. 


DISTANCE. 


176/  The  effect  of  a  variation  in  the  length  of  a  railway  on  the 
value  of  the  property  we  have  seen  (Chap.  III.)  to  be  peculiar  in 
this— that,  alone  among  all  the  details  of  alignment,  it  has  a 
direct  and  material  effect,  not  only  on  expenses,  but  on  the  reve- 
nue or  receipts,  which  tends  very  materially  to  reduce  its  finan- 
cial disadvantage.  As  a  contrary  view,  leading  to  a  feeling  that 
any  longer  distance  between  termini  is  an  unmitigated  mis- 
fortune, and  a  great  one,  is  common  even  with  engineers  and 
practical  railroad  men,  and  as  this  view  is  as  mistaken  as  it  is 
common,  and  leads  to  much  mistaken  action,  it  will  be  well,  be- 
fore proving  affirmatively  that  this  view  is  an  error,  to  point  out 
the  nature  and  source  of  the  error  (which  is  easily  enough  seen), 
since  the  presumption  is  strong  that  any  view  which  is  widely 
held  is  a  true  one. 

177.  Its  origin  lies  in  a  series  of  plausible  nou-sequiturs,  which 
are,  in  a  few  words,  these — no  one  of  them  being  true  : 

1.  Rates  are  (usually  and  whenever  possible)  fixed  at  so  much 
per  mile,  because  (fallacy  i)  it  costs  so  much  per  mile  to  transport 
the  passenger  or  freight.  Ten  per  cent  more  or  less  distance 
means  ten  per  cent  more  or  less  fare,  and  "  necessarily"  (fallacy 

2)  ten  per  cent  more  or  less  expense. 

2.  But  on  our  particular  railway  the  service  rendered  is  just 
as  valuable,  if  transportation  be  furnished /;w;/  the  point  desired 
to  the  point  desired,  whether  the  intermediate  distance  be  90 
miles  or  100  miles,  and  hence  (by  a  long  but  unconscious  jump 
over  a  vast  hiatus  in  the  reasoning)  we  shall  **  of  course"  (fallacy 

3)  receive  the  same  money  for  it.     Therefore,  necessarily. 


I 


t » 


If 


W 


,96  VJI.-DISTA^■CE-RELATION   TO  BATES  AND  EJCPENSES^ 

,  All  extra  distance  adds  greatly  to  the  cost  of  the  service 
/fMHcv  I  and  .);  adds  nothing  to  the  value  of  the  service  (true 
int'h  with  ce  tain  limitations);  hence  adds  nothing  to  revenue 
(falla°Jr3),  and  hence  is  among  the  greatest  of  disadvantages: 

^  The  truth  is,  not  one  single  item  of  railway  expenditure  large 
or  sm'l  not  even  fuel  or  wear  of  wl.eels.  varies  in  direct  ratio 
with  d  'tance.^  in  anything  like  direct  -tio  and  mo,,  t  an 
Llf  of  them  are  very  slightly  if  at  all  affected  thereby     On  te 

other  hand,  a  very  large  P-PO''-"— --^./^ir,^  .^'fcr 
whole-of  the  receipts  does  vary  directly  with  the  distance. 

U8.  The  reason  why  rates  are  so  generally  based  more  or  less 
dir  cUy  on  distance  hauled,  and  on  nothing  else  except  necessity 
i  no      n  the  least  that  it  is  a  primary  factor  ,n  the  cost  of      e 
service    but   simply  this:    The   sale  of  transportation,  like  the 
salof'any  other  commodity,  is  governed  by  the  one  universal 
busin  -  iL  of  selling  whatever  is  saUd^le  as  "early  as  po-bl 
for  at  least  as  dearly  as  is  prudent  and  wise),  regardle  s  of  the 
lost  o    production      The  selling  price  of   no  marketable  com- 
modify  whether  transportation  or  houses  or  cotton  cloth,  is  fixed 
bv  the  erst  of  production,  except  that  if  it  will  not  bring  a  pro- 
fit  on   itscost  it  is  no  longer  produced  ;  and  for  railways  any 
such  attempt  would  be  particularly  senseless,  for  the  reason  that, 
as  we  have  elsewhere  seen  (par.  40,  i8,),  the  cost  of  any  par- 
dc^lar  sale  of  transportation  may  be  considered  as  varying  any- 
Tere  f--  "'o  "P-rds  ;  depending,  to  a  <- J-;'-  -'  , 
than   in   any  other  commercial   transaction,   simply   upon  the 

amount  that  can  be  sold.  . 

179.  Thus  it  has  happened  that  the  distance  transported  as 
been  made  the  basis  for  tariffs  (when  they  have  any  basis  w  la  - 
ev  r  other  than  the  amount  which  it  is  possible  to  col le  )  a 
measurincr  in  a  rude  wav,  not  the  cost  of  the  service,  but  the 
Tonsumei^s  idea  of  its  value.  In  point  of  fact,  the  distance  trans- 
no"  ed  U  but  one  of  many  circumstances-and  certainly  not 
th      1st    important-which    fix    the    cost   of    transportation. 


yir.-DISTANCE-RELATJO^^^^^S  AND  EXPENSES.  I97 

Grades,  curvature,  cost  of  construction,  ^M^^^T^^Z^^^^, 
ume  of  traffic,  whether  the  cars  return  full  or  em^ty-al  U.ese 
have  very  much  more  to  do  with  the  cost  of  service  than  tl  ! 
mere  distance  transported,  but  they  are  entirely  neglected  in  fix! 
■  ng  schedules  of  rates,  simply  because  the  consumer  is  no  con- 
scious of  receiving  any  value  when  he  is  transported  over  Lrva 

ZZZl       '""""v  ''  '^"""'^"^  °^  -eiving'value  whin  Te   s 
transpoited  over  distance.     For  this  very  humble   reason  only 

t:xes"hmf"r  """  '^^"^"-"-'   ^^-'y-  'Mile  r^I; 
taxes  him  for  the  one  service  and  not  for  the  other,  so  that  it  mav 

even,  to  a  certain  extent  and  under  certain  circum  tances  an^so 
long  as  those  circumstances  continue,  be  a  positive  advantage    o 
a  line  to  have  a  few  miles  of  extra  distance"  especially  wl  en  a^ 
ditional  way  traffic  is  thereby  secured  ^ 

nec^Ll'Tn  l'"r'""\'^°^  '"'"  "'"'"'  '"^•^"  ''  --a-ably 
nece  sary,  ,n  considering  the  effect  of  distance,  to  consider  its 

effect  on  revenue  as  well  as  on  expenses,  even  if  the  former  be 

considered  only  to  be  disregarded.     To  disregard  it  is  often  the 

Pue,rTniibr""''r°''"":  "^^°"  '^  "°  °"^^-  A^  -  ^"-■°» 

pu.ely  of  public  policy-that  is   to  say,  if  the  interests  of  the 

i:7.zz\:r '"  ^""^"^"^  ^"'"'-^  '^^"''-'  --^^^'^  ^^- 

terests  of  the  community  as  a  whole-tlie  effect  of  distance 
upon  operating  expenses  would  be  the  only  one  which  here 
would  be  need  to  consider,  and  its  effect  on  revenue  sho  Id  n"I 

Lid  f"  ::  ''  ""•  '■°''^'""  '""^  ^^^'  --'"  rendered  and 
paid  for  IS  the  transportation  of  persons  or  property  from  one 

erm.nus  to  another,  the  precise  length  of  track  between  the  two 
should  have  no  more  effect  upon  the  price  paid  than  the  prec  se 
amount  of  curvature  or  rise  and  fall,  and  much  less  than  tlfe  il  es 
of  uling  grades.  All  should  be  considered  or  none  should  ie 
An<l  even  in  the  case  of  railways  constructed  bv  private  en-' 
rnrr%    T'"""""-^  P''°''''  "'"'°"^''  "^e  fact  that,  both  by  law 

hiy^A.       ^"■^^""""^  --""'e  a"d  not  to  other  disadvantages 
■s  entitled  to  a  certain  legitimate  weight,  yet  the  nature  of  tfils 


m 


198   VII.-DISTANCE-RELATION   TO  RATES  AND  EXPENSES, 

<:redit  side  greatlv  affects  the  expediency  of  relying  on  it  ;  for 
it  is  obtained,  not  by  rendering  more  valuable  service,  nor  by 
decieasin-  the  cost  of  the  service,  but  by  the  corporation  avail- 
ing itself'of  an  arbitrary  custom  to  transfer  a  portion  of  the 
burden  arisin-  from  one  element  of  an  unfavorable  line  (and 
not  of  others)^from  its  own  shoulders  to  the  public  at  large,  or 

to  its  connecting  companies.  , 

Moreover,  this  is  a  variable  power,  which  does  not  always  exist 
at  'dl  We  will  therefore,  for  the  present,  postpone  all  discussion 
of  that  side  of  the  question,  and  neglect  it  wholly,  until  we  have 
determined  the  effect  of  distance  upon  operating  expenses. 

181.  As  illustrating  the  vastly  greater  effect  of  other  causes  than  distance  on 

the  cost  of  iransportaiion:  . 

Wm  von  NSrdling.  one  of  ihe  most  eminent  of  Austrian  engineers,  m  a 
study  on  the  cost  of  railway  transportation,  apropos  of  »  P^?"^"'""  '°7°"- 
s  ructing  large  canals  to  connect  the  Danube  with  the  Oder  and  the  Elbe. 
Tubrnts  some  interesting  calculations,  in  ,vhich  he  avoids  '"e  m.stalce  so 
commonly  made  in  such  calculations  (and  oftener  in  Europe  than  elsewhere) 
of  calculating  the  .r.ra,.  cost  per  mile  of  transportation  on  'h^  radr-^;  -^ 
assuming  that  to  be  the  measure  of  the  cost  of  transporting  any  greater  or  less 
amount  of  traffic  any  greater  or  less  distance. 

Af.er  calculating  that  the  average  cost  per  ton  per  m.le  on  tl^e  T^eiss  Ra^ 
„ay  of  Austria,  in  1875.  »as  0,98  cent,  exclusive  of  loadmg  and  unload  ng.  he 
Tnds  that  addi.ional  freight  under  ordinary  conditions  ,vould  h^'e  cos  0^4  7 
«n,  »i.h  cars  full  one  way  and  returning  empty,  0.392  cent;  and  full  bo  h 
Z'.  o  U5  cent  per  ton  per  mile;  while  back  load  for  cars  that  otherwise  would 
Tetmn  empty  would  have  added  only  o.  .3o  cent  per  ton  per  mile  to  the  expenses. 

THE   EFFECT   OF   DISTANCE   ON    OPERATING    EXPENSES. 

182  The  cost  of  operating  additional  distance  not  only  is 
.,ot  the  same  per  mile  as  the  average  cost,  but  is  not  even  a  con- 
stant quantitv  per  unit  of  additional  length;  that  ,s  to  say,  .s 
by  no  means  'the  same  per  mile  when  the  addition  to  be  cons.d- 
ered  is  one  mile  as  when  it  is  twenty.  With  the  small  changes 
of  distance  which  most  frequently  occur,  the  number  of  yearly 
trips  of  rolling-stock,  the  number  of  buildings  and  s.dtngs,  and 


ClfAP.   VII.-DISTANCE-EFFECT  ON  EXPENSES. 


199 

the  considerable  class  of  expen^res  which  vary  ther"^^^^^irTr 
ma,n    pract.cally  constant,  as    well   as   (very    freque     J    '„?„ 
ages,   and   are   not   perceptibly  affected    until    the    change"" 
length  amounts  to  a  considerable  percentage.      How  much  such 

183.  Maintenance  of  Way  — -Th^  /»«f ;^^       .     r 

to    e  performed.     It  is  essentia,  for  safety  that  tL'Tsl  Lm  be  a  In^Z 

numl;rrse«i:'s%  'luVtirirn'r  :r  "  '''^"''  ""  ""°  ^  "- 
-signed  to  each,  whose  dut/'^rit  a  arte  p::Z":;':h  """"^.^  ""  "'^" 
watchfulness  and  -tinkering.  "     1^;=  „T  T  /  ^  ^^'  "  "'"'P'^ 

sprins  and  summer  that  he"amoa„  ^r  L  '"'^  "  ''"  """""  '"  ""^ 
«rictly  with  the  distance  P"'  "P°"  ""=  '^^"^"^  ^^"«« 

do  when  the  distances  hecoJlZZZ:^!:;  ?  V  t"  T"'"'^ 
tances  of  a  few  feet  or  «=.,;„       .t  °f  ==  or  3  miles;  but  for  dis- 

other  Items  this  Lrtl  en  T  H  T  ''^"°"^'"^  possibility  that 
'n  direct  ratio.  '*'''  ''^"^"'  ^""^  ^^"""S  will  increase 

^'^^^'^cZ^:;^^::^,^-^^f  of  the  consumption  of 
cost  of  kindling  fires  alone  a~l  «  '"'^'  '^"'^""^  ™"-     The 

shown  in  Table  84.  A  fire-box  J'f  °\  '°  '^^  "'"'  "'  "'=  '°'^'-  ''■^ 
is  drawn,  which  was  lnrn^I,l  "'  '^  ""'*^'*  ^''^'y  ^'""^  the  fire 

an  avera:.e  o   a  Jholl  roaH  ^  """'  '°°  ""'''"'  ™"'  ">"'  -  "o.,  on 


^^*r 


;i 


h 


200        CHAP,   VIL— DISTANCES-EFFECT  ON  EXPENSES. 


Table  84. 

Showing  the  Relative  Cost  of  Wood  for  Kindling  on  the  Philadel- 
PHIA  &  Reading  Railroad  for  a  Series  of  Years. 


Ybak. 


1867 

1869 

1873 

Average. 


Percentage  of  the  Cost  of 
Kindling-wood  to  Re- 
maining Cost  of  Fuel. 


Prices  of  Fuel. 


Passenger 
Trains. 


14.2 
8.8 
9.7 


10.9 


Freight 
Trains. 


10. 
6.4 
6.2 


7.5 


Coal 
Trains. 


5^1 
3-6 

4.1 


4-3 


Wood 
per  Cord. 


$5 

79 

5 

50 

5 

94 

Coal 
per  Ton. 


$5  74 


$3  15 

3  So 

3  25 


Average  Consumption  of 
Wood  for  Kindling. 


$3  40 


Passenger  trains,  .I3c'd 
Freight  **         .15    " 

Coal  *•        .22   '• 


The  above  does  not  include  the  cost  of  any  coal  used  in  kindling.  The  consumption 
of  wood  seems  very  small;  Mr.  Trautwine  (•*  Engineers'  Pocket  Book,"  p.  Sio)  gives  ^6 
cord  as  the  average  consumption. 

When  this  road  was  using  wood  fuel  entirely,  passenger  trains  used  2.7  cords  per  too 
miles,  or  about  2^  cords  per  daily  run  of  93  miles.  Allowing  ^  cord  for  getting  up 
steam  would  amount  to  exactly  10  per  cent. 

Mr  William  Stroudley.  Loc.  Supt.  London,  Brighton  &  South  Coast  Railway, 
in  a  paper  before  the  Institution  of  Civil  Engineers  (1885)  shows  that  the  number  of 
pounds  of  coal  burned  to  raise  100  lbs.  of  steam  from  water  at  70'  F.  was  about  450  lbs., 
eqi'ivalent  to  from  3  to  4  lbs.  of  coal  per  train-mile  when  kindling  fires  once  a  week,  or 
every  650  to  8co  miles  run.  This  amounts  to  almost  exactly  10  per  cent  of  the  total 
quantity  of  coal  burned  per  mile.  He  gives  also  tables  showing  that  his  passenger  engines 
spend  nearly  half  the  time  that  they  are  nominally  in  service  either  in  switching  or  standing 
still  (mostly  the  latter),  and  only  half  the  time  running. 

motive  from  expansion  and  contraction.  This  terminal  wastage  alone 
will  average,  therefore,  some  400  or  500  pounds  per  100  miles,  sufficient 
to  run  a  locomotive  5  to  10  miles,  or  5  to  10  per  cent  of  the  total  con- 
sumption. Whether  the  fires  are  drawn  or  not.  a  fire-box  full  of  coal  at 
least,  and  usually  more,  is  wasted  at  the  end  of  every  trip. 

185.  The  consumption  due  to  stopping  and  starting  and  to  standing 
idle  in  yards  and  on  side  tracks  is  also  a  heavy  item,  and  may  be  considered 
as  nearly  independent  of  distance  in  the  case  of  two  nearly  equal  lines 
operated  with  the  same  number  of  steps  and  sidings  between  the  same 
termini.  The  direct  amount  of  loss  of  power  in  stopping  a  train  run- 
ning at  1 5  miles  an  hour  is  sufficient  to  lift  it  vertically  nearly  8  feet,  as  wiU 


ClfAP.   VII.~DISTANCE~EFFECT  ON  EXPENSES. 


201 


be  seen  in  Table  118.  and  at  30  miles  an  hour  four  times  that  heioht  or 
nearly  32  feet.     The  roiling  resistance  of  a  loaded  freight  or  pas^en^rer 
train  in  motion  on  a  level  being,  as  will  be  seen  hereafter,  equivalent  to 
that  of  a  grade  of  less  than  16  feet  per  mile,  we  have,  from  stopping  and 
starting  only,  a  waste  of  power  sufficient  to  run  the  train  one  half  mile 
in  the  one  case  and  two  miles  in  the  bther.  causing  a  loss  for  an  avera-e 
number  of  stops  for  stations  and  crossings  of  something  very  dose  to  To 
per  cent  of  the  total  consumption.    In  such  extreme  cases  as  tlie  Manhat- 
tan (elevated)  Railway  of  x\ew  York,  where  there  are  stations  about  every 
three  eighths  of  a  mile,  very  nearly  three  quarters  of  the  total  consump- 
tion of  fuel  has  been  shown  to  be  due  to  this  cause.     As  to  the  wastnge 
while  standing  idle,  experiments  made  by  Mr.  Reuben  Wells  show  that 
an  engine  with  jacketing  in  perfect  order,  standing  idle  all  day  Ion-  in  a 
yard,  wholly  protected  from  wind  and  using  no  steam  in  the  cylinders 
requM-es   from   25  to  32  lbs.  of  coal  per  hour  to  keep  up  steam  in  the 
bo.ler.  or  nearly  enough  to  run  it  a  mile  in  service.     For  the  short  stops 
m  actual  service  at  least  twice  this  amount  per  hour  is  probably  wasted 
including  what  is  blown  out  of  the  safety  valve,  owing  to  all  paits  of  the 
engine  being  hot.  and  a  surprisingly  great  amount  of  time  is  spent  on  an 
average  freight  trip,  and  even  passenger  trips,  in  simply  standing  stilL 
It  will  average  over  4  hours  per  day.  if  not  more,  in  freight  service  on 
single-track  roads,  not  including  the  time  lost  at  the  beginning  and  end 
of  the  trip;  and  on  the  very  fastest  express  runs  experience  has  shown 
that  fully  one  fourth  of  the  time  between  termini  is  lost  by  stops.     This 
amounts  to  a  further  waste  of  3  to  6  per  cent. 

186.  From  all  these  causes  together  it  is  a  verv  moderate  estimate  that 
about  one  third  oi  the  total  cost  of  fuel  is  not  affected  by  a  slioht  chancre 
more  or  less  in  the  length  of  the  line.  The  average  consumption  of  fuel 
per  train-mile  in  both  directions  is  not  so  greatlv  affected  bv  grade  that 
we  need  consider  the  question  of  whether  the  additional  distance  is  on  a 
grade  or  on  a  level.  Going  up  grade  the  consumption  is  greatly  m- 
creased,  but  there  is  no  consumption  of  steam  at  all  in  going  down 
grade,  so  that  the  average  is  only  slightly  increased. 

187.  Repairs  of  Engines  and  Cars—U  is  exceedinqly  common 
and  for  certain  purposes  proper  enough,  to  assume  these  expenses  to 
vary  directly  with  distance,  but  for  our  present  purpose  this  is  very  erro- 
neous. The  wear  and  tear  of  rolling-stock,  it  is  plain,  arises  from  several 
d.stmct  causes,  of  which  the  regular  running  wear  when  in  motion  is 
only  one.    These  causes  are ; 


202        CHAP.    VII.— DISTANCE— EFFECT  ON  EXPENSES. 


1.  Deterioration  from  time  and  age:   Varying  'with  time. 

2.  Stopping  and  starting:    Varyittg  with  number  of  stops. 

3.  Terminal  service,  getting  up  steam  and  drawing  fires,  switchings 
making  up  trains,  etc.:  Varying  with  the  number  of  trips,  independent  of 
their  length. 

4.  Effect  of  curvature  and  heavy  grades:  Varying  with  the  character 
/}f  the  alignment.     And,  finally,  we  come  to 

5.  Effect  of  regular  running  between  stations  on  a  tangent:  Varying 
-with  distance  (the  additional  effect  of  any  curvature  on  a  given  distance 
being  a  separate  matter). 

All  of  these  causes  contribute  to  increase  the  cost  of  maintaining  roll- 
ing-stock, and  as  the  whole  cannot  be  greater  than  the  sum  of  all  its 
parts,  the  effect  of  any  one  of  them  alone  must  be  much  less  than  the 
total  cost  unless  the  effect  of  the  other  four  is  insignificant.  Each  item 
will  be  seen  to  vary  with  a  different  cause  and  only  with  that,  and  only 
one  of  these  causes  is  the  exact  length  of  track. 

188.  The  mere  statement  of  these  facts  at  once  makes  probable  that 
rolling-stock  repairs  cannot  vary  very  directly  with  distance  alone  when 
the  other  causes  of  deterioration  remain  the  same,  although  precisely 
how  much  each  cause  contributes  to  the  total  will  probably  always  re- 
main an  indeterminate  problem.  Nothing  but  the  most  exhaustive  ex- 
periments could  settle  it  accurately.  Hence  we  find  that  when  men's 
attention  is  specially  fixed  upon  the  disadvantages  of  some  one  of  these 
causes  they  are  very  apt.  with  entire  good  faith,  to  exaggerate  the  effect 
of  that  one  cause,  simply  from  momentary  forgetfulness  of  how  many  other 
causes  are  also  co-operating  to  make  up  the  aggregate.  If  the  effect  of 
distance  is  under  discussion,  the  whole  cost  of  rolling  stock  repairs  will  be 
charged  off  as  so  much  pei  mile  run.  as  if  no  other  cause  but  mileage  had 
any  effect ;  but,  on  the  other  hand,  if  the  disadvantages  of  some  grade 
crossing  is  in  question,  we  shall  have  the  wear  and  tear  resulting  from 
that  cause  spoken  of  as  something  fabulous.  And  so  about  the  injurious 
effect  of  some  particularly  crowded  yard  or  objectionable  curvature. 
But  starting  from  the  premise  that  the  total  effect  of  all  these  causes 
cannot  be  more  than  100  per  cent,  we  have  in  Table  Sj.a  subdivision  of 
this  total,  item  by  item,  between  the  above  five  causes.  As  this  has  been 
done  with  great  care  to  get  the  best  attainable  authority  for  each  (which 
it  would  occupy  too  much  space  to  give  in  detail),  the  margin  for  possible 
error  is  not  great  enough  to  be  of  moment,  although  no  absolute  exact- 
ness can  be  claimed  for  it. 


CHAP.    VII.-DISTANCE^EFFECT  ON  EXPENSES.        203 


Table  85, 

Distribution  of  the  Cost  o.  Encne  RnPAms  to  its  Various  Contrib. 

UTiNG  Causes. 


Itbm. 


5°'^^r 

Running  gear 

Machinery 

Mountings 

Lagging  and  painting.*.! 

Smoke  box,  etc 

Tender: 

Running  gear 

Body  and  tank 


Total 

Cost  of 

Item 


Distribution. 


p.  C. 
20.0 
20.0 
30.0 


Effect  of 

Time, 

Age, 

and 

Exposure. 


Stopping  .Terminal :  Curvatu 


and 

Starling 

at  Way 

Stations. 


p.  C. 


I. 


Total 


12.0 
50 

lo.o 
3.0 


4. 
I. 


p.  c. 

2. 

4. 
7. 


Getting 
Up  Steam, 

Making 
UpTrains 


re 


lOO.O 


p.  C. 

7- 
2. 

3- 


and 

Grades. 

(Approx. 

Average.) 


Distance 

on 
Tangent 
between 

Stations. 


p.  C. 
4- 

7. 
5. 


7. 


15. 


p.  c 

7- 

7. 

14. 


2. 

I. 

6. 
3. 

I. 
I. 

3- 
19. 

4- 
I. 

17. 

42. 

Table  86, 
Distribution  op  the  Cost  ok  Freight-Car  Repairs  to  its  Various  Con. 

TRiBUTiNG  Causes. 


Wheels 

Axles,  brasses,  and  boxes 

Springs 

Truck  frame  and  fittings 

Brakes ._ 

Draw- bars ,' 

Sills  and  attachments..'.*. 
Car  body,  painting,  etc. . 

Total. 


Total 

Cost  of 

Item. 


Distribution. 


p.  C. 

30. 

30. 

ID. 

5. 

5. 
ID. 

5- 


Effect  of 
Time  and 

Age.  in- 
dependent 

of  Work 
and 

Mileage 


p.  c. 


Stopping 

and 
Starting. 


2. 


100. 


I. 

3- 


6.0 


p.  c 

5 

5 
2 
I 

2 

4 
2 
O 


Terminal 
Making 

Trains, 
etc. 


21.5 


p.  c. 

2. 
2. 
I. 
I. 
I. 

4. 
2. 


13.5 


Curvature 

and 

Grades 


p.  c. 
13. 

5- 

I. 


2. 
2. 


Distance 

only 
between 
Stations 

on 

Straight 

Track. 

p.  C. 
10. 
18. 

6. 

I. 


23.0 


36.0 


The  proportionate  cost  of  wheels,  axles,  and  brasses  above  is  perhaps  lar^P  n.H  TiTT 
Of  brakes  and  draw-ba.  sn^all,  but  it  is  in  accordance  with  the  ^J1^^:^,::^J^:l 


204        CHAP.   VII.— DISTANCE— EFFECT  ON  EXPENSES. 

189.  In  Table  85  each  of  the  smaller  items  is  as  small  as  it  can  rea- 
sonably be  made.  Consequently  not  more  than  42  per  cent  of  the  cost 
of  the  engine  repairs  appears  to  vary  with  the  minor  changes  of  length. 
The  distribution  to  curvature  and  grades  will  be  spoken  of  hereafter,  h 
will,  of  course,  vaiy  greatly  on  different  roads.  Table  86  is  a  similar  dis- 
tribution of  the  cost  of  freight-car  repairs  based  in  part  upon  Tables  71 
to  75,  ajid  in  part  on  Table  87. 

190i  It  will  be  seen  that  a  considerably  larger  proportion  of  car  re- 
pairs than  of  engine  repairs  is  independent  of  distance,  as  is  but  natural. 
The  cost  of  passenger-car  repairs  may  be  considered  as  not  greatly  differ- 
ent per  train  from  that  of  freight  trains,  but  the  maintenance  of  the  seats, 
furniture,  and  inside  and  outside  ornamentation  make  up  much  more 
than  half  the  cost  of  passenger- car  repairs,  so  that  the  cost  per  train  of 
all  kinds  of  running  wear  is  much  less  considerable. 


Table  87. 

Estimated   Cost   New,  Scrap  Value,  and   Rate  of   Depreciation   op 

Freight  Cars  of  Various  Kinds. 

[Deduced  from  data  published  in  the  National  Car-Buiid*r  of  April,  1880.] 

Box  Cars. 


Labor. 

Material. 

Total. 

Scrap 
Value. 

Total 
Deprec'n. 

Average 

Life. 

Years. 

Annual 
Deprec'n. 

Wheels 

$90.00 
4500 
10.00 
94-94 

$35.00 

15.00 

4.00 

25.00 

$55- 

30. 

6. 

70. 

4 

8 

3 

35 

$13-75 

Axles 

3.75 

Rras<;es 

2.00 

Frame. ...... 

2.00 

Truck 

Brakes 

Draw-bars 

Frame 

Roof 

Floor 

Sides 

Patntintj 

Trimmings.. . 
Trusses 

$227.82 

7.33 
26.08 

52.85 

25.49 
10.76 

36.78 

5.25 
13.29 

5.89 

$12.12 
2.16 

2.95 
6.79 
3.34 
1.12 

7.58 
2.16 
6.23 

I. 13 

239-94 

9-49 
29.03 

59-64 

28.83 
11.88 

44.31 
7.41 

19.52 
6.02 

79.00 
2.00 
6.00 

10.00 
4.00 
1. 00 
2.00 

300 
300 

161. 

7.50 

23. 
50. 

25. 
II. 

42. 
7.50 
16. 

3- 

*"*6" 
6 

15 

8 

10 
20 

7 
20 

20 

$21.50 
1.25 
3.83 
3-33 
3.12 

I.IO 

2.10 

1.07 

.80 

.15 

Total,  box  c. 

410.54 

45.58 

456.12 

110.00 

346. 

$38.25 

Stock  cars 

388.72 

42.68 

431.40 

\ 

(ov< 

:r.) 

CHAP.   VII.-DISTANCE-EFFECT  ON  EXPENSES. 


205 


Table  87. — Continued. 
Flat  and  Coal  Cars. 


Total  Cost 
New. 


Scrap 
Value. 


Truck  (as  above) $239.94 

Brakes   ^  j^^-^ 


Draw- bars. 
Frame   . . . 

Floor 

Sides 

Fittings.. . . 
Trusses  . . 
Painting. . . 


Total. 


9.49 

29.03 

45.00 

12.00 

8.00 

5  00 

6.00 

6.00 


$360.46 


$79 
2 

6 

10 

I 

I 

I 


Total 
Depreciat'n. 


Average 

Life. 

Years. 


50 


$103. 


I 


$161 

7 
23 
35 
II 

7 

4 

3 
6 


$257-50 


6 
6 

15 
10 
20 
20 
20 
7 


Annual 

Depreciat'n. 

$21 

•50 

I 

.25 

3 

.83 

2 

33 

I 

10 

0. 

35 

0. 

20 

0. 

15 

0.88 


$31.59 


Per  Cent  of  Total  Depreciation. 


Wheels 

A.xles  and  brasses, 
Truck  frame 


Flat  Cars.    I    Box  Cars, 


43.5 

18.2 

6.3 


Total  truck. 

Brakes 

Draw  bars. . . . 

Frame 

Other  parts... . 


Total. 


68.0 

4.0 

12. 1 

7-4 
8.5 


36.0 
15.0 

5.2 


Average. 


100. o 


56.2 

3.3 
10. 0 

8.7 
21.8 


40. 

16.6 
5.7 


100. o 


62.3 

3.6 

II. o 

8.0 
15. 1 

100. o 


this  table  is  at  least  equally  trustworthy.  ^''     ^"  ^^^  ^^^^e. 

The  rule  of  the  Master  Car-Builders'  Association  is  that  6  i^r  r^nt  r^ 
shall  be  allowed  for  depreciation  in  value  of  freLht  ca^s  Iwn  to  1  ^' '^'^'■' '''' '"'^  ^^' 
cent  of  their  original  cost.  ^  '  ^°'^°  '°  *  minimum  of  40  per 

191.  Train  WAGES.-The  tendency,  as  already  stated  roar  ic.>»    ,'« 
more  and  more  to  fix  all  train  wa-esdi recti v  bv  th.  ^i      ^^^'-.'^f)'  »s 
the  larger  lines  made  up  of  several  di^Sl'^dut^^^ 
where  the  total  number  of  trios  a  cre«r  r«n  r.,/  ,     ^      ''^^' 

Propcuonec  a,™ost  exacU,  .?  ^"Z^JZJZr^:':^^^ 


?         ! 


I 


CHAP.   VII.-DISTANCE-BFFECT  ON  EXPENSES. 


2c6  

iimit  is  fixed  varving  from  2600  to  35oo  miles,  as  =1  month's  work 
dTv  dine  tltrs  by  the  length  of  each  division  gives  the  number  of  trip 
to  con  titut  a  month's  work,  the  fraction  being  disregarded  .n  favor  o 
the  employe.  On  a  division  ,00  miles  long  26  tr.ps  ,s  a  ■"""'h  s  wo^k 
o  a  dilision  90  or  ,05  m.les  long  28.89  and  24.76  tnps  ^-^'^^^^^fl 
a  month's  work,  but  the  fraction  would  be  '^-PP^'^  "'  '^.^^^/^l"'  '" 

mil  "e  ™n?lnd  others  (including  probably  over  half  'he  mUeage  o  the 
U: -^Stat.)  adopt  the  -P-ise  P.n  al^^^^^^^^ 
but  under  any  orcumstances  .t  »  "  '>^  f  ^^^^^^  j^,,  „;„   iect  trai« 
that   slight  changes  of   le.-^th  of  ^  '^ *  ~/„(,^,^^„.     Thecircum- 

and  excluded.  ^,„^„^,    Fxpenses   and  TAXES.-Taxes  are 

10*^   Station  and  General  ii,xpfc-Nbii.a  ai^^^ 

„o^Lf;L.med._^^^^^ 

r"'"lV^reler   bt<l  orvaTue  and  not  on  cost,  it  can  hardly  be 

pTofJ-^^to      nXiasv^ 

Td^unless  a  longer  line  between  two  ^-n  points  increases  the  vaU,  of 
th^  nrnnertv  thev  should  not  increase  with  distance  at  all.  btatton. 
term^arrd  general  expenses  are  of  course  entirely  unaffected  by  any 
sr^";  changes"  of  lengtll.  unless  the  volume  of  business  or  number  of 
stations  and  side  tracks  is  also  increased. 

,94.  Sutntning  up  the  effect  of  distance  on  the  various  items 
of  operating  expLses,  as  in  Table  88,  we  obtain  as  a  final  resut 
that  fractional  changes  of  distance  increase  or  decrease  expenses 
bv  only  25  to  40  per  cent  of  the  average  cost  of  operating  an 
equal  distance,   According  as   train  wages  are  affected  or  u. 
affected      The  limit  of  possible  variation  or  error  m  this,  as  m 
an  other  such  estimates,  is  no  doubt  a  considerable  percentage 
but  this  is  unavoidable.     Exactitude  enough  to  make  us  certain 
of  hlvfng  avoided  grave  error  and  hopeful  of  having  avoided  all 
error,  is  the  utmost  that  is  possible.         .__ 

6000  or  more  miles  as  a  monih's  work. 


CHAP.   VII.-DISTANCE-EFFECT  ON  EXPENSES.         20J 

Table  88. 
Estimated    Approximate    Effect    on    Operating    Expenses    of    Minor 
Changes  of  Distances,  Measured  by  Feet  or  Stations,  and  Not  bit 
Miles. 

[Cost  of  train-mile  assumed  at  $i.oo.] 


Item. 


Fuel 

Water. ...   .*.*.*!!!.*[!!! 

Oil  and  waste 

Engine  repairs 

Switching  engines 

Train  wages 

Train  supplies *  * '  ] 

Car  repairs * '  * ' 

Car  mileage * 

Rail  renewals WW 

Adjusting  track .*!!.*.*.'.*.* 

Tie  renewals ^ 

Earthwork  and  ballast !!!!.* 

Yards  and  structures *  [  * . 

Station,  terminal,  general,  and  taxes.. 


Total  Cost 

by 

Table  80. 

Cts.  or  p.  c. 


7.6 
0.4 
0.8 
5.6 
5-2 


Proportion  of  Same 

Increasing  wuh 

Distance. 


14 

O 
10 

2 

2 

6 

3 

4.0 

8.0 

30.0 


9 
5 
o 

o 
o 
o 
o 


67  per  cent, 
unaffected. 
50  per  cent. 
40 

unaffected. 


35  per  cent, 
100 


Cost  of 

Runniner 

One 

Additional 

Train-Mile. 


5.1 


Total, 


80 

50        * 
100        ' 

TOO  * 

unaffec 


0.4 
2.2 


ed. 


100. o 


If  train  wages  vary  exactly  with  distance. 


24  8  per  cent. 


3.5 
20 

1.6 
30 
3.0 
4.0 


24.8 


For  more  considerable  changes  of  distance  see  Table  89. 


39-7 


In  the  first  edition  of  this  treatise  the  cost  of  small  additions  to  distance  was  estimated 
as  follows : 


Fuel 

Oil,  waste,  and  water..,.!!! 
Kepairs  of  engines  and  cars. 
Train  wages 


Total  Cost  of 

Item  at  $1  Per 

Train-Mile. 


Maintenance  of  way 

Station  and  general  expenses. 


Total. 


10  cts. 
2    " 
19    " 

13     " 

30 


Proportion  of  Same 

Increasing  with 

Distance. 


$1.00 


70  per  ct. 

so      " 

unaffected  by  small 

changes, 

all  but  yards  and 

s;ructures. 

unaffected. 


Cost  of  Runn'g 

One  Afidiiional 

Mile. 


14 


7  cts. 
I    " 


20  cts. 


42  per  ct. 


42  cts. 


m 


opeltin^f  H  v'  T     :"  ^"^  '^'  ^^"'  '''™"'^  '^  P^^^y  ^"-^"^  '«  -^^-^--  " 

dft^n.   ?  T^'^'''''^  ^;^  P^'^'y  *°  "^^--^  ^^^••'•^^  ^^timate  of  the  actual  effect  of  ..light  ad 

t  atth         TT'  '^"  '™'  '^'  ^"'  ^'''°"  °^  '''''  "'^'•^  '^'^  Published  an  estimate 

cos  wal  1°'  °^."P^f' "^  ^f  •^■°"^l  distance  was  only  about  42  per  cent  of  the  average 
St  was  something;  of  a  novelty,  yet  it  really  was  an  over-estimate. 


I  Nil 


Tf.  i 


,  ■ 


iii 
i.! 
'& 


208        CHAP.    VII.- 


.DISTANCE-EFFECT  ON  EXPENSES. 


T^.TTTTT    HF    TREAT    AND    SMALL    REDUCTIONS    OF 
COMPARATIVE    VALUE    OF    GREA 1 


DISTANCE. 


i^oo  ^f  HiQtance  is  more  considerable 
fOR    AXT'Vif n  the  saving  or  loss  ot  aisiancc  is  "i^-- 

distance.     The  train  -''^^%^f^l''^l\°l^^  and  starting, 
almost  certainly  f^/-J,tg;a„dr:Kbor  generally  will 

maintenance  of  J^^*!!  ^f  J^J^^f^^'^iu  be  in  detail  about  as  com- 
also  be  increased.     This  increase  wi" 

puted  in  Table  89. 

Table  89. 

Ksx.MX.Kt.  AP.K0X,M.x.  Er.BCX  o.  G...X  ...  SM...  D....™  o. 

Distance. 
•    ..  in  Table  ^i   for  small  differences  of  distance,  and  the 

[Cost  of  train-mile  assumed  at  $i.oo.J 


Itbm. 


Total  Cost 
by  Table  80. 


Fuel 

Water 

Oil  and  waste 

Engine  repairs 

Switching-engines 

Train  wanes 

Train  supplies 

Car  repairs 

Car  mileage 

Rail  renewals 

Adjusting  track 

Tie  renewals 

Earthwork  and  ballast 

Yards  and  structures • 

Station,    terminal,     general, 
and  taxes 


Cts.  or  p.  c. 

0.4 
0.8 

5.6 

5-2 

14.9 

0.5 

lO.O 

2.0 
2.0 
6.0 

30 
4.0 

8.0 


Increase  for  Greater 

Differences  of  Distance  of 

Per  Cent  var>Mng  wuti 

Distance- 


Total  Ana'at 
Per  Train- 
Mile 
for  Greater 
Differences 
of  Distance. 


from   67  p.  c 
o 


t( 

K 

(< 

<< 

(( 

<( 

<< 

<( 

<< 

<( 

<t 


50 
40 

o 
o 
o 

35 
100 

80 

50 

100 

100 

o 


«< 
<t 
<< 
(I 
t< 

4< 

•  < 
<< 
<< 

<< 
(f 
«< 

'«t 


to 

<( 
<« 

<< 
(( 
tl 
l( 

14 

«< 

<< 

(< 

14 

It 

«1 


85    P- 
50 
50 

57 

o 

100 

40 

50 
100 
100 
100 
100 
100 

50 


.^__ 

c. 

6.5 

t« 

0.2 

<< 

0.4 

<( 

3.2 

<  1 

4( 

14.9 

14 

0.2 

41 

5-0 

11 

2.0 

41 
41 
44 

11 
11 


2.0 
6.0 

30 
4  o 

4.0 


Total 


from  24.8  P.O.  to5i4P_g: 


If  train  wages  are  not  affected,  we  have 


CHAP.    VII.-DISTANCE-EFFECT  ON  EXPENSES.        209 


196.   From  the  aggregates  at  the  foot  of  Tables  88  and  80 
we  find  that  the  total  cost  per  train-mile  for  great  and  small 
changes  of  length  compare  about  as  follows  : 


COST  PER  train-mile. 

Minor  Changes. 
(Measured  in  Keet.) 


Greater  Changes. 
(Measured  in  MiJes.) 


It  »-^«  «.  x^-xv-oauicu  lu  rcci.;  (Measured    n  MiJes  ) 

ram  wages  are  affected,   .     39.7  cts.  or  per  cent.  51.4  cts.  or  per  cent 
If  train  wages  are  not  affected,  24.8  cts.  or  per  cent.  36.5  cts.  or  per  cent. 

Multiply  these  sums  by  365x2,  and  dividing  the  product  by 
5280  m  the  first  column  only,  we  obtain  the  following  : 

yearly  cost  PER  DAILY  TRALV   (ROUND  TRIP)   OF  GREAT  AND   SMALL 

CHANGES  OF  LENGTH. 


Train  wages  affected,    .    . 
Train  wages  not  affected,  . 


Minor  Changes. 
Per  Foot.        Per  Mile. 


5.49  Cts. 
3-43  cts. 


$290 
$181 


Greater  Changes. 
Per  Mile. 

S375 
266.50 


These  sums,  divided  by  the  assumed  or  actual  rate  per  cent 
which  must  be  paid  for  capital,  .05,  .06,  .08,  .10,  etc.,  will  give  the 
justifiable  expenditure  to  save  one  foot  or  one  mile  of  distance  as 
respects  its  effect  on  expenses  only.  Thus  at  10  per  cent  cos't  of 
capital  we  may  spend  t^  =  $3750  per  mile  to  save  considerable 
additions  to  distance. 

These  exact  figures  are  of  course  hypothetical,  to  illustrate 
the  general  law,  and  need  to  be  made  up  anew  for  any  particular 
case-at  least  to  the  extent  of  correcting  the  assumed  cost  per 
train-mile,  which  averages  80  to  90  cts.  rather  than  $1.00. 

197.  For  very  large  and  considerable  differences  of 
DISTANCES,  amounting  to  20  to  30  miles  in  100,  the  value  of  sav- 
ing distance  may  properly  be  still  further  increased,  even  up  to 
the  figures  at  which  all  saving  of  distance  without  distinction  is 
sonietimes  estimated.  The  conditions  are  then  very  greatly 
modified.  The  number  of  yearly  trips  of  rolling-stock  is  then 
attected,  and  their  number  must  be  correspondingly  increased  or 
aiminished,  whereas  smaller  changes  have  no  such  effect.  Gen- 
14 


■"■r 


210        CHAP.   VII.— DISTANCE— EFFECT  ON  EXPENSES. 


CHAP.   VII.-DISTANCE-EFPECT  O.V  J!ECEIPTS. 


h ' 


HH 


eral  expenses  even  will  then  be  perceptibly  affected,  and  almost 
every  item  of  expenditure  except  the  cost  of  making  up  trams 
and  getting  up  steam  will  be  very  largely  increased  by  the  extra 
distance.     The  total  cost  of  all  train  and  maintenance  of  way 
expenses  amounts  in  our  assumed  average  (Table  80)  to  70  cents 
or  per  cent ;  but  as  all  experience  seems  to  indicate  that  even 
direct  train  expenses  cannot  be  reduced  in  practice,  and  will  not 
increase  in  direct  ratio  to  distance,  even  if  the  difference  of  dis- 
tance were  as  much  as  50  per  cent  (although  it  may  appear  that 
they  should  in  theory),  it  is  probable  that  80  or  90  per  cent  of 
the  above-mentioned  total  of  way  and  train  expenses,   or  say 
56  cents  per  train-mile,  is  the  maximum  effect  of  the  most  con- 
siderable changes  of  distance.     Or  to  put  the  whole  thmg  mto 
even  figures  :  the  average  cost  of  a  train-mile  being  taken  for 
even  figures  at  $1.00  (it  is  now  usually  less)— 


The  minimum  effect  of  extra  distance,  measured 
in  feet,  is  per  train-mile • 

The  minimum  effect  of  distance,  measured  in 
miles,  not  affecting  train  wages,  is 

The  maximum  effect  of  the  most  considerable 
change  of  distance  is 


25  per  cent  or  \ 

36.5  "      "    or  i 

56  to  63  •'      "     or  \ 

198  Between  the  extremes  above  given,  the  true  valuation 
may  be  almost  anywhere  under  different  circumstances.  There 
are  even  certain  conceivable  cases,  which  have  sometimes 
occurred  in  practice,  where  the  assumed  maximum  is  not  ade- 
quate, as  for  instance,  in  comparing  two  routes  for  a  transconti- 
nental  line  differing  by  100  to  800  miles.  The  number  of  operat- 
ing  divisions  will  then  vary,  and  with  it  a  very  large  proportion 
of  the  eeneral  and  station  expenses,  so  that  the  extra  distance 
may  cost  (or  may  not)  90  or  even  100  per  cent  of  the  average 
cost-  but  such  extreme  cases  are  too  exceptional  for  discussion 

199.  The  effect  per  year  upon  operating  expenses  of  any  given 
distance  having  been  thus  determined,  the  capital  sum  for  which 
this  yearly  cost  represents  the  interest  will  plainly  be  the  sum 
which  (neglecting  all  effect  on  revenue)  we  are  justified  in  ex- 
pending to  cut  out  that  distance.     Thus,  if  distance  be  found,  as 


211 

above,  to  cost  3.43  cents    per  ^d^\^~^^^^^^  " 

year,  a  road  running  10  trains  n.r  H.  l  '  ^"""'"^  """^ 

iS>2.oo  per  foot,  more  or  Ip*;*:  r^c  i^u^  ^  ,  Please, 

,  iiiuic  or  less  as  the  case  may  be  as  th«^  rr^^t  ^e 
superstructure,  rig-ht  of  vvpa^  a„^   r       •        ^      '       ^^^  ^°^^  ^^ 

that  su.  Withke^o^helir/^rofeonr^,; r  T^Z^^' 

sub-grade  then  enters  in,  to  determine  whether  or  noffh» 
improvement  will  cost  more  than  it  is  wortk  ^""" 

va>u?o;  faZ;  'ra'""bv°r'"'''  "T""'  '"  '  '"^'  exaggeration  of  ,,e 
«ructing  a  mile  oH  ne  comlf  !      "  '"'    ""°'^  ""^'S'  "^'   «'  "". 

like  the  value  of  everythinTelTe  i,  L  T  '  ^^  ""  '"'"^  °^  <"^'^"«. 
n.a„e„.  works  beneat'h  he  ^k  be  costlv  cr'n"' '"  T''  ^''"-"  ">=  P"" 
that  part  of  the  length  of  the  roaV:,  "h'^  sal^'";;-  L"  "^  °'  T"'  °" 
same  traMc.  We  therefore  first  estimate  the  vTl'  If  ,L°''  """  '"= 
«..mate  both  alternate  lines  to  see  whether  »;  nrt'lhMi::  e^el  tt^cor 

and   has  no  effect  uZ  ^''^"'"'"''  '^  ^  P^'^  ^o^rce  of  expense 

THE    EFFECT    OF    DISTANCE    ON    RECEIPTS 

into  °  th^lS^a^ -".f  Sir,!"  "-7"  P-'-«  roughly  divided 

.oca.  is  a  n^'ter^nar  rg'defi'nTtio^n'^VL'  tXltte"  "'^'  '= 
Of  the  word  "  through"  freight  would  be  freth  '  '?'''''''''°" 
the  entire  distance  between  termini  , .;»,/,,  ^  ^  '""^  °''" 
other  iines  or  not,  and  2!:::^^^' ^^^^^J^^^'^  ^^ith 
fymg.  Another  basis  for  subdividing  Z)r  °"°"'f^  '"  ^'assi- 
'oca,  is  that  adopted  in  the  Ma  s  ch„  tf RTn^o'dp"''  """ 
V.Z.,  to  call  all  traffic  "local  "  which  isconfined  to  21  "'"'V 
and  simply  passes  from  one  station  of  the  road  tlf' 
Whether  those  stations  are  the   termini^r  ^orand^ru^affi^ 


^^ir 


I 


212 


CHAP.   VIL— DISTANCE-EFFECT  ON  RECEIPTS, 


"  through"  which  is  (under  this  definition)  not  local,  but  passes 
over  parts  of  two  or  more  lines,  although  the  total  haul  may  be 
only  a  few  miles  between  small  non-competitive  stations  ;  where- 
as "  local "  traffic  may  be  hauled  the  entire  length  of  the  road  at 
competitive  rates,  and  be  for  all  practical  purposes  what  is  ordi- 
narily understood  as  '*  through"  business. 

202.  Neither  basis  of  division,  therefore,  is  a  particularly 
happv  one  for  accomplishing  the  end  sought,  and  the  reason 
why  neither  can  be  is  easy  to  see.  The  difficulty  is  that  each  of 
them  is  an  attempt  to  include  under  only  two  classifications /z^^f 
distinct  classes  of  traffic,  each  one  governed  by  different  laws  as 
respects  rates  and  other  business  considerations.    These  classes 

are 

Non-competitive  local. 

Non-competive  exchange. 
Competitive  local. 
Competitive  exchange. 

Partially  competitive  (i.e.,  competitive  only  with  the 
disadvantage  of  a  local  haul  in  ad4ition). 
More  in  detail,  the  nature  of  these  sub-classifications  are  as 

^^^^^^^  *  f  I.  Local  or  home  traffic  proper,  having  no 

choice  of   route   and   confined  to- 
one  line. 

2.  Exchange  traffic,  or  (by  Massachusetts 
classification)  "through"  traffic, 
having  no  choice  of  route,  but 
passing  from  one  line  to  another. 

3.  Local  or  home  traffic,  confined  to  one 
line,  but  having  a  choice  of  an- 
other route  (a  class  of  traffic  once 
small,  but  rapidly  increasing  with 
the  multiplication  of  railways). 

4.  Exchange  or  "  thromh  "  traffic  ^*^ai»er, 
passing  between  the  more  imoox- 
tant  railway  centres,  and  with  a 
choke  of  twa  or  more  routes. 


A. 

B. 
C. 


l:: 

I'- 


A.    NON-COMPETITIVE. 

(The  whole  of  it  being  what 
is  ordinarily  referred  to 
by  the  term  "  local "  traf- 
fic.) 


V 
r 


B.  Competitive. 

(The  whole  of  it  being  what 
is  ordinarily  referred  to 
by  the  term  "through 
traflac") 


I 


CHAP,   VII.^DISTANCE^EFFECT  ON  RECEIPTS.         213 


C.  Partially 

Competitive, 


■ 


5.   Traffic     (usually      exchange     or 
"through")  detween  non-competitive 
local  points  and  important  railway 
centres   having  a   choice  of  route 
only  at  disadvantage,  by    paving 
a   local   rate    in   addition    to '  the 
"through."      This  class  does  not 
exist,    practically,    for    passenger 
service. 


203.  Out  of  all  these  five  classes   there  is   only  one-viz 
Class  B,  3  ;  traffic  confined  to   the  home   road   and    the.  J^ 
purely  local,  but  having  a  choice  of  ron,^  h,  tne.etoie 

and  therefore  co.petitife-on  wT .L:  a  Zger'LT,rast^:^S 
whatever  to  increase  receipts,  but  is  a  pure  disadvantage  This 
class  ,s  also,  on  most  roads,  the  smallest  class  of  all,  anfon  very 

CcVon":'"'v"°"r'"^"'-  °"  -''-•^."owev'e.asfo.  Z 
-tance  on  a  new  hne  between  New  York  and  Philadelohia  it 
would  be  the  bulk  of  the  traffic.  It  is  rapidly  increasingir;™ 
portance,  moreover,  from  the  prevalent  tendencv  to  confo  idaTe' 
hnes  mto  great  systems,  and  even  when  this  consolidation  not 
formal  and  complete,  there  is  often  such  community  of  in  eres 
from  common  ownership  as  to  amount  to  very  neady  the  IZ\ 

Receipts  from  ail  the  other  classes  are  affected  materially  bv 
the^  d,stance  ;  but  in  different  ways,  which  we  proceed  to  Ln- 

non'?!"  ^'  ^°^-C°«'>"",yE  (Class   i  and  .).     Traffic  between 

7ZT    IT""  "'^  P°'"'''  ^•'^"'^'-  »"««  P°'nt^  are  on  the 
same  or  different  roads.  ^ 

-war' traffic' if  '"'^''  "''f  ''  "''^'  "'^  P°P"'-'y  -eant  by 
way    faffic,  .s  an  immense  factor  in  the  freight  revenue  of  any 


II 


I 

4 


214         CJIAP.   VII.— DISTANCE— EFFECT  ON  RECEIPTS, 


railway,  varyinjr  ordinarily  from  5010  75   per  cent  of  it;  and 
rarelv 'falling  below  50  per  cent,  except  on  lines  of  heavy  through 
traffic    running    through    sparsely    settled    districts.      The    old 
Canada  Southern  (now  Michigan  Central)  is  a  peculiar  and  very 
exceptional  example  of  a  line  of  the  latter  character,  its  local 
ton-mileage  having  averaged,  before  its  consolidation,  below  8 
per  cent  of  the  total.     Even   in   this  extreme  case,  however,  its 
revenue  from  local  freight  appears  to  have  been  from  25  to  30, 
per  cent  of  the  total.     The  Cleveland,  Columbus,  Cincinnati  & 
Indianapolis  Railway,  which  carries  perhaps  as  small  a  propor- 
tion of  non-competitive  freight  as  any  other  line  for  which  precise 
statistics  are  available,  and  which  is  certainly  exceeded  in  that 
respect  by  very  few,  derives,  as  an  average  of  9  years  (1873-81), 
36  per  cent  of  its  tonnage,  23  per  cent  of  its  ton-mileage,  and 
about  38  per  cent  of  its  freight  receipts  from  "  local  freight, 
which  in   this  case  includes,  practically,  non-competitive  of  all 
classes.     In  its  passenger  traffic  this  line  enjoys  an  even  larger 
proportion  of  non-competitive  traffic,  being  at  much  less  disad- 
vantage  in   that  respect,  and  in  fact  representing  as  nearly  as 
may  be  the  average  condition  of  the  whole  American  railway 
system.     This  is  the  more  fortunate  as  it  is  one  of  the  very  few 
lines  which  give  statistics  of  the  passenger  or  any  other  traffic 
in  such  form  that  it  can  be  accurately  separated  into  at  least  four 
of  the  five  classes  of  traffic  which  actually  exist,  as  above  speci- 
fied.    The  following  Table  90  gives  the  percentage  of  each  of 
these  classes  (omitting  fractions  and  distributing  a  trifling  sum 
for  miscellaneous  receipts)  for  the  average  for  the  9  years  1873- 
1881.     The  table  may  be  accepted  as  giving,  in  a  rough  way, 
about  the  general  average  of  the  whole  American  railway  system 
for  passenger  service. 

205.  Table  91  gives  some  corresponding  details  for  the 
freicrht  traffic  of  the  same  road,  which  can  hardly  be  accepted  as 
so  representative,  and  in  Table  92  (as also  in  various  other  tables  r 
—see  Index)  are  given  data  as  to  average  train  loads.  The 
variations  in  such  matters  are  limited  only  by  the  number  of 
roads,  and  are  often  very  great. 


CH^  VII.-DISTANCE^EFFECT  ON  COMPETITIVE  TRAFFIC.  215 

There  is  a  certain  portion  of  even  non-competitiveT^ 
It  must  alvvaysbe  remembered,  on  which  rates  are  governed' 
solely  by  what  it  will  bear,  without  any  reference  to  distance 
and  on  many  roads  a  very  large  proportion,  as  where  there  ij 
miich  suburban  traffic ;  yet  in  the  main  the  rates  are  nominally 
fixed  by  the  mile  on  all  this  traffic,  and  on  a  certain  large  pro- 
portion they  are  by  law  or  fixed  custom  actually  so  fixed 

Before  considering  what  weigiit  should  be  given  to  these 
facts  ,n  estimating  the  value  of  distance  (for  which  see  par.  227) 
we  will  consider  the  conditions  which  exist  with  the  three  re- 
mainmg  classes  of  traffic. 

206.  Competitive  traffic,  whether  confined  to  one  line  or  not- 
(classes  3,  4,  and  5,  above).  The  total  through  rates  on  all  com^ 
petitive  traffic  are,  in  nearly  all  cases,  arbitrarily  fixed,  with 
little  regard  to  the  mileage.  For  this  reason  it  may  appear,  and 
may  be  too  readily  taken  for  granted  by  engineers  not  familiar 

Table  90, 

Comparative  Magnitude  op  the  Separate  Classes  op  Through  an,> 
Local  Competitive  and  Non-Competitive  Passenger  Trapp^  o"  th^ 
Cleveland,  Columbus,  Cincinnati  &  Indianapolis  Railway 

Average  of  9  years,  1873-1881. 

ITbis  Uble  may  b.  accepted,  in  a  rude  way,  as  not  far  from  the  general  average  of  the  whofe 

^^^^^  American  Railway  System,] 


Class  of  Traffic  as  Subdivided  on  page  122. 


A.  Non-Competitive. 


B.  Competitive. 


1.  Local  home  road 

2.  Local  or  exchange  between 

local   points  in  different 
roads  

3.  Local  traffic  between  com- 

petitive termini  (only  par- 
tially in  this  case) 
Competitive  through 


Per  Cent  of 
No.  of  Pas- 
sengers. 


Partially  Competitive.     (Non-existent  in  pass,  service.) 


74 


14  J 


:} 


88 


Per  Cent 
of  Pass. 
Mileage. 


Per  Cent 
Contributed', 
to  Revenue, 


12 


52 


1 


100  p.  c. 


.3   { 


48 


13 


6s 


ICXJ  p.  c. 


26  ("39 


100  p.  c. 


11 


Si 


I 

i 


'I 


216  CH.  VII.— DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC. 


Table  91. 

Fluctuations  and  Distribution  of  the  Different  Classes  of  Freight 
Traffic;  Cleveland,  Columbus,  Cincinnati  &  Indianapolis  Railway. 

Local  Freight. 


East-Bound. 

West-Bound. 

Total. 

Year. 

Tons. 
1,000. 

Ton- 
Miles. 

1  = 
i,ooo,uuo. 

1 

Rev. 

$1,000. 

Tons. 
1,000. 

Ton- 
Miles. 

i,cxx>,ooo. 

Rev. 

I  = 
$1,000. 

Tons. 

Ton- 
Miles. 

Rev. 

1873. .. 
1875... 
1880... 
1885... 

419 
401 
564 
451 

50.0 
43-3 

74.6 
43.3 

908.9 
686.7 

749-8 
469.7 

211 
253 
311 

355 

20.8 

27.7 

33-6 
41.0 

434.8 
465.0 
451.6 
406.3 

630 
654 
874 
806 

70.8 

71.0 

108.2 

84.3 

1344. 

I152. 

1201. 

876. 

Through 

Freight. 

1873.., 

870 

166.5 

1895. 

181 

37.1 

I 

1 
496.8 

1050 

203.5 

2392. 

T875... 

747 

145-5 

1093. 

209 

46.8 

402.8 

957 

192.3 

1495. 

1880... 

I189 

232.0 

1539. 

378 

80.3 

588.0 

1567 

312.2 

2127. 

1S85... 

I140 

226.9 

997. 

569 

117.4 

598.6 

1 70S 

344.4 

1596. 

The  above  indicates  the  nature  and  extent  of  the  fluctuations  which  have  occurred 
during  the  thirteen  years  covered  by  the  table.  The  following  are  averages  for  the 
ten  years  1876-1885 : 


Percentages  of  Total  Tons  Carried. 


East-bound. 
West-bound. 


Total. 


Through. 


48.4 
17.7 


66.1 


Local. 


19.9 
14.0 


33.9 


Total. 


68.3 
31.7 


100. 0 


Percentages  of  Total  Ton-Miles. 


Through. 

Local. 

Total. 

East-bound . .  . 
West-bound... 

56.5 
21.8 

12.5 
9.2 

69.0 
31.0 

Total 

78.3 

21.7 

100. 0 

Percentages  of  Total  Revenue. 

Average  Receipts  Per  Ton-Mile. 

Through. 

Local. 

Total. 

Through, 

Local. 

Total. 

East-bound . .  . 
West-bound.  . . 

44.5 
20.0 

20.3 
15-2 

64.8 
35.2 

East-bound. 
West-bound 

Total .... 

.556  ct. 
.656   •' 

1. 161  Cts. 
I.2I0    '* 

.674  CL 
.818    •♦ 

Total 

64.5 

35.5 

100. 0 

.591  ct. 

1. 182  Cts. 

.719  Ct. 

<'f:^^ff;^:^^STANCE-EFFECT^  COMPETITIVE  TSAFFIC.  217 

Table  92. 

Average  Train-Load  of  Fretpht  Av.r^  d.o 

OF  freight  and  Passengers  in  the  United  States 
Groups  of  Statfs    Avn  ^x,  -r  ,  ^^i^niiij  oiates, 

oiAjEs,  and  on  Trunk  Lines. 

^Computed  from  the  Census  Statistics  of  1880.] 


Passenger  Traffic. 


I.  New  England 

IL  Middle,  with  Md.rMich..*ind. 

ilL  Southern 

IV.  111.,  la..  Wise.;  MoV,  Minn*.*.'. 

V.  La.,  Ark.,  Ind.  T 

VI.  Tex.,  Kan.,  Dak.,  and  Far  W 


Av.  Train' 

Load. 

No. 


Total  United  States. 


53.3 
44.2 
21.3 

37.1 
18.3 

48.0 


Av.  Haul, 
Miles. 


Freight  Traffic. 


16.8 

17.4 
44.1 
41.9 

39.8 
44.8 


Av.  Train 

Load. 

Tons. 


Av.  Haul. 

Miles. 


41.5 


21, 


Trunk  Lines. 

Boston  &  Albany 

New  York  Central... 

N.  Y.,  L.  Erie  &  W... *.;*.;*. 

Pennsylvania \\' 

Baltimore  &  Ohio. . .... 

N.  Y.,  Penna.  &  0....\.\\' 

N.  Y.,  N.  Haven  &  Hartf . *  , 


90.6 
163. 

55.7 
122.5 

61. 
95.5 

T29. 


55.7 
106. 1 

103.7 

153.3 

34.6 

166.9 

III. 


72. 

65. 
55. 
52.4 
38. 

41. 
90. 


no. 
218. 
211. 

233. 
185.5 
"3- 
IJ^3. 


With  operating  practices,  that,  for  this  class  of  traffic  at  least  anv 
additional  distance  must  be  a  pure  disadvantage   inaeS    "^ 
pense,  but  not  affecting  revenue.     And  this  is  ^^l^^^xl^^^^ 
i-espect  to  such  competitive  traffic  as  begins  and   end     on  one 
W,  or  on  one  system  of  lines  with  intereL  wholl/in  00^^ 

Whole  of  it  on  the  smaH^  liles   is  tl^lg^^t,,^^^^^^^^^^^^    '- 
passes  over  parts  of  several  lines.     On  ^1  suclf  t  a^'    'et^^^ 
rate  from   shipping  point   to  destination    is    indeed   nrh!        , 
xed   without  regard  to  mileage,  and  oft^n  In  S    n     n vT  ^ 
at  00  u;  but  of  the  division  of  this  total  rate  between  trplr 

i:rrm:rsTe':;:"" '-  "-^  --^^-^^  — ^  t,  zi 


M\ 


2lZ  CH.  VIL— DISTANCE—EFFECT  ON  COMPETITIVE  TRAFFIC. 


n 


I 

ii 


207.  The  division  in  all  such  cases  is  by  a  percentage  which  is 
regulated  strictly  in  accordance  with  the  relative  distance  hauled, 
although  not  necessarily  in  direct  ratio  to  that  distance  ;  for 
there  are  frequently  "  Arbitraries"  of  various  kinds,  and  granted 
for  various  reasons,  as  for  terminal  expenses,  to  be  first  deducted 
before  the  final  division  or  percentage  is  distributed  according 

to  mileage. 

208.  So,  too,  it  is  not  uncommon  for  some  line  to  have  some 
strategic  advantage  of  another,  so  that  it  can  exact  from  it  cer- 
tain special  concessions,  in  excess  of  its  exact  mileage  propor- 
tion, such  as  allowances  for  "  constructive  mileage,"  etc,  etc. 

The  Erie  Railway  formerly  bad  a  great  strategic  advantage  of  this  kind  over 
the  old  Atlantic  &  Great  Western  Railway  (New  York,  Pennsylvania  &  Ohio), 
the  nature  and  efifect  of  which  we  shall  shortly  see  (par.  2i6). 

209.  Again,  when  shipments  are  for  extremely  long  dis- 
tances they  are  quite  frequently  subject  not  to  one,  but  to  the 
sum  of  two  competitive  rates,  and  the  total  is  divided  accord- 
ingly. All  freight  passing  through  Chicago  is  a  remarkable 
example  of  this.  It  is  not  common  to  make  rates  past  Chicago 
to  points  on  either  side  otherwise  than  by  adding  the  two 
Chicago  rates  (which  latter  is  very  common),  except  when,  as  to 
"Missouri  River  points,"  special  circumstances  make  it  abso- 
lutely unavoidable.  The  tendency  to  make  Chicago  a  terminal 
point  for  competition  and  start  afresh  from  there,  is  strong. 

There  are  some  apparent  partial  exceptions  to  this  rule,  but  they  are  hardly 
real  ones.  Thus  in  i886,  after  considerable  controversy  and  irregularity, 
rates  from  New  York  to  "  Mississippi  River  points,"  including  a  large  number 
of  points  north  of  St.  Louis,  were  by  agreement  adjusted  at  the  fixed  rate  of  ii6 
for  ICO  to  Chicago.  This  was  then  divided  between  the  lines  east  and  west 
of  Chicago  (there  being  half  a  dozen  or  more  lines  interested  on  each  side),  by 
assuming  the  distance  for  all  lines  to  be  220  miles  west  of  Chicago  and  970 
miles  east,  these  being  about  the  average  of  the  actual  distances,  which  of 
course  varied  with  each  road.  The  total  rate  was  then  divided  in  exact  propor- 
tion (as  nearly  as  might  be)  to  these  distances,  viz.,  i8i  per  cent  west  and  Bii 
per  cent  east  of  Chicago.  Exactly  these  divisions  would  have  been  18.487  and 
81.513.  so  that  the  rate  on  0.15  mile  of  haul  west  of  Chicago  was  given  away  to 
the  lines  east  to  obtain  a  round-numbered  percentage. 


CH.  VII.-DTSTANCE-EFFECT  ON  COMPETITIVE  TRAFFIC.  219 

arer"Jaldl!sso7H"?'  '"".^"« '"^  «-"»' ^'^  ">a,  through  competitive  rates 
are  regardless  of  distance  is  extended  likewise  to  a  first  division  of  those  rates 
mto  two  parts.     What  the  arrangement  reallv  means,  however  is  "hat  akhoulh 

.ntere  t  of  peace  and  good-will,  yet  the  distance  was  so  great  and  the  confl  ct 
■  ng  .nterests  so  multifarious  that  it  was  more  convenient  to  regard   hs  rate  as 
made  up  of  two  separate  and  distinct  through  rates,  than  to  regL  i  as  as  Lie 
through  rate  to  be  divided  in  the  usual  manner  * 

Compacts  of  this  kind  may  increase,  but  at  present  they  are  too  exceptional 
to  merit  more  than  passing  notice.  /      c  100  exceptional 

andtn  °r  !"'"'"'  °'  "  ""'"■^■•y"  allowances,  a  large  part  of  the  business  from 
and  to  local  points  near  large  cities  really  comes  under  the  head  of  ihroueh 

vLt       L     T  y       •         ■"«»"«.  being  usually  made  the  same  as  to  New 
Iei:v;re"d',h:':f''^'  "  ""  '"''''  "-  P--^~  a^uany  takeVtot: 

its  effect  uornth"'  """"";'  "°'  "'"'^  ^^  ""=  ""'"S''  "«  ''  -  «•«  same  in 
Its  effect  upon  the  receipts  of  the  connecting  lines  as  if  it  were. 

210.  Certain  considerable  allowances  for  terminal  cliarees  at 
points  where  sucl.  charges  are  heavy  are  very  commonly  and 
very  justly  deducted  from  the  through  rate  before  the  latter  is 
distributed,  as  notably  at  New  York,  where  the  terminal  allow- 
ances are  very  heavy  (4  to  5  cents  per  100  lbs.),  although  hardiv 
enough  to  cover  the  direct  and  indirect  expense  to  the  terminal 

In  fact  the  variations  and  exceptions  in  the  fixing  and  division 
of  rates  are  endless,  but  through  them  all  the  general  law  holds 
good  that  all  "through"  rates  between  connecting  lines  are 
divided  precisely  a^.^r^ng  to  the  actual  mileage,  and  to  a  verv 
large  extent  directly  as  the  mileage. 

211.  These  facts  result  in  a  curious  and  apparentlv  contradic- 
tory law,  as  respects  the  through  traffic  of  a  new  or  old  road 
which    ,t    may  be   highly  important  that  the  engineer   should 
understand.     That  law  may  be  thus  expressed  : 

I.  It  is-  extremely  desirable  that  any  new  line  should 

FORM    A    PART    OF    THE    SHORTEST    ROUTES    BETWEEN     IMPORTANT 
CENTRES  OF  TRAFFIC. 

2.    It  is  not  DESIRABLE,  AND  OFTEN  THE  REVERSE  OF  DESIRABLE, 


220  CH.  VIL— DISTANCE-EFFECT  ON  COMPETITIVE  TRAFFIC, 


THAT  IT  SHOULD  MAKE  ANY  EFFORT  TO  BRING  ABOUT  THIS   RESULT, 
EXCEPT  IN  SELECTING  ITS  CONNECTIONS. 

The  reason  for  each  half  of  this  law  is  not  difficuh  to  see. 
212.  As  respects  the  first  part  of  it : 

The  through  rate  being  altogether  independent  of  distance, 
the  receipts  per  ton-mile  or  per  passenger- mile  on  competitive 
traffic  will  be  the  greater  the  shorter  the  line  is — a  consideration 
plainly  of  immense  importance. 

We  may  see  a  striking  proof  of  this  by  comparing  the  New 
York  Central,  Erie,  and  Pennsylvania  lines.     The  operating  ex- 
penses of  the  Central  and  Erie,  as  shown  in  Tables  37  and  76, 
average  continually  a  much  heavier  percentage  of  their  receipts 
than  on  the  Pennsylvania,  yet  they  are  operated  with  substantially 
equal  efficiency— at  least  there  is  far  less  difference  than  super- 
ficial observers   often   conclude  from   this  very  fact.     The  true 
cause  of  it  (with  which  other  causes  may  co-operate,  but  only  to  a 
minor  extent)  is  simply  this  :  that  the  Pennsylvania  has  the  short- 
est line  from  almost  every  point  in   the  West  to  New  York  and 
Philadelphia,  and  hence  its  receipts  per  mile— from  the   same 
through  rates — are  unavoidably  materially  larger  than  the  Cen- 
tral's or  Erie's.     This  fact,  however,  does  not  show  so  much  as 
it  otherwise  would  in  the  average  receipts  per  ton-mile  of  these 
roads,  as  published,  simply  because  the   Central   and   in   less 
degree  the  Erie  have  an  immense  local  business,  which  both  pays 
more  and  costs  more,  thus  bringing  up  the  average  receipts  ;  but 
the  through  business  proper  leaves,  and  must  continue  to  leave, 
a  very  small  margin  per  mile  to  both  lines  compared  with  what 
the  Pennsylvania  obtains.     No  ingenuity  or  skill  will  ever  be 
able  to  materially  decrease  the  large  percentage  of  advantage 
for  through  business  which  its  geographical  position  gives  to  the 
latter  road ;  because  the  total  through  rate  will  always  be  the 
same  by  all  competing  lines,  and   the   long  lines   must  conse- 
<iuently  forever  suffer  in  receipts   per  mile,  unless   causes   not 
now  possible  to  foresee  shall  change  the  conditions. 

213.  But  notwithstanding  this  fact,  we  have   in   these  same 
a-oads  a  striking  illustration  of  the  truth  of  the  second  half  of 


CH.  VII^-DISTANCE^EFFECT  ON  COMPETITIVE  TRAFFIC  221 

our  contradictory  law.  Neither  the  New  York  Central  nor  the 
Ene  have  any  interest  whatever  in  shortening  their  own  lines  (if 
we  consider  the  interests  of  both  as  terminating  at  Buffalo) 
notwuhstanding  that  they  suffer  so  much  from  "the  fact  that 
they  are  links  in  a  long  route.  Thus  the  Erie  now  constitutes 
Shn"'  i  M-  T  ^"Z  York-Chicago  connection  via  the  Lake 
Shore  &  Michigan  Southern  Raihvay,  and   receives  on  a  ic-ton 

r.T"  r  K^'/  ^Tr'  "^'"  ^^^-55  out  of  $90,  assuming  the  through 
rate  to  be  divided  according  to  distance  only,  without  arbitral, 
or  terminal  allowances.     If  its   length  were   10  miles  shorter  it 

would  receive  onlv  l£lZli°  „,  "^'^  „f  *.  a 

ve  oniy  ^^^_^^  or  —  of  $90,  or  $39.00—3  loss  of 


05s  per  car-loau,  which  is  about  three  times  what  would  be  the 
actual  extra  cost  of  hauling  the  car  over  that  extra  distance. 

214.  On  the  other  hand,  if  some  of  its  Western  connections 
were  to  shorten    their  line  ten  miles  the  Erie  would  be  g    X 
benefited;  for  then,  for  the  very  same   service,  it  would  Leive- 
from  the  Lake  Shore  &  Michigan  Southern  Railwav,  for  example 
— ■  instead  of  — -  of  $90,  or  $39.95  instead  of  $39.SS-an  increase 
of  40  cents,  or  about  i  per  cent,>/-  nai/tin^. 

Spending  money  to  shorten  one's  own  line  for  through  busi- 
ness, therefore,  must,  except  under  peculiar  circumstances  be 
classed  among  those  charitable  actions  for  which  a  reward  mav 
possibly  be  hoped  for  in  the  next  world,  but  hardly  in  this  The 
only  important  exceptions  are :  .»  -    ^  iic 

First,  When  a  road  reaches  all  important  points  over  its. 
own  lines,  as  the  Pennsylvania  ;  or 

r>rofZ"'!l' '  ■'^''""  "  ''  """'  ^°^  °'''='-  ■•^^^°"^  than  direct 
profit  to  the  investors,  as  the  Cincinnati  Southern  Railway  or 
lines  built  by  the  State.  -"vvay,  or 

Even  these  exceptions  are  in  all  cases  only  partial.     There  is 
ways  some  credit  side  to  the  disadvantage  of'distance, Iherea 

Bade,    v?'""  '?"'"'   ''"'  '°   "^^   S--^^'^"'^  °^  <='-ature. 

.0  themf       'k"'   ^'■''"""''  ""^  '"^"-^^"y  have  a  credit  side 

them,  from  being  necessarv  to  reach  certain  traffic  points,  but 


222  CH.  VII.-DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC, 


\ 


in  themselves  they  are  vvliolly  harmful,  whereas   extra  distance 

is  not. 

215.  A  notable  example  of  these  antithetic  effects  of  distance, 
and  of  the  danger  of  disregarding  them,  may  be  found,  among 
many  others,  in  the  old  Atlantic  &  Great  Western  (now  New 
York,  Pennsylvania  &  Ohio)  Railroad.  It  enjoys  the  unique  dis- 
tinction of  being  now,  as  it  was  when  first  built,  the  longest  line 
in  existence  even  between  its  three  termini— New  York  in  the 
East,  Cincinnati  and  Cleveland  in  the  West.  It  has  always  two, 
and  generally  three  or  four,  more  favored  rivals  between  each 
considerable  point  in  the  East  and  every  considerable  point  in 
the  West.  Yet  even  in  this  extreme  case,  if  its  own  line  had 
been  ten  miles  longer  between  Cleveland  and  Cincinnati  and 
New  York  it  would  have  been  better  off.     It  would  then  have 

received  — -  or  46  per  cent  (see  par.  220)  instead  of  -—  or  45 


872 


223 


per  cent  on  all  Cincinnati  and  New  York  business,  and  -— 


or 


35  per  cent  instead  of  |^  or  34  per  cent  on  all  Cleveland-New 

York  business,  assuming  in  both  cases  that  receipts  were  divided 
strictly  according  to  distance. 

216.  As  it  happens,  this  is,  or  was  until  within  a  few  years  (the 
old  Atlantic  &  Great  Western  is  now  leased  to  the  Erie),  one  of 
the  cases  in  which  the  division  was  not  strictly  as  the  distance  ; 
the  Erie  Railway  having  formerly  insisted  on  being  allowed  a 
CONSTRUCTIVE  MILEAGE  of  46  miles  from  the  junction  point  at 
Salamanca  to  its  terminus  and  junction  with  the  Lake  Shore  & 
Michigan  Southern  Railway  at  Dunkirk  :  an  unjust  exaction, 
which  it  had  power  to  enforce  because  it  was  the  only  eastern 
connection  of  the  Atlantic  &  Great  Western.  Whereas,  there- 
fore, a  division  exactly  according  to  distance  would  have  given 

the  Erie   on   Cleveland-New  York  business  ~  or  66  per  cent, 
and  the  Atlantic  &  Great  Western  |i|  or  34  per  cent,  the  actual 


<:H.  VII.— DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC.  22'i^ 
division  was  ~^^  or  -g  ((^Z  per  cent)  to  the  Erie  and  only 

2  I  "2 

— ^-  (32  per  cent)  to  the  Atlantic  &  Great  Western.  Neverthe- 
less, in  this  as  in  all  other  cases  divisions  were  ultimately  based 
upon,  although  not  in  strict  accordance  with,  the  precise  relative 
hauls. 

217.  From  this  example  the  over-hasty  conclusion  should  not 
by  any  means  be  drawn,  that  a  road  should  lengthen  its  line  of 
set   purpose,  for  this  end  alone,  for  that  would  probably  lead  to 
acts  of  folly  ;  but  it  does  clearly  follow  that  whenever  a  better 
line  in  all  other  respects  can  be  thus  obtained  it  will  ordinarily 
be  folly  not  to  take   it.     As  it   happens,  such   lines  did   exist  at 
several   points  along   the  Atlantic  &   Great  Western,   affording 
better  grades,  more  traffic,  and  cheaper  work,  at  the  cost  of  some 
distance;  but  unfortunately  the  original  projectors  sinned  against 
both  of  the  cardi-nal  principles  laid  down  in  par.  211:  they  ne- 
glected the  vital  end  of  securing  short  and  favorable  connections, 
but  exerted  themselves  to  shorten  their  own  road  by  striking  an 
air-line  wherever  possible,  at  almost  any  sacrifice  of  gradients  ; 
running  it,  in   literal   truth,  "over  the  hills  and    far  away"  from' 
traffic.     The  consequences  of  such  engineering  may  be  read  in 
the  financial  history  of  the   road— a   history  which   might  have 
been   anticipated   with   certainty  in   the  beginning,  and    may  be 
counted  on  with  certainty  to  continue  to  the  end.     It  has  now 
found  its  greatest  and  only  real  use  as  a  feeder  and  competing 
•weapon  in  the  hands  of  the  Erie,  but  considered  as  a  separate 
property,  apart  from   one  or  two  profitable  leases  which  have 
alone  kept  it  in  as  good  a  position  as  it  has  had  (see  Chap.  XXI.), 
it  can  never  by  possibility  more   than   barely  pay  operatinjr  ex- 
penses for  any  period  of  years  ;  for,  however  great  may  be  the 
growth  of  traffic,  and  however  great   the  future  improvements 
tending  to  reduce  expenses,  other  lines  also  share  these  advan- 
tages, and  through  rates  will  continue  to  fall  in  proportion,  down 
to  the  lowest  point  which  affords  the  most  favored  line  2i  handsome 
'but  not  exorbitant  profit,  and  way  rates  likewise  will  continue  to 


I 


i; 


224  CI/.  VII.'-DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC, 

fall  in  proportion  down  to  a  reasonable  but  not  excessive  per- 
centage (usually  from  50  to  75  per  cent)  in  excess  of  the  through 
competitive  rates. 

218.  In  a  certain  important  sense,  indeed,  vi'e  may  say  that  all 
rates  are  fixed  by  competition,  for  the  fact  that  non-competitive 
way  rates  do  adjust  themselves  quite  closely  to  the  through  rates 
is  well  determined.     In  illustration  of  this  fact,  which  has  been 

Table  93. 

Statistics  of  Passenger  Traffic,  Cleveland,  Columbus,  Cincinnati  & 

Indianapolis  Railway,  1873-1885. 


Year. 


1873. 
74. 


1875- 


1876. 

77. 
78. 

79- 


Local  Pass. 


Through  Pass. 


Av.  Haul. 
Miles. 


2q.8 

27.8 


27.1 


1880. 


1881. 
82, 
83. 
84. 


1885, 


28.3 
27.9 

27-3 
28.6 


Rects. 

Per  Mile. 

Cts. 


3-47 

2.83 


2.63 


2.48 
2.41 
2.42 
2.46 


29-5 


27.6 
28.7 

30-5 
295 


28.9 


2.39 


Av.  Haul. 

Miles. 


198 

185 


1S8 


192 

183 
182 
186 


Rects. 

Per  Mile. 

Cu. 


2.53 
2.55 


^38^ 
1.89 
2.24 
2.10 
1.82 


Per  Cent 
Throusrh  of 
Local  Rate. 


730 
90.0 


90.5 


193 


2.51 
2.60 

2.51 

2.47 


2.57 


184 

115 
121 
118 


121 


1.82 


1.77 
1.78 

I. 81 
1.73 


1. 61 


76.2 
93.0 

86.8 
73.9 


76.1 


70.5 
68.6 
72.0 
70.0 


62.6 


Decrease  per  cent  in  through  rate  in  12  years,  36.4  per  cent. 
.4  4*         44  local  "  *'       "     25.9        " 

Summary  of  Average  Decrease  from  Average  of  1873-5  to  Average  of  1878-81. 

3  y'rs,  1873-75, 1.766  cts. 


Through  Freight...  -j 


3  y'rs,  i873-75»    -979  Ct. 
3  y'rs,  1879-81,    .593  " 


Adecreaseof 38601. 

Or,  in  percenuge ViMiV-  c- 

j  3  y'rs,  1873-751  a-487  cts. 
Through  Passenger  ^^  ^  y^^  1879-81,  1801  " 

A  decrease  of 0.686  ct. 

Or,  in  percentage ayJiP'C- 


Local  Freight . 


(  3  y  rs.  I 
1  3  y'rs.  » 


879-81,  1. 157 


Adecreaseof eogct. 

Or,  in  percentage 34^  P-  c- 

i  3  y'rs,  1873-75,  2.978  cts. 
L»cal  Passenger. . . .  -j  ^  y,„^  ,879-81,  a.455  "'_ 

Adecreaseof 523Ct. 

Or,  in  percenuge 13*3  P*** 


CH.  VII.-DISTANCE-EFFECT  ON  COMPETITIVE  TRAFFIC.  225 

Table  94. 
Statistics  or  Freight  Traffic,  Cleveland,  Columbus,  Cincinnati  & 

Indianapolis  Railway,  1873-1885. 
Through  Freight. 


Year. 


East-Bound. 


West- Bound. 


Averasre 
Haul. 
Miles. 


1873. 
74 


1875 


191 
215 


76. 

77- 
78. 

79- 


1880 


195 


Receipts 

Per 
Ton-Mile 

cts. 


1. 14 
.92 


Averajfe 
Haul. 
Miles. 


205 
214 


Receipts 

Per 

Ton-Mile, 

cts. 


•75 


215 
202 
208 
203 


.64 
.67 
•57 
.52 


81. 
82. 
83. 
84. 


195 


1885. 


193 
184 

185 

2Q2 


199 


.66 


.50 

•59 
.62 

•50 


223 


231 
223 
221 
217 


1-34 
1.24 


.86 


Per 
Cent 
West- 
Bound. 


23^3 
26.2 


212 


.44 


2X1 

200 
202 
206 


.68 
.88 
.84 

•73 


207 


_-73 
.60 
.61 

•71 
•59 


28.7 


Per 

Cent 

Through. 


62.5 
59-2 


26.8 
26.2 
22.7 
26.2 


28.2 


51 


35.2 

35.4 
35-6 

37.4 


59-4 


Average 
Receipts 

Per 
Ton-Mile. 

cts. 


I -175 
.984 


64.7 
64.8 
67.4 
67.6 


64.2 


36.7 


64.9 

68.9 
65.1 
64.9 


68.0 


Local  Freight, 


778 


650 
716 
613 

565 


68  r 


532 

591 
652 

525 


463 


Year. 


East-Bound. 


1873. 
74. 


1875. 


Average 
Haul. 
Miles. 


119 
120 


76. 

77. 
78. 

79  • 


1880. 

81. 
82. 
83 

-Jil 
1885 


108 


106 
108 
116 

115 


Receipts 

Per 
Ton-Mile. 

CIS. 


West-Bound. 


1.82 
1.65 


1.58 


132 


105 

97 

loi 

95 


1.42 
1.48 
I-I5 
^•15 


Average 
Haul. 
Miles. 


98 
93 


Receipts 

Per 
Ton-Mile. 

Cts. 


109 


I. GO 


96 


1. 10 
1. 17 
1. 12 
1. 14 


107 

102 

98 

100 


2.09 
2.08 


Average 
Receipts 

Per 
Ton-Mile 

cts. 


Per  Cent  Through 
OF  Local  Rate. 


1.68 


108 


1.08 


112 
no 

117 
126 


1.44 
1.64 
1. 61 

^•34 


,899 
776 


1.622 


East- 
Bound 
only. 


62 


•34 


116 


1.20 

1. 18 

1.03 

.91 


1.429 

i^538 
1.303 
1. 215 


47 


I. no 


66 


•99 


1. 146 
1. 176 
1.079 
1. 018 


•039 


40.8 


Total. 


61.9 

55.4 


48.0 


Per  Cent  of  Decrease,  1873-1885. 

-bound.  West-bound.  Av'e. 
61.4  62.0  60.7 

40.7  52.7         453 


45.5 
46.6 

47.0 

46.5 

61.3 

46.4 

50.3 
60.3 
51.6 


44.5 


I  n  rough  rales. . 
Local  rates  . 


15 


Per  Cent  of  Decrease,  18 75-1 885. 

T,.  ,         Eftst-bound.  West-bound.  Av'e. 

Through  rates  .  41.3        40.7        39.5 
Local  rates  ... .  31.6        41.0        3I.9 


226  CH.  VII.—DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC. 


Table  95. 

Comparative  Through  and  Way  Rates,  Lake  Shore  &  Michigan  Southern 

Rajlway. 

•m 

(Cents  per  ton-mile.) 


East-Bouno. 

West-Bound. 

Total. 

Ybar. 

Through. 

Way. 

Through. 

Way. 

1868 

1869 

1870 

1871 

1872 

1.56 
1.49 
1. 13 
1. 17 
1. 13 

3.49 
3.68 
2.67 

2.35 
2.04 

2.02 
1.78 
1-53 
1. 18 
1.49 

4.07 
4.05 
2.84 
2.26 
2.01 

2.43 
2.34 
1.50 

1.39 
1.37 

Comparative  Rates,  taking  Rates  of  1868  as  i.oo. 


i860 ..•••• 

1869 

1870 

1871 

1872 


1.00 

•954 
.723 
.750 
.723 


1.00 

X.055 

.755 

.673 

.685 


1.00 
.882 
•758 
.585 
•  738 


1.00 

.996 
.698 

.556 

.494 


1.00 
.962 
.617 

.573 
.563 


Since  1873  the  rates  have  not  been  made  public  in  this  form,  for  through  and  way 

separately. 

It  will  be  seen  that  the  non-competitive  way  rates  fall  in  close  sympathy  with  the 
competitive  rates,  and  vary  more  directly  with  each  other  than  the  East-bound  and  West- 
bound. 

already  alluded  to  (par.  54),  a  comparison  of  the  course  of 
through  and  local  rates  on  the  Cleveland,  Columbus,  Cincinnati 
&  Indianapolis  Railway  is  given  in  Tables  93  and  94,  and  on 
the  Lake  Shore  &  Michigan  Southern  Railway  in  Table  95,  which 
illustrate  the  fact  very  strikingly.  Few  roads  publish  reports 
from  which  such  statistics  can  be  obtained,  but  the  law  holds 
substantially  true  everywhere.    . 

219.  From  these  examples  it  takes  no  great  intelligence  to 
perceive  how  inexorable  is  the  law  that  the  line  which  places 
itself  originally  at  any  serious  disadvantage  has  no  escape  from 
the  consequences  of  its  folly  but  to  remedy  those  disadvantages. 


Apparent  advantages  from  the  general  progress  in  wealth  and 

I.r  fn  tlU      rt"" '°  r  "^"'  "  ^'  '"•  ^'""  ^"  "-hare 
own"  U        ,^-        u^  '""P'y  "^'"«  "  '»  hold  its  own,  and  "  its 

divided  h'  ""^^       ^^^^^'  "•^'  "^^  ""-""gh  rate  is  nearly  always 
divided  by  some  even  percentage,  and  consequently  triflinrdif 
ferences  are  not  likelv  tn  off.„»  .1      j-   •  .  ^"'■'^y  tnnmg  ait- 

-■<:  noi  iiKely  to  affect  the  division  either  way.     Thus  a 

line  entitled  by  its  exact  mileage  to  receive  either  ^27  ^^403 
would  probably  receive  40  per  cent.     H  i.  length  e'nmied  I't^" 
7^  It  would  probably  receive  4.  per  cent.     The  fractional  per- 
to  hoM  th^""'  ^on^etimes  insisted  on  by  the  line  which  happens 

iind°'ta  el  T:f"  r'°"'  ""  "^"^"^  ^"^  ^'^-"-««^  "^  'ha 
Kind   takes  the  form   of  some  terminal  or  arbitrary  allowanr^ 
instead  of  a  modification  of  the  percentage  ^""vvance 

^h."''  f'"r  """  ""^"'P'"  °^^"y  °"<=  -""ad  from  competitive  ex 
change  traffic  vary  (i)  with  the  total  haul  on  each  unifo     raffiT 

Zt}"\r'\  '"'^   '"■°P'"-"°"   "■^■•-^  -   'he  homeind  forS 
roads,  the  effect  of  any  given  change  in  the  length  of  V.T^ 

^oad  wn.  be  different  on  traffic  between  all  possif  ,e  t    ffit^  TnTs*^ 

All  that  can  be  done,  therefore  (or  all  that  is  in  the  least  neces: 

sary  to  do  .  ,s  to  form  some  rude  idea  of  the  centre  oTo^^^^^^ 

of  the  initial  and  terminal  points  of  shipment  at  each  end  of  thi 

;|ne.  Which  Will  often  be  quite  different  for  different  pans  0/  tt 

ternale  lines  are  under  comparison  in  other  reslTs  'he^  J„ro  T°  "^ 

^uh  the  utmost  caution.  anotner,  should  be  admitted  only 


228  CH.VII,— DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC. 


222.  The  effect  on  the  receipts  of  the  home  road  from 
through  competitive  traffic  of  an  increase  in  its  own  length  only, 
the  haul  on  its  connections  remaining  unchanged,  may  be  stated^ 
with  adequate  exactness,  in  this  very  simple  way: 

The  interpolation  of  additional  distance  by  the  adoption  of  a 
longer  alternate  line  between  the  same  termini  will,  for  all  ordi- 
nary and  moderate  changes  of  length  (under  20  or  25  per  cent 
of  home  haul),  leave  the  earnings  per  mile  of  the  original 
(shorter)  line  unchanged,  and  enable  the  home  road  to  earn  on 
its  extra  mileage  as  large  a  percentage  of  the  average  per  mile  on  the 
shorter  line  as  the  percentage  of  the  foreign  haul  to  the  total  haul. 
This  law  holds  essentially  true,  regardless  of  the  amount  of  the 
added  mileage. 

For  example,  on  traffic  which  has  70  per  cent  foreign  haul,. 
if  the  home  road  were  longer  it  would  receive  out  of  its  added 
proportion  of  through  competitive  freight  enough  to  earn  70  per 
cent  as  much  per  mile  on  the  added  mileage  as  on  the  original 
mileage,  the  earnings  on  the  latter  remaining  unchanged. 

223.  To  put  the  rule  in  another  and  shorter  way:  With 
through  competitive  traffic — 

The  per  cent  of  home  haul  in  the  total  haul  -|-  the  \  =  100  p.  c. 
per  cent  of  average  earnings  per  mile  realized  v  (always  a  lit- 
by  home  road  by  extra  mileage )      tie  less). 

The  maximum  and  minimum  "limits"  to  this  rule  are: 
I.  When  the  home  road  has   100  per  cent  of  the  haul  it  rea- 
lizes o  per  cent,  or  nothing,  on  any  extra  haul. 

3.  When  the  home  road  has  originally  o  per  cent  of  the  haul 
the  gain  to  its  receipts  from  any  haul  it  may  gain  is  100  per  cent 
of  the  average  rate  per  mile. 

224.  A  simple  geometric  demonstration  of  this  law  is  given 
in  Figs.  7  to  12,  with  their  accompanying  explanation.  The  law 
is  only  approximate,  and  f6r  very  great  changes  of  length  be- 
comes materially  in  error;  but  the  largest  probable  differences 
which  can  come  under  the  consideration  of  the  engineer  are 
from   10  to  25  per  cent  in  the  home  haul,  and  for  such  differ- 


*nces  the  law  is  sufficiently  exact,  as  is  evident  in  Table  06 
which  gives  the  exact  effect  on  receint<!  nf  .^^^ifi  /""'^  90, 
and  .0  per  cent  in  the  home  haul        '^  niod.ficat.ons  of  xo 


Table  96, 

ErPBCr  OP  CH*NOES  OP   D.STANCB  O.  E.K«.«CS  P.OM  Th>.OUOH  (ExCHXKOK) 

Competitive  Traffic. 

divine  U.«  ««.  .ffec.  and  mustrating  .he  essentia,  truth  of  aad  amount  or  eLr  in  the 

approximate  rule  in  paragraph  223. 

^^''^  "f  ^O  A'-  ^^nt  Increase  of  Distance. 


Per  Cent  of 

'Original 
Total  Haul 

on  the 
Home  Road. 


10 
30 
30 
40 
50 
60 
70 
80 
90 
100 


Corresponding 

Receipts  of 

Home  Road 

out  of  $1.00 

Rate. 


If  the  Home  Road 

were  Ten  Per  Cent  longer  its 

Keceipts  would  be— 


10  cts. 
20 


I  ( 


30 
40 
50 
60 
70 
80 
90 
100 


•  < 

<< 
<i 

<4 
<( 
(< 
<( 


iVff  X 

TIFT  X 

8  8      V 

fAx 
Mx 


X 
X 
X 
X 
X 


$1.00 
1.00 
1. 00 
1. 00 
1. 00 

1.00  : 
1. 00  : 
1. 00  : 
1. 00  : 
1. 00  : 


:      10.891 
=      21.57 

■  32.04 

■  42.31 
52.38 
62.26 
71.96 
81.48 
90.83 

100.00 


Per  Cent  of 

extra  Receipts 

on 

extra  Haul 

to  Average. 

89. 1 

78.5 
68.0 
57.8 
47.6 

37.7 

28.0 

18.5 

9.0 

None. 


Sum  of 

Percentages 

in  First 

and  Last 

Colun:n.s. 


99- 1 

98.5 
98.0 

97.8 
97.6 

97.7 
98.0 

98.5 

99.0 

lOO.O 


Effect  of  20  per  cent  Increase  of  Distance. 


10 
20 
30 
40 
50 
60 
70 
80 
90 
100 


10  cts. 

T^^irXli.oo 

20  " 

ToV  X    1. 00 

30  *' 

At  X    1.00 

40  " 

rVff  X    1. 00 

50  " 
60  " 

AirX  i.oo 
t'AX    1.00 

70  " 
80  '* 

Ax  1.00 
A%X    100 

90  '• 

ffX    1.00 

100  *♦ 

f^X    1.00 

-■  "-765 
■   23  07 

3396 
44.44 
54.545 

64.284 

73.68 
82.80 

91.53 

100.00 


88.2 
76.8 
66.0 

55.5 

45.5 

35.7 
26.3 

17.5 
None. 


98.2 
96.8 
96.0 

95.5 
95.4 
95.7 
96.3 
97.5 
98.5 
100. o 


II 


230  Cir.  VIT.— DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC^ 


Figs.  7  to  12,  Diagrams  illustrating  the  Effect  on  Receipts  from  Com- 
petitive Through  Traffic  of  a  Longer  Home  Line  between  the  same 
Termini. 

/*     E 
A', 


D^  D    E' 

Fig.  7.  F'G-  8.  P»°-  9- 

{On  these  diagrams  the  interpolated  mileage  on  the  home  road  (/)  is  assumed  to  be  ONET 

eighth  0/  the  total  //a«/.] 


Figs.  7-10   One  quarter  of 
total  haul  on  home  road. 


Fir.s.  8-11.  One  half  of  to- 
tal haul  on  home  road. 


Figs.  9-12.  Three  quakters  ok 
total  haul  on  home  road. 


Fig.  XI. 


Fig.  la. 


Fig.  10. 

\0n  these  diagrams  the  interpolated  mileage  on  the  home  road  ( f)  is  assumed  to  be  ON& 

quarter  0/ the  total  haul.^ 

Explanation  of  diagrams,  and  demonstration,  from  Figs.  T  to  \2,  of  law 

stated  in  par.  222. 

225.  In  each  diagram  let  the  base  DC—  the  total  haul  on  any  given  unit  of 
through  competitive  traffic,  in  part  over  the  home  road,  H,  and  in  part  over  one 
or  more  foreign  roads,  F. 

And  let  the  altitude  AD=  BC=  the  average  receipt  per  mile  on  this  unit 
of  traffic. 

Then  will  the  area  ABCD  —  the  total  through  rate  per  unit  of  traffic  (less 
any  terminal  or  other  constant  deduction),  and  the  areas  .^and  F  =.  the  frac- 
tions thereof  appertaining  to  the  home  and  foreign  roads,  respectively. 

Assume  the  total  haul  increased  to  DC  by  the  addition  of  the  distance  DLf 
to  the  home  road.  Then,  since  the  total  through  rate  remains  the  same,  we 
shall  obtain  a  new  average  rate  per  mile.  A' D' ,  of  such  amount  that  the  area  of 
the  new  rectangle  A' B' CD'  =  area  of  original  rectangle  ABCD. 


CJr.  yil.-DISTANCE-EFJ^ECr  ON  COMPEriTIVETR^,.^,r  23, 
Furthermore: 

^^^'iroade.clusi.elyUor.Zr,.,.^^^^^^^^ 

But  if  we  assume  the  earnings  of  the  home  rold  on  ,  ^^'"'^^^^^• 

be  unaffected  by  the  addition  thereto,  then  wT,  hTree^Ie^'ir -Th^^'^  " 
amount  lost  by  the  foreign  road  through  the  longer  ha  "l  -  t.  ^'°'" 

rate,  and  this  area  only  will  represent  the  'xL  rec  "  ts  of  the  h'  ""'  f'"^' 
extra  mileage,  which  let  =  rectangle  A"D,  '°^^  °"  ''* 

Then  we  have,  geometrically, 

A'D       EB, 

Net  rate  per  mile  realized  ]  f  average  1        , 

h^ni  /  "J^    '""^^  T^   ^^^^"^  \  throulh  foriginal 

haul  (rate  reahzed  by  home   ^is  to^  rate  pi  mile  las  \  ^^"'  «« 
road    on   original    mileage   |  j  on  new  and  I        H^^^'gn 

being  supposed  unchanged)  j  [longer    haulj        1^°^^^ 

For  example:  If  25.  50.  or  75  per  cent  of  the  original  haul  (befor.  ,  J   k 

me  was  lengthened)  was  on  the  foreign  road,  the  home  Lad  l  ,  ta^e  (^^^^^^^^ 

a  trifling  error,  shown  in  Table  06)  2*:    en  r.r  ^r  ^  /     ^^^^'^^  (within 

through  rate  per  mile  on  any  added  Lleage  without  ™T        "'  ""'  """^-^ 

.ion  as  its  connections  havel  suffer  onXV-tT^la^r^  ='"''  ^"^•'  «''- 

In  practice,  the  changes  of  length  which  the  engineer  is  called  „nn„  , 
sider  w,ll  ordinarily  be  so  small  that  the  through  r^te  per  mUe  0,?°        •""" 
fre,ght  will  be  but  little  affected,  so  that  we  may  say  ,n  fIL   i  M  ,,1'"''"""'"' 
ca  V  AD'  —  An  ,«i,«„^  t.         ,  ^    ^         ^^-  7  to  12  that  practi- 

nyAU  _  AD,  whence  we  have  the  approximate  law  of  par.  222. 

Table  97. 
P.0P0KT,0N  OF  THROUGH  AND  LocAL  Fke.cht  .k  e.ch  Cens,;s  Group  op 

THE  United  States. 

[Computed  from  Census  of  ,88o.]     (Earnings.) 


forigi. 

isto^"^^ 
I  total 

I  haul. 


Census  Group 


I.  New  England 

II.   Middle  to  Indiana. 

III.  Southern 

IV.  N.  W.  Central.'.*..*.* 
V.   Louisiana  and  Ark 

VI.  Far  West 


Total  United  States. 


Classed  as     through    ,s  competitive  traffic,  by  any  means. 


Not  all  the  freight 


»r  ■ 


232  CH.  VII.— DISTANCE— EFFECT  ON  COMPETITIVE  TRAFFIC, 


Table  98. 

Freight  Movement,  Through  and  Local,  East  and  West,  on  Pennsyl- 
VANiA  Railroad  (P.  R.  R.  Div.  only)  for  Thirty-five  Years. 

(Paying  freight  only.     Statistics  exist  no  farther  back.) 


Tons  Carribo. 

Ton-Mileacb. 

I 

—  1,000,000. 

1  —  1,000,000. 

Ykar. 

ThrouRh. 

Local. 

Through. 

Local. 

Total. 

Total. 

East. 

West. 

East. 

West. 

East. 

West. 

East. 

West. 

1851  — 

.005 

.008 

.008 

.005 

0.026 

•   •  •      •  • 

52... 

.013 

.019 

.021 

.015 

0.069 

a. 35 

I'7 

6.9 

4-3 

16  8 

53  •   • 

.036 

.038 

.049 

•037 

0.160 

8.30 

8.27 

la.i 

11  4 

40.0 

54... 

.050 

.043 

.089 

.054 

0.237 

12.5 

10.6 

26.6 

11.9 

61.6 

55  ••• 

.106 

.065 

.128 

.065 

0.365 

26.9 

16.3 

41.7 

17-3 

102.  a 

»85I-5•• 

.051 

.042 

.072 

•043 

0.207 

12.51 

958 

21  82 

11.20 

55-13 

I8s6.... 

.089 

.076 

.196 

.092 

0-454 

22.0 

19.0 

55  4 

234 

119.8 

57-... 

.094 

.077 

.385 

.406 

0.964 

23s 

19.1 

67.3 

30.8 

140.7 

58.... 

.141 

.080 

.404 

.421 

1.047 

35.0 

19.8 

75.6 

31-7 

162.1 

59.... 

.130 

.103 

•571 

.366 

1.170 

46.5 

37-2 

69.5 

273 

180,3 

60  ... 

.176 

.100 

.642 

.429 

1.346 

63.0 

35-7 

89.9 

26.4 

215,1 

1856-60. 

.126 

.087 

.440 

.343 

0.996 

38.0 

26.16 

71.54 

27.92 

163.63 

t86i.... 

0.31 

0.08 

0.86 

0.37 

1.63 

111.2 

28.1 

120.9 

20.0 

280.3 

62..., 

0-37 

0.13 

I  13 

0.43 

2.06 

I3».5 

45-9 

163.8 

351 

376-a 

63  ... 

0-35 

0.13 

1.23 

0.56 

2.27 

124.9 

45-5 

»77.7 

45-6 

393-7 

64.... 

0.32 

0.15 

1.48 

0.63 

a-59 

"55 

53  0 

300. 0 

52  a 

420.6 

65   ... 

0.30 

o.i6 

1.42 

0.67 

a. 56 

108.4 

57-6 

203.9 

5o.t 

420.1 

1861-5.. 

0.33 

0.13 

i.aa 

0.53 

2.22 

118.30 

46.02 

173.26 

40.60 

378.18 

1866.... 

0.32 

0.16 

1.84 

0.86 

319 

"3- 

58.8 

276. 

65.0 

513- 

67.... 

0.31 

0.17 

2.21 

1. 03 

3-71 

110. 

62.0 

322. 

72.1 

566. 

68.... 

0.39 

0.22 

».58 

1.24 

4-43 

141. 

77-3 

373- 

84.8 

676. 

69... 

0.47 

0.23 

a. 82 

J. 47 

5.00 

169. 

835 

402. 

98.9 

753. 

70.... 

0.54 

0.23 

3.07 

1.58 

5-43 

104. 

83. 

439- 

no. 

826. 

1866-70. 

0.41 

0.20 

2.50 

1  23 

4.35 

145 -4 

72.9 

362. 

86.2 

667.0 

1871 

0.71 

0.31 

370 

1.85 

6.58 

254- 

113. 

533- 

"3- 

I013. 

7a.... 

0.79 

0.36 

4.22 

2.47 

7.84 

283. 

130. 

62s. 

»52. 

1190. 

73-. •• 

0.87 

0.32 

548 

a. 54 

9.21 

312. 

114. 

821. 

137. 

1385. 

74.... 

1.07 

0.30 

4.92 

a-34 

8.63 

381. 

108. 

764. 

119. 

>373- 

75--- 

1. 00 

0-35 

5-39 

2.37 

9.12 

358. 

126. 

863. 

133. 

1479- 

1871-5.. 

0  89 

0.33 

4-74 

2.31 

827 

317.6 

118. 2 

721.2 

130.8 

1287.8 

1876.... 

1.32 

o'.29 

5-79 

2.52 

9.92 

473- 

105. 

915- 

136. 

1630, 

77..,. 

1.02 

0.39 

5-7» 

2.72 

9-74 

364. 

103. 

869. 

159- 

1495  • 

78.... 

1-45 

0.29 

6.20 

3  01 

10.95 

519- 

103. 

936. 

»75- 

1732. 

79... 

1.69 

0.38 

7-59 

4.01 

13.68 

605. 

137. 

1138. 

257. 

2137. 

80  ... 

1.58 

0.49 

8.51 

4.79 

15-36 

565. 

174- 

1230. 

329. 

2298. 

1876-80. 

1.41 

035 

6.76 

3  41 

"•93 

505.2 

124.4 

1017.6 

211. 2 

1858. 4_ 

1881.... 

1.64 

057 

10.12 

5-91 

18.23 

586. 

203. 

1452. 

414. 

26^5. 

8a.... 

1.35 

0.59 

11.91 

6.51 

20.36 

483. 

213, 

'755- 

430. 

2880. 

83... 

1.38 

0.56 

12.47 

7.27 

21.67 

494- 

199. 

1853. 

451- 

2997. 

84... 

1.29 

0.53 

13.33 

7-43 

22,58 

468. 

192. 

1938. 

484. 

3082. 

8s.... 

1.68 

0-57 

13.88 

7.91 

24.05 

612. 

209. 

1969. 

529. 

33'8. 

1881-5.. 

1.47 

0.56 

12.34 

7.00 

31.38 

528.6 

ao3.3 

»793-4 

461.6 

2986.4 

'^J^^'-DISTANCE-EFFECJ^ONCOMPETITIVE  TRAFFIC.  233 


Table  ^^, —Continued, 
Summary  by  Half- Decades. 


Year. 


Toms  Carried. 
1  =  1,000,000, 


Ton- Mileage. 
1  =  1,000,000. 


Percentages  and  Average  Local  Haul. 


Year. 


Tons, 


Per  Cents  op  Total. 


1851-5 

1856-60 

1861-5., 

1866-70. 

1871-5.. 

1876-80. 

X881-S  . 


Through, 


West. 


East. 


24.5 
12.7 

15.0 

9-4 
10.8 
II. 8 

6.9 


Local. 


East, 


20,5 
8.7 

5-9 
4.6 

40 
2,9 
3.6 


34.5 
44.2 

55.1 
57-7 
57-3 
56.7 
57-7 


West, 


Ton-miles, 


Through, 


20.5 

34  4 
24.0 
28.3 
27.9 
28.6 
33,8 


East, 


22.7 

23-3 
31-3 


West, 


17-3 
16,0 
12.1 


21.8 

10,9 

247 

9.1 

27,1 

6.7 

17.6 

6.8 

Local. 


East. 


39-6 
43-7 
45-7 
54-4 
56.0 
54.8 
60.3 


West. 


Average  Haul 

on 
Local  Freight. 


20.4 
17.0 
10.9 
12.9 
10,2 
11,4 

«S.4 


East,      West. 


30 

163 
141 

145 
151 
150 

145 


26.0 
81.0 

76.5 
70. a 
56,6 
61  9 
66.0 


226.  From  the  additional  receipts  thus  realized  is  to  be  ri^ 
ducted  the  additional  cost  of  earning  it,  which  we  have  seen  may 
vary  anywhere  from  .5  to  40  or  (for  great  changes)  50  per  cen^ 

De  realized  from  longer  home-haul  of  competitive  frei<rht  unless 

he    o,e,^n  haul  is  greater  than  .5  to  40  or  50  per  c^nt'of    he 

total        But   with    any   foreign    haul   whatever   there   is   .nm! 


I-  f.i 


•"Tir 


W 


I 


M\ 


234    CJ7^P.   VJI.^DISTANCE— EFFECT  ON  WAY   TRAFFIC, 

.  227.  Let  US  now  see,  in  continuation  of  par.  205,  how  much 
weight  should  be  probably  given  to  differences  of  distance  as 
RESPECTS  WAY  TRAFFIC.  Table  92  and  various  Others  will  show  that 
it  is  a  fairly  low  estimate  to  assume  40  passengers  or  100  tons 
of  freight  as  an  average  train-load,  about  one  half  of  which  (see 
Tables  97  and  98)  will  be  local  traffic,  at  rates  fixed  by  the  mile 
or  at  the  will  of  the  company.  The  fluctuations  from  this  average 
are  very  great  indeed,  and  a  nearer  estimate  can  easily  be  formed 
in  any  particular  case.  Assuming  the  above  average,  however, 
at  \\  cents  per  mile  for  freight  and  2^  cents  for  passengers,  this 
purely  local  traffic  would  net  50  to  62^  cents  per  train-mile.  On 
the  other  hand,  we  have  already  estimated  (Table  89  and  par.  195) 
the  actual  cost  of  running  an  extra  mile  at  from  25  to  50  cents. 
This  sum  includes  all  expenses  for  running  such  distance,  so  that 
any  additional  receipts  arising  therefrom  must  be  credited  against 
it  in  full. 

228.  Accordingly,  it  is  plain  that  whenever  way  rates  are 
actually  determined  by  the  distance  alone,  any  reduction  of  dis- 
tance would  be  very  apt  even  to  entail  a  balance  of  loss  upon 
the  company.  For  example,  it  would  undoubtedly  entail  a  net 
loss  on  the  New  York  Central  Railroad,  from  their  way  business 
alone,  to  shorten  their  line  by  several  miles,  even  if  it  could  be 
done  without  cost  to  them,  provided  all  their  business,  "  way"  as 
well  as  "through,"  had  to  be  transported  over  the  new  line;  for 
60  cents  would  be  a  very  high  estimate  of  the  actual  cost  of  run- 
ning extra  distance  on  that  road.  On  the  other  hand,  taking  an 
average  train-load  (on  main  line  only)  of  100  passengers,  and 
assuming  the  very  low  proportion  of  one  half  as  that  on  which 
the  receipts  are  fixed  by  the  legal  limit  of  2  cents  per  mile,  we 
have  an  average  gross  loss  of  100  cents  per  train-mile,  or  a  net 
loss  of  40  cents  for  every  mile  cut  out  of  the  line.  And  if  the  gross 
loss  had  been  but  10  cents  instead  of  100,  it  would  have  operated 
to  reduce  the  value  of  any  saving  of  this  distance  by  so  much, 
although  not  entirely  destroying  it. 

229.  All  way  traffic,  however,  is  not  by  any  means  rated  solely 
by  the  mile ;  nor  would  any  railway  think  of  attempting  to  so 


CHAP.    V/T.-DISTANCE-EFFECT  OAT  IVA  V   IRAFFIC.  235 

rate  it,  even  if  it  had  the  power  to  do  so,  without  destroyi^ 
business.    Tables  93-5  dearly  show  this.     Table  98,  showing  the 
enormous  and  growing  proportion  which  local  traffic  makes  of 
the  total  traffic  of  a  line  like  the  Pennsylvania  even,  which  is 
often  thought  of  as  chiefly  a  through  trunk  line,  makes  it  still 
clearer  that  it  is   impossible  that  local  traffic  should  be  all  so 
rated.     And  yet  a  line   no  miles  long  instead  of  100,  between 
two  given  points,  will,  or  can  be  made  to,  derive  some  addition 
to  gross  receipts  without  working  either  hardship  or  injustice 
The  local  passenger  rates  would  be  perhaps  $3.30  instead  of  $3 
-a  difference  which   those  who  may  be  called  floating  or  occa- 
sional travellers  (those  making  one  or  two  or  ten  trips  a  year) 
can  well  afford  to  pay,  and  would  pay,  probably  without  feeling 
the  difference.     If  we  estimate  the  total  extra  cost  of  running  the 
10  miles  extra  distance  at  $3,  which  would  ordinarily  be  ample 
It  would    require  but   10  such  passengers  per  train  to  whollv^ 
counterbalance   the  cost  of  running  the  extra  distance.     That 
road  would  be  the  exception  perhaps  which  did  not  average  la 
such  passengers  per  train,  and  substantially  the  same  condition 
of  things  exists  on  many  roads  in  freight  business  also 

For  the  remainder  of  the  traffic,  to  which  the  greater  rate  for 
the  extra  distance  would  be  a  real  hardship  and   burden   it  is 
entirely  at  the  discretion  of  a  railway  company  to  do  away  with 
he  extra  burden  by  special  rates  based  on  volume  of  business 
furnished;  and  this  is  the  true  and  just  principle  of  fixing  rates 
under  all  circumstances;  for  the  interest  both  of  the  stockholders 
and  the  general  public.     A  man  who  travels  or  makes  a  ship- 
ment over  a  line  once  a  year  is  not  greatly  burdened  by  even  a 
considerable  difference  of  rates,  and  it  may  equitably  be  col- 
lected  from  him.     A  constant  patron  of  the  line,  on  the  other 
hano,  finds  the  same  difference  of  rate  a  very  great  burden 

230.  Thus  we  seem  driven  to  the  conclusion  that  it  is  rather 
worse  than  money  thrown  away  for  any  average  road  to  spend 
money  in  shortening  its  line,  nor  is  there  any  escape  from  the 
conclusion  that  there  is  only  one  class  of  road  to  which  it  can 
under  any  circumstances,  be  any  great  object  to  do  so;^those' 


^mr 


2^6    CHAP.    VII.—DISTANCE^EFFECT  ON  WA  V  TRAFFIC, 


namely,  whose  traffic  is  mostly  hauled  over  their  own  lines  ex- 
clusively, while  at  the  same  time  the  rates  on  a  large  portion  of 
it  are  directly  or  indirectly  fixed  by  competition,  as  on  two  or 
three  of  the  great  trunk  lines.  A  large  non-competitive  way 
traffic  alone  may  entirely  neutralize  the  pecuniary  value  to  the 
company  of  saving  distance. 

231.  But  these  conclusions,  although  undeniably  true,  should 
be  acted  upon  with  even  greater  caution  than  those  already  sug- 
gested with  respect  to  through  business,  and  only  when  there  is 
no  possible  doubt  as  to  the  interests  of  the  company.  For  as  a 
question  of  public  policy  the  conditions  which  bring  about  a 
credit  side  to  distance  have  no  force  whatever,  the  ultimate  loss 
to  the  community  from  an  unproductive  and  avoidable  service 
being  the  same  whether  borne  directly  by  the  railway  company 
or  transferred  by  it  to  the  general  public.  And  inasmuch  as  the 
prosperity  of  a  railway  is  intimately  connected  with  that  of  its 
supporting  population,  the  policy  under  certain  circumstances — 
perhaps  under  any  circumstances — of  thus  counting  in  as  a  make- 
weight a  possibly  avoidable  tax  (a  large  fraction  of  which  is,  so 
to  speak,  spent  in  collecting  it),  however  fairly  distributed  and 
lightly  borne,  may  be  questioned,  especially  as  the  ability  to 
collect  it  through  absence  of  competition  is,  by  its  very  nature, 
temporary  and  changeable.  Nevertheless  a  railway  is  a  busi- 
ness enterprise  and  not  a  charitable  institution,  and  it  has  the 
same  right  as  any  private  citizen  to  take  every  reasonable  pre- 
caution to  secure  pecuniary  success. 

232.  The  future  returns  to  the  investors  are  always  more  or 
less  problematical,  while  the  benefit  to  the  public  is  not  prob- 
lematical, and  always  far  ahead  of  any  possible  profit  to  the  in- 
vestors. It  is  hardly  reasonable  to  demand,  therefore,  that  rail- 
ways shall  increase  their  investment  for  the  sake  of  decreasing 
the  return  on  that  investment  paid  by  the  public;  and  sound 
policy  requires  and  justifies  this  at  least— that  the  expenditure 
should  be  mainly  directed  not  to  shortening  the  line,  but  to  re- 
ducing the  gradients  or  vertical  distances,  which  we  shall  find  to 
be  immensely  more  important  than  linear  variations  in  their  ef- 


CHAP.   Vn.-DISTANCE-SECVHmG  WAY  BUSINESS.    2^7 


233.  Especially  when  the  nii*»ct;^r,  ^^ 
THE  LINE    TO  SECURE  WAV  BUsmESS  "^  "  ""/•'  "''°™^^'''° 

we  may  almost  say  th^wTe '     t   '  t     ^^^"        '"  ^'"'P'^^  "^•' 

the  increase  becomes  considerable      Of  frei<rh     h 

nearly  true   that  S„  «,-  Height  business  it  is  so 

profitVver  th    acLal  co^t'oT  ""'  ''  ''"'  °'  '  ^'^  '^'^  '^  ^'-^ 
(See  also  par  ,80  °'  ''"^  °"^  ^^""^"'^^  -"-  ^"'P-enU 

234.  Let  us  suppose,  for  example,  that  the  A   <^  R  Po-i 
loo  miles  long,  is  deflected  lo  miles  north  to  sfni..  ^^^'  ^'^'  '^- 

The  increase  of  length,  if  "^^  "^"'^  ^'^^  P^'^t  C 

the  road' were  all  a  straight  fOZ 

line,  would  be  as  nearly  as 

/oo 


may  be  two  miles,  and  the  ,00 -=^  p 

extracost  of  running  those  Fig.  13 

tw^^mUes  probably  fifty  to  seventy-five  cents  per  train,  as  already  esti- 

;n  a  way  and  for  reLns  ^o^f^-r  red^r  [1^  -^xvm  ^7"'' 
engineers  are  rarely  trained  in  ^nrh  r^.^.  T  ,  ^^"^P"  ^-?^vIII.).      Young 

.heir  „i„ds  Of  impfess-r::-  r„'f,:r  :rd  ::Lti2t  "^'-^ '°  '"^'-^ 

..ons  in  .His  respect  which  have  a  ™ere  shadow  oTfourdaliorinTcr  """""• 

amo^n'to's'eirto  LT," tr'  ''"  '""T  '"''^  ''"''  ^''y-  '"'^  >°-  would 
nish  as  much  business  a/,,    r''    -^  f"^  '■"^■gnificant  town  will  fur- 
iiiucn  ousmess  as  that,  as  wil    be  evident  frr>,r.  t„ki  „ 

The  average  payment  to  railways  in  the  North  rir  J^  '*  '°  '*' 
about  $.3  per  head  per  year,  an  average  vuL^e  of  ,oS  to  ^  'T  '""« 
be  a  sufficient  inducement  for  such  a  dJlcti^l^u  5°°  P^°P'«w°"l<i 
e«reme  fluctuations  in  the  probable  L^lTi;"™  T::^^:^^! 


It? 


i 


238    CHAP.    VII.-DISTANCE-SECURING  WA  Y  BUSINESS. 

A  village  of  coal-miners  will  produce  ten  times  that  traffic  at  least,  and 
some  retired  hamlet  not  a  tenth  of  .t  ^.^^^ 

236.  The  preceding  is  independent  of  the  enect  01  i 

the  general  puonc  offtrreeate  railway  mileage  has  been  unnec- 

;,./'">!>  guides,  to'be  leviated  from  only  as  special  reason  to  the  con- 

trary  "PP^^'^f  =  ^,,1,^^  will  increase  the  average  PER  mile  of 

,OAD  0/ TRIBUTARY  POPUI-ATION  (weighing  the  latter,  of  course,  m 
tL  to  thLr  revenue-producing  capacity)  is  all  but  certamly  ex- 
''TnT  becluse  i    irmathematically  demonstrable  that  the  longer  hne 
rugrlhentoTe  fo:  the  Joint  advantage  of  the  community  and  the  ra.l- 

""VTve^n'tSn  be  considerably  less  than  this,  the  deviation  may 
easily  L  (and  P-bably  is)  for  the  interest  of  the  railway,  although  not 
Tthat  ci  ex^dient  in  itself,  as  a  question  of  public  polrcy. 

J38.  AH  the  preceding  conclusions  as  to  the  comparatively 
slight  importance  of  distance  (and  the  same  ,s  true  of  all  the 
iinor  details  of  alignment)  may  well  lead  to  ruinous  conse- 
quences If  hey  are  stretched  until  they  crack  to  support  some 
Tended  aid  radical  change  materially  modifying  the  cost  and 
extenaea  ,„ncoortation,  and  so  discouragmg  traffic ;  for 

"t^lTt'^verL  o  t  s  gh   of.  'that  anything  which  tends  to  per- 
.,      nLase  bv  ever  so  little  the  cost  to  the  public  of  any 
SrerSre TdisSvIn^ageous  to  all  parties,  although  its  dis- 
fdvantages  may  be  more  than  made  up  to  one  party  by  the  gam  , 
::n1h\di«e  ence  .e  e.^^^^^ 

rgVt°  otinTo"!  ihaTetn  in  extrLe  cases  there  always  .s 


C//AP.    VII.— DISTANCE— MORAL  EFFECT. 


239 


•a  credit  side  of  considerable  importance  to  increase  of  distance 
—contrary  to  the  idea  which  prevails  to  an  unfortunate  extent, 
that  a  short  and  direct  line  is  the  first  desideratum,  to  which 
almost  everything  else  must  bend.  On  the  contrary,  it  would 
be  hard  to  put  the  general  rule  whicii  should  govern  action 
about  obtaining  a  short  line  in  a  simpler  and  safer  form  than  to 
say  that  it  is  the  one  desideratum  about  a  railway  which  it  is  a 
good  thing  to  have  if  it  costs  nothing,  but  which  must  give  way 
to  other  considerations  in  case  of  conflict,  and  is  not  worth  spend- 
ing much  money  for. 

There  are  cases — as  for  instance  a  line  between  New  York 
and  Philadelphia— where  it  is  of  great  importance;  but  the  excep- 
tional position  of  distance  as  the  one  element  of  cost  of  trans- 
portation which  is  used  as  a  basis  for  collecting  revenue  makes 
such  exceptions  rare.    If  the  conditions  were  different— if,  for  ex- 
ample, we  could  charge  the  passengers  we  did  get  more,  because 
we  had  sacrificed  the  chance  of  getting  some  others  in  order  to 
carry  them  more  quickly— all  this  special  pleading  would  fall  to 
the  ground,  and  distance  would  take  its  true  relative  position 
with  the  other  elements  of  the  cost  of  transportation  on  the  basis 
of  cost  alone.     But  the  very  fact  that  this  is  not  the  case  seems 
to  have  had  the  effect  of  reversing  a  reasonable  deduction  from 
the  premises,  in  the  minds  of  the  more  ignorant  and  thoughtless, 
by  leading  to  some  such  hazy  chain  of  reasoning  as  we  noted  in 
the  beginning  of  this  chapter. 

239.  There  is  another  argument,  of  much  the  same  vague 
kind  as  that  last  referred  to,  but  of  a  more  reasonable  and  tan- 
gible character,  which  is  sometimes  brought  up  as  a  reason  for 
saving  distance,  viz.,  the  "moral  effect"  of  a  short  line  in 
helping  to  secure  traffic.  Nor  is  this  argument  wholly  unjusti- 
fied, for  there  are  numerous  lines  throughout  the  country  which 
do  apparently  suffer  simply  from  the  length  of  their  line  fright- 
ening away  passengers  and  fast-freight  traffic.  We  may  see 
that  this  effect  is  feared  by  the  current  fashion  of  misrepresent- 
ing geography  in  railway  advertising  circulars. 

240.  Many  lines  which  are  not  particularly  direct,  however. 


240 


CHAP.  Vll— DISTANCE— MORAL  EFFECT. 


CHAP.    Vir.-DISTANCE-MORAL  EFFECT.  24I 


do  not  do  this,  and  the  prosperity  of  a  single  conspicuous  line, 
the  New  York  Central  &  Hudson  River  Railroad,  will  show  that 
there  is  nothing  in  distance  pure  and  simple  to  deter  travel  until, 
as  in  the  case  of  the  Grand  Trunk  Railway  in  competing  for 
'  American  business,  the  difference  of  distance  becomes  so  great 
as  to  seriouslv  lengthen   the  total  time  of  the  trip-a  result 
not  commonly  to  be  feared  from  probable  engineering  modifica- 
tions of  any  given  line.     The  enormous  proportion  of  the  New 
York-Chicago  travel  which  the   New  York   Central  secures  in 
spite  of  being  the  longest  of  three  prominent  lines  (970  miles- 
against  961   by  the  Erie  and  912  by  the  Pennsylvania),  and  in 
spite  of  taking  passengers  150  miles  north  before  they  begin  to 
go  toward  their  destination  at  all,  is  sufficient  proof  that,  if  a 
line   be   equally    comfortable    and    well    managed,   and    makes 
equally  good  through  time  (as  all  lines  do,  for  the  most  part, 
by  general  agreement,  which  ticket  through  at  the  same  price 
and  as  any  line  can  successfully  insist  on  doing  when  its  length 
is  not  in  excess  over  10  or  15  per  cent),  it  will  not  suffer  to  any 
material  extent  from  this  cause  alone.     That  the  New  York  Cen- 
tral is  no  very  great  sufferer  hardly  needs  further  demonstration 
than  may  be  found  in  various  tables  by  referring  to  the  Index. 

241.  The  difficulty  is  (par.  51)  that  the  lines  least  favored  as  to 
distance  are  generally  less  desirable  in  other  respects.  There 
are  more  connections  to  make,  less  favorable  through-car  arrange- 
ments, a  less  number  of  and  slower  trains,  etc.,  etc.  At  the  very 
worst,  moreover,  this  objection  only  applies  to  a  very  small  por- 
tion, and  that  the  least  profitable  portion,  of  the  traffic  ot  a  road; 
and  it  does  not  apply  at  all  to  those  small  changes,  of  a  f^w  miles 
more  or  less,  which  the  engineer  is  most  frequently  caUed  upon 
to  consider,  and  to  which  this  chapter  has  mainly  referred- 

242.  The  conclusions  reached  in  this  chapter  have  rarely  been  recog- 
nized in  the  practice  of  engineers,  but  instances  are  not  wanting  where 
they  have  been  clear  enough  to  operating  officers^  As  one  '"st^r,  J 
the  latter,  on  the  "Pan  Handle"  road  (Pittsburg, C.nc.nnat.  &St_Lou>s^ 
a  tunnel  near  Steubenville.  O..  saving  two  miles  of  distance  and  much 
curvature,  but  costing  $300,c»o.  was  avoided  ^y^  temporary  line.  When 
at  last  means  became  sufficient  to  construct  it.  the  general  manager 


the  Ime  objected  to  its  construction  on  the  ground  that,  even  though  the 
greater  part  of  their  traffic  was  local  to  the  vast  Pennsylvania  system  the 
loss  from  revenue  on  the  two  miles  saved  would  far  more  than  counter- 
balance the  saving  in  operating  expenses ;  and  proved  it  so  conclusively 
that  the  construction  was  for  some  years  postponed.  Subsequently,  on 
account  of  the  exceptionally  commanding  position  of  the  Pennsylvania 
roads.  It  was  believed  that  the  old  distance  could  be  considered  as  con- 
structive  y  stUl  existing  so  that  this  loss  would  not  arise,  and  the  tunnel 
was  built.  Whether  or  not  this  expectation  has  been  maintained  the 
writer  cannot  state,  nor  does  it  affe«  the  force  of  the  example. 

16 


CHAP.   VIII.— CURVATURE, 


243 


■I 


CHAPTER  VIII. 


CURVATURE. 

243t   It  is  the 

peculiarity  of  cur- 
vature that  all  its 
disadvantages  lie 
upon  the  surface, 
visible  to  every 
eye  and  compre- 
hensible by  every 
mind.  A  heavy 
grade  is  very  un- 
obtrusive. The 
most  skilful  and 
observant  eye  can- 
not detect  differ- 

^  Fig.  T4.*— Illustrating  THAT  ECONO-  en ces     of     grade 

MY    OF    CONSTRUCTION.   AVOIDANCB  ^j^.^^  dCCrCaSe  by 
OF  CURVATURE  AND  THE   SKCURING 

OF  WAY   TRAFFIC  ARE  NOT  NECHSSA-  a       lafgC        perCeHt" 

RILY       IN      ANTAGONISM      TO      EACH  ^  ^J^^     operating 

OTHER.  ^.  .        .  ,. 

value  of  the  line. 
But  curves  attract  instant  attention,  and  their  disadvantages  ap- 
peal even  more  strongly  to  the  imagination  of  the  inexpert  than 
to  the  instructed  judgment  of  the  engineer.     A  visible  defect  or 

*  This  illustration  the  writer  borrows  from  the  heading:  to  a  chapter  on  "  Railway 
ConstTuc  ion"  oai  English  engineering  work.  Whether  or  not  it  is  a  mere  fancy  sketch 
heJanno  say  ;  but  it  at  least  has  no  little  verisimilitude  to  not  a  few  actual  works  The 
I^f,fet;nn  natiirallv  arise^  what  the  curve  in  the  foregrround  is  for,  especially  if  the  steepie 
?n  the  middk  d&e  is  a  hint  of  a  town,  or,  if  a  curve  was  deemed  necessary,  why  it 
was  not  mlde  a  mUe  longer  There  may  likewise  be  found  in  the  picture  a  hint  as  to 
Jit^v?L7^o  which  a  larger  expenditure  for  construction  necessarily  implies  a  better  line. 
'Ae  f Xr  moratw^^^^^^^^^  is  calculated  to  teach  may  be  left  to  the  ingenuity  of 

the  reader. 


danger  is  always  more  keenly  appreciated  and  dreaded  than  one 
which  it  requires  special  training  to  detect;  and  since  there  is 
always  a  natural  tendency  to  correct  the  faults  which  everv  one 
sees  and  to  forget  the  faults  which  no  one  thinks  of,  it  is  evi- 
dent  that  this  simple  fact  must  always  have  a  powerful  if  unde- 
tected  influence  while  human  nature  remains  what  it  is. 

244.  And  when  we  come  to  consider  what  are  the  more  solid 
objections  to  curvature,  we  find  at  once  that  a  formidable  and 
undeniably  true  list  of  objections  to  it  may  be  made,  consisting 
of  many  counts  ;  as  thus  : 

1.  It  causes  a  considerable  loss  of  pou>er  and  considerably  more 
wear  and  tear  of  rolling-stock  and  road-bed,  thus  increasing 
expenses. 

2.  It  does  or  may  limit  the  length  of  trains,  and  thus  still  more 
increase  expenses. 

3.  It  causes  a  considerable  expense  for  extra  watchfulness  and  track- 
walking,  and  thus  indirectly  still  more  increases  expenses. 

These  three  are  what  may  be  called  the  definite  and  positive 
objections  to  curvature.  We  can  estimate  them  with  some  de- 
gree  of  certainty  and  exactness.  But  there  are  still  others  which 
are  essentially  indeterminate,  and  which  for  that  very  reason  if 
behooves  us  to  examine  into  the  more  closely,  lest  the  haze  of 
doubt  which  unavoidably  surrounds  them  should  on  the  one 
hand  unduly  obscure  them,  or,  on  the  other,  have  a  mirage-like 
effect,  magnifying  them  into  undue  proportions.  Among  these 
causes  are  : 

4.  The  danger  of  derailment  is  increased,  and  the  consequences 
of  such  derailment  when  it  occurs  are  more  likely  to  be  seri- 
ous. 

5.  The  danger  of  collision  is  increased  by  the  obstruction  of  the 
view. 

6.  There  is  more  difficulty  in  making  time,  and  thus  passenger 
travel  is  likely  to  be  affected. 

7.  //  injuriously  affects  the  smooth  riding  of  cars,  and  thus  deters 
travel. 

8.  //  impresses  the  imagination  of  travellers  with  a  feeling  of  danger 


244 


CHAP.   VIII.— CURVATURE. 


« 


% 
I 

I 


even  if  none  exists,  and  thus  in  a  third  way  affects  travel  unfavor- 

ably;  and,  finally, 

9.  //  is  more  or  less  an  obstacle  to  the  use  of  the  heaviest  atid  most 

poiverful  types  of  engines. 

This  is  a  formidable  indictment,  indeed,  and  when  it  is  ex- 
tended from  curvature  in  the  abstract  to  sharp  curvature  as 
against  easy  curvature  it  becomes  still  more  so  ;  for  there  is 
then  more  wear  and  tear,  more  danger  of  limiting  trains  and 
more  injurious  effect  upon  the  safety  and  speed  of  trains,  the 
comfort  of  travellers  and  the  reputation  of  the  line. 

245.  It  is  therefore  not  unnatural  that  a  very  general  course 
of  reasoning  on  the  question  should  be  :  "  Each  one  of  these  ob- 
jections to  curvature  amounts  to  something  ;  plainly,  therefore, 
in  the  aggregate  they  must  amount  to  a  great  deal,  although 
no  one  can  ever  determine  exactly  how  much.  If  the  curvature 
be  sharp  they  will  be  several  times  more  serious,  and  in  fact  will 
then  become  entirely  inadmissible  for  such  a  line  as  ours..'" 
Thence  may  follow,  perhaps  too  quickly,  a  conclusion  in  the  form 
of  an  order  to  the  engineers  who  are  to  examine  the  country,  to 
the  effect  that  "the  minimum  radius  of  curvature  permitted  on 
this  line  will  be,"  etc. — an  order  from  which  thereafter  there  will 

be  no  retreat. 

246.  Notwithstanding  this  plausible  reasoning  and  formidable 
indictment,  it  may  be  said  at  once  that  investigation  seems  to 
indicate  that  the  prevailing  error  in  respect  to  curvature  among 
engineers  is  too  great  dislike  of  curvature,  and  especially  of 
sharp  curvature,  and  too  great  readiness  to  spend  money  to  avoid 
it  although  a  few  go  to  great  extremes  in  the  other  direction. 
This  conclusion  seems  to  necessarily  result  from  analysis  in 
detail  of  the  weight  to  which  each  of  the  above  objections  is 
entitled;  but  without  presupposing  this,  and  abandoning  all 
prepossessions  in  either  direction,  we  will  consider  each  objection 
to  curvature  as  impartially  as  possible,  beginning  with  what  may 
be  called  the  indeterminate  or  imaginative  (but  not  therefore 
imaginary)  objections,  4  to  9,  which  cannot  be  reduced  to  avala- 
ation  in  dollars  and  cents. 


CHAP.    VIII.-CUR  VA  TURE^A CCIDENTS  FROM.  245 


THE    DANGER    OF    ACCIDENT    FROM    CURVATURE. 

247.  Railway  accidents  come  from  a  great  variety  of  causes 
of  which  curvature  is  one.  How  great  a  cause  it  may  be  is  made 
difficult  to  determine  by  the  fact  that  accidents  are  rarely  re- 
ported as  directly  chargeable  to  curvature,  its  effect  bein<r  rather 
to  aggravate  them,  or  to  prevent  timely  discoverv  that  \here  is 
danger  of  accidents  from  other  causes,  than  to  cause  them  itself 

Nevertheless  we  can  determine  certain  maximum  and  mini- 
mum  limits  for  its  possible  effect  as  a  contributing  or  agoravat- 
ing  cause  of  accidents.  The  total  number  of  accidents  to  trains 
per  year,  of  sufficient  seriousness  to  get  into  the  newspapers  as 
shown  by  the  best  available  statistics  (which  are  very  imperfect) 
IS  given  in  Table  99  for  some  thirteen  years  past,  with  some  fur- 
ther details  as  to  accidents  in  Table  100;  and  by  comparison  of 
these  statistics  for  the  eight  years  ending  with  1880,  accidents 
appear  to  have  occurred  very  nearly  at  the  following  rate,  for 
the  railway  system  existing  in  1880: 

Collisions, 400,  causing  120  deaths  and  430  injuries. 

Derailments,  ....  800         «         150      "  "     r.Q 

Other  train  accidents,     80         "  30      "  «      40 


1,280 


300 


1,000 


Of  the  collisions,  about  5  per  cent  are  crossing  collisions,  not 
likely  to  be  affected  by  curvature.  It  is  possible  to  conceive, 
however,  that  any  one  of  the  400  collisions  might  be  injuriously 
affected,  if  not  caused,  thereby. 

Of  the  derailments,  about 

25  per  cent  come  from  broken  or  loose  rails 
8        " 

5 
12 

i6 
34 


« 


« 


100  per  cent  in  all. 


cattle  on  track, 
washouts, 

accidental  and  malicious  obstruction, 
misplaced  switches,  and 
other  miscellaneous  causes  not  likely  to 
be  affected  in  any  way  by  curvature. 


i  T 


■<" 


246 


CHAP.   Vin.—CURVATURE^ACCIDENTS  FROM, 


CHAP.   VIIL-CURVATURE-ACCIDENTS  FROM.  247 


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4)      1-1  -<  flj  i? 


O      O      (^      V      o 

3    o  "^    c 


r:     in 


E   ^ 


JJ     PS     rt     <o 


o 
H 


•5  ^  5  rt  ^ 

a;  *.    S    O  .2 
°  -   ^  .2   a 

5   E   rt   g   fe 

S     w     CO     <^    §* 

o   <8  "rt  ^   a, 

J-      C8     ^     *j      to 

a,  ^  2  S   ^  .; 

«     -  a;    ,0    •=    3 
H   8  H   E  .S   3 

fe       3  "S  "S 

J3  O    2    rt 


248 


CHAP.   VIIL—CURVATURE— ACCIDENTS  FROM, 


Table  100. 

Casualties  Caused  by  the  Different  Classes  of  Accidents  for  Seven 

Years. 

Killed. 


In  CoUisioDS. 

In  Derailments. 

In  Other  Ace. 

Toul. 

1885 

158 
172 
227 
177 
209 
156 
94 

141 
192 
229 
200 
190 

143 
97 

8 

25 
17 
3 
15 
16 

4 

307 

IS84 

389 

1883 

473 

i832 

380 

1881 

414 

1880 

315 

1870 

195 

xu /y . 

Average 

170 

170 

13 

353 

Injured. 


1885. 
1884. 
1883. 
1S82. 
1881. 
1880. 
1879. 


Average. 


547 
624 
716 

578 
565 
412 
286 


533 


03 
1.062 

1,145 

975 

995 

714 

389 


20 
74 
49 
35 
37 
46 

34 


1,530 
1,760 
1,910 

1,588 

1.597 

1,172 

709 


892 


42 


1,467 


Of  the  1,217  accidents  reported  in  1885,  193  caused  the  death  of  one  or  more  persons 
each,  while  282  caused  injury  to  persons  but  not  death  ;  a  total  of  475  accidents,  leaving 
742,  or  61  per  cent  of  the  whole  number,  in  which  there  was  no  injury  to  persons  con- 
sidered serious  enough  for  record. 

The  accidents  recorded  in  1886  wer«  about  three  for  every  1,000,000  train  miles,  and 
wereTdivided,  according  to  their  nature  and  the  classes  of  trains,  as  follows  : 


Accidents. 

Collisions. 

Derailments. 

Other, 

Total. 

To  passenger  trains 

To  a  passenger  and  a  freight 

To  freight  trains • 

47 
102 

315 

247 

•    •    •    • 

434 

51 

•   • 

21 

345 
102 
770 

Total  

464 

681 

72 

1,217 

Allowing  two  trains  in  each  collision,  this  shows  accidents  to  a  total  of  1,681  trains, 
of  which  494,  or  29  per  cent,  were  passenger  trains,  and  1,187,  or  71  per  cent,  were  freight 


CHAP.    VIII.-CURVATURE^ACCIDENTS  FROM,  249 


^^^A     f  '^f  ,^"'7  '"'''''''''''^  ^^'^  than  the  true  proportion  of  freight-train  accidents,  if 

Tosf  ofte  or  ve r"        "-''' r '''''' ^  '"^  '  ^"^^"'"  ^  ""'^^  P^P^^'^  «^  ^^^^  ^-Iv  "g 
loss  01  lite  or  very  serious  damage. 

,S^T^^^^^""T'  ""'"SS--'e^'*=°f  *-  "--ported  train  accidents  of  the  six  years 
laao-ibbs  (7,949  in  all)  were  :  ^ 


Winter  Months. 


Spring  Months, 


Dec. 

687 

fan. 

882 

Feb. 

812 

Total 2,381 

Per  cent.  .     30.0 


March,  620 
April,  490 
May,     483 


Summer  Months. 


1,593 
20.0 


June,    438 

July,   556 

Aug.     705 


1,699 
21.3 


Fall  Months. 


Sept. 

Oct. 

Nov. 


770 
789 

717 

2,276 

28.7 


248.  There  were  in  the  United  States  in  the  year  1880  about 
90,000  miles  of  railroad  in  operation,  employing  about  450,000 
men,  and  over  which  some  5,000,000,000  passenger-miles  were 
run  each  year  and  perhaps  2,000,000,000  or  more  employe  or 
free-pass  miles,  counting  both  passenger  and  freight  service  the 
number  of  freight  trains  being  at  least  three  times  greater  than 
passenger  trains.  ^ 

The  number  of  curves  will  average  considerably  over  one 
per  mile,  as- shown  in  the  following  Tables  loi  to  104  (see  es- 
pecia  ly  summary  to  Table  102,  page  263),  or  say  at  least  128,000 
for  the  whole  United  States.  This  is  almost  certainly  no  an 
over-estimate.  ^ 

249.  Performing,  then,  the  simple  arithmetical  operation  of 
dividing  128,000  curves  by  .280  annual  accidents  and  by  the 
given  number  of  deaths  and  injuries,  we  find  that  if  all  train  ac 
cidents  which  are  serious  enough  to  get  into  the  newspapers 
ZZJT^  '^'"'"•geable  to  curvature  and  to  nothing  else  there 
would  be  on  an  average  one  such  accident  per  year  for  every  ,00 
curves,  one  death  for  every  4.7  curves,  and  one  injury  for  every 

wav'T'n  ,         ■"■"•?'  '^'  "'^"'"^  °f  'h^^«  fig"'--^  '"  a   clear 
way    If  all  train  accidents  were  caused  by  curvature  alone,  there 

^^ould  on  any  one  given  curve  be  an  accident  of  some  kind  worth 

P  oye  killed  once  .n   4.7  years,  and  a  passenger  pr  employe  in- 
juied  once  in  128  years.  i     /     m 


■•  i 


250  CHAP.   VI II. —CUR  VA  TURE—A  CCI DENTS  FROM. 


CHAP.    VIII.-CUR  VA  TURE—A CCIDENTS  FROM.  25  F 


250.  Such  an  exaggeration  of  the  effects  of  curvature,  how- 
ever,  is  of  course  wholly  beyond   reason.     It  does    not  appear 
probable  from  the  record  of  Tables  99  and  100  that  more  than 
half  the  individual  accidents  are    of  such  a  nature  as   to  have 
been  at  all  modified  or  affected  by  curvature,  and  of  those  which 
are  likely  to  be  at  times  so  affected— such  as  collisions,  broken 
rails,  cattle   on    track,  washouts,  landslides,  breaking  in  two  of 
trains,  etc.,  etc.— a    large   percentage  are   well  known    to  arise 
from  causes  which  the  alignment  would  not  greatly  affect,  such 
as  frogs,  misplaced  switches,  accidents  to  running  gear,  etc.,  and 
others  are  only  likely  to  be  aggravated  by  curvature.     It  is  ex- 
tremely  doubtful,  therefore,  if  more   than    30  or  40  per  cent  of 
train  accidents  are  in   any  measurable  degree  modified  or  af- 
fected by  curvature  ;  and  in  many  of  these  the  effect  is  so  slight 
or  so  doubtful,  that  if  we  were  to  assume  that  from  15  to  20  per 
cent  of  all  accidents  are  wholly  caused  by  curvature,  it  would 
probably  be  giving  it  its  full  weight.     It  will  be  safer,  however,, 
especially  as  our  record  is  not  entirely  satisfactory,  to  assume  as 
a  mean  of  possible  extremes  that  25  per  cent  of  the  accidents 
are  caused  by  curvature,  and  curvature  alone. 

251.  In  that  case  we  shall  have  on  any  one  particular  curve, 

and  caused  by  that  curve — 

A   train  accident    serious  enough    to  be   mentioned  in   the 

newspapers  once  in  400  years: 

A  passenger  or  employe  killed  once  in  1708  years; 

A  passenger  or  employ^  seriously  injured  once  in  512  years. 

If  we  make,  now,  some  simple  computations  in  compound 
interest  (Table  17,  p.  80)  we  reach  some  rather  surprising  results: 

We  find  that  if  we  were  to  invest  one  dollar  at  4  per  cent 
compound  interest  at  the  time  of  construction  we  should  have 
$6,506,088  to  repair  the  damage  arising  from  the  first  serious 
accident  occurring  on  any  given  curve,  and  caused  by  the  fact 
that  it  was  a  curve  instead  of  a  straight  line  ;  $526,201,500  with 
which  to  heal  the  wounds  of  the  first  man  injured  ;  and  a  sum 
an  innumerable  number  of  million  times  greater  than  the  last 
again  (being  what  it  would  amount  to  at  compound  interest  in 


1 196  years)  as  a   fund  wherewith  to   assuage  the  grief   of  the 
dependent  survivors  of  the  first  man  killed. 

Cliange  these  figures  as  we  will,  and  keep  within  the  bounds 
of  reason,  and  we  shall  yet  find  the  result  substantially  the  same. 
?62.  Nevertheless,  an  accident  of  the  most  terrible  descrip- 
tion  may  happen  within  a  week  on  any  curve,  and  be  directly 
caused    thereby.      On  some  one  of   the    128,000  curves  in  the 
United  States  it  probably  will.     Accidents  of  some  gravity  are 
continually  reported  which  appear  to   have  been  due   to  or  to 
have  been  aggravated  by  curvature,  and  more  than  one  such  per 
day  must  happen  in  the  United  States  by  our  assumptions      It 
IS  also  undeniable  that  all  curves  are  not  by  any  means  equally 
dangerous.      When  very  sharp   and  on  heavy  grades  thev  are 
materially  more  dangerous  than  elsewhere.     But  on  the  whole 
and   within    the  limits  of   ordinary  and  reasonable    practice   it 
would  almost   appear,  as  if,  even    it  the   question  were  simply 
curvature  or  no  curvature,  the  only  proper  conclusion  would  be 
that  the  question  of  safety  was  not  entitled  to  any  weight  what- 
ever in  deciding  on  the  line  to  be  adopted  or  the  expenditure  to- 
be  incurred.     Only  when  all  other  considerations  were  equally 
balanced  should  it  be  made  the  ground  of  a  decision. 

253.  But  the  bald  question,  curvature  or  no  curvature  never 
IS  the  question  before  the  engineer.  The  general  character  of 
the  line  is  irrevocably  fixed  by  the  topographical  conditions. 
He  IS  not  called  upon  to  decide  between  the  crooked  solid  line 
and  the  straight  dotted  line  in  Fig.  15,  but  between  a  little  more 


ii! 


Fig.  15. 

and  a  little  less  curvature  as  indicated  by  the  solid  and   nearly 
parallel  dotted  line.  ^ 

If  we  could  eliminate  all  curvature  from  railways  we  mi<rht 
perhaps  decrease  by  25  or  50  per  cent  the  danger  to  life  and 


252 


CHAP.    VIII.— CURVATURE— ACCIDENTS  FROM. 


CHAP.    VIII.— CURVATURE— ACCIDENTS  FROM. 


■;X 


property.  But  this  is  practically  impossible;  and  as  between 
the  common  case — such  alternate  lines  as  are  shown  in  Fig.  15, 
— let  the  reader  pause  for  a  moment  and  intelligently  consider, 
first,  what  the  probabilities  are  of  an  accident  on  either  line  due 
to  all  its  curvature,  and,  secondly,  what  the  danger  amounts  to 
of  an  accident  on  the  one  line  due  to  the  difference  in  its  curva- 
ture from  the  other?  For  example,  we  have  in  Fig.  16  a  view 
of  one  of  the  famous  accidents  of  1885  (the  Monte  Carlo  dis- 
aster), which  may  be  said  to  have  been  entirely  chargeable  to 
■curvature  in  one  sense,  because  the  crookedness  of  the  line  pre- 
vented the  two  approaching  trains  from  seeing  each  other,  and 
this  on  a  line  where  enormous  sums  were  spent  to  avoid  curva- 
ture or  to  increase  its  radius,  and  on  the  very  top  of  one  of  the 
most  costly  works  for  that  purpose — the  immense  retaining-wall 
shown  in  that  view.  How  much  was  the  danger  of  accident 
diminished  by  these  works  below  what  would  have  existed  had 
the  line  been  more  closely  fitted  to  the  contour  by  throwing  it 
back  on  to  the  solid  in  the  view,  at  the  necessary  cost  of  some- 
what more  and  somewhat  sharper  curvature  ? 

254.  This  question  is  so  important  that  it  seemed  essential 
to  make  the  facts  entirely  clear.  A  natural  and  commendable 
.aversion  to  anything  which  seems  to  imperil  life  and  limb  may 
lead  to  a  dissent  from  the  above  conclusions  on  general  prin- 
ciples, as  somewhere  involving  a  fallacy,  but  that  they  are 
practically  true  seems  to  be  proved  positively  in  another  way — 
by  the  immunity  from  accident  which  many  very  crooked  lines 
enjoy  in  common  with  more  fortunate  rivals,  and  by  the  fact 
that  the  number  of  accidents  is  certainly  no  greater  (in  fact  it 
appears  from  the  last  (1880)  census  to  be  some  18  times  less)  in 
the  States  east  of  Ohio  which  have  two  or  three  curves  to  the 
mile,  than  in  the  States  west  of  Ohio  which  have  a  curve  only 
every  two  or  three  miles,  as  an  average. 

255,  Unfortunately,  from  the  very  fact  that  curvature  plays 
so  small  a  part  as  a  cause  of  accident,  no  general  statistics  can 
be  given  as  to  the  number  of  cases  in  which  it  does  have  an  in- 
Jfluence;  but  a  very  interesting  little  volume  by  Charles  Francis 


254 


CHAP.    VIII,— CURVATURE— ACCIDENTS  FROM. 


Adams,  Jr.,  on  '' Railroad  Accidents"  supplies  this  defect  in  a 
measure.  Mr.  Adams  gives  the  details  of  many  of  the  more 
notable,  or  rather  typical,  accidents  which  have  occurred  in  the 
history  of  railways, — some  42  in  all, — and  apparently  by  mere 
accident  specifies  the  character  of  the  alignment  in  almost  every 
case.     Out  of  these  there  were 

8  accidents  on  curves,  killing  253,  injuring  497;   total,  750 


24 
10 


*'    tangents,  "        604, 
unspecified. 


t( 


H03; 


(i 


1707 


Average  per  accident  on  curves, 
•*  *•  "  "    tangents. 


Deaths. 

Injuries. 

31.6 

62.2 

25.2 

46.0 

This  is  mere  chance  collection,  and  proves  nothing  definite, 
especially  as  a  number  of  bridge  and  other  accidents  are  in- 
<;luded,  with  which  curvature  or  the  lack  of  it  had  nothing  what- 
ever to  do.  It  is  perhaps  noteworthy,  however,  that  the  propor- 
tion of  accidents  occurring  on  curves  (about  one  fourth)  is  hardly 
«o  great  as  might  be  expected  if  it  were  a  pure  matter  of  chance 
whether  accidents  occurred  on  tangents  or  curves.  Several  ter- 
rible collisions  occurred  **  when  rounding  curves:"  but  fog  seems 
to  be  a  still  more  fruitful  cause,  as  at  Revere,  Mass.;  and  not  a 
few  are  due  to  pure  and  utter  carelessness,  as  in  the  frightful 
accident  on  the  Richelieu  River  in  Canada,  one  of  the  most  de- 
structive on  record,  about  one  hundred  having  been  killed  out- 
right and  several  hundred  injured.  In  this  case  the  engineman 
ran  into  an  open  drawbridge  on  a  long  straight  line  (as  seems 
clear  from  the  text)  past  a  danger  signal  in  full  view  1600  feet 
from  the  bridge. 

266.  Still,  we  have  fog  and  carelessness  always  with  us,  of 
course,  whether  on  curves  or  tangents,  and  such  risk  as  there 
may  be  from  curvature  is  in  addition  thereto,  so  that  these 
instances  of  terrible  catastrophes  on  tangents  do  not  even  tend 
to  prove  directly  that  curvature  is  a  trifling  cause  of  accident; 
but  what  they  do  prove  is  that  the  unfamiliar  and  occasional  is 
the  most  fruitful  source  of  accident.     The  drawbridge  signal  in 


CHAP.   VIIL-CUKVATURE-ACCIDENTS  FROM. 


255 

the  last  accident  recorded  was  not  looked  for   because  the  H,-.   ' 
was   rare  y  open-  and  in   n,»   .  .         '  "^'^^"^^  '"e  draw 

greater  feeling  of  danger  andn^o""  "  "   ■"'"'^'"^  ^"^'  "'^ 

springs  fro.  the  exist  fee  of  lrrureT„r"'  '""'°"  "'""^^ 
much  curvature  makes  if  i!    ''""•''"'^«' ^"'1  more  especially  of 

accidents  as  JeU  as  a M  rhreoT'oT- ^^'t^"^'-''  ''»'''"'' 
explained  the  undeniable  safety  whh  wl  '"  ""'  ^^^  ""  ''^ 
numerous  yery  crooked  roads  aTeoperrted''  ^^  ^  """^  °^  ^^"• 

The"\r?seySi:: nSd  Ss  of  t^-  '^l  --~^ 
on  Which  there  is  practically  o  break  of  ::u:err''"^  ^^'"■°^' 
but  trains  rise  into  yiew  on'the  hc^tn  as  ^'se  "  As  ^™''' 
natural  consequence    it  wa,  »t  ^       .  ^^  ^  ^'^"'y 

degree  is  yet   the  cus'toL^^  u""''  ^"'^   P"'''^P^  '"    '««s 

•   j-a  custom  to  operate  the  road  with  almn«f  »„►• 

indifference  to  time-tables  or  train-orders      W  " 

train  "hoye  in  sight"  both  made  for  ^h.  •  ''"  oPPOsing 

pened  to  be  nearest  between  them   and  "TT^  "T'  "''*=''  '"P" 
this  point  was  hannened  Th    !,  ^  "''"'  "^'^  ^'  '°  """ere 

"back  out  T  V  u*^      .   '°  ^^  'I'fferent,  one  or  the  other  would 

i"  of  safety  yt  Tf"u 'or"  ^-^  T'  '''"'  "  '"'"'  '^^  '"/"- 

leelinsf  of  securitvpiiH  hoKif  ^^  i  •^'<*vcijing,  loi   the 

engendered  in"mnl^i!  carelessness  which  would  thus  be 

c\nr^^^   '      .1  UCI1&C  rogs  or  sudden  snow-storms  nr  a 

w  d  'b"e  i::fZT\  '':'■'"- ' "'"'"  °"'--  p-^'"° ' 

Which,    under    cond    ions  "^  "'°"'  °^'^^^'°"'"  --''-' 

would'nothaye  occurred     ^'"""^  S-ter  habitual    yigilance. 

^  s::  /:i:LTtoir  uX  ff-trci^t,:;:- 

.he  ErrRaT  '"'""''"'  ^-^  ^  ^^°^^"  -"  at  Carr's  R  ^^  :• 

<>    a  irtSe  ?:;:T"'  '""T  °"  '  '''''  '""'^  ""  ^'^  ^'C 

this  de  cr  n  "nV   but  ?  """'''  ""■"'^  '"^  '^"°>«   '"'^  -  ''f 

descnption),   but  another  one,  precisely  like  it,  occurred  in 


256 


CHAP,   VIII.— CURVATURE^ACCIDENTS  FROM. 


CHAP.    VIII.-CURVATURE-ACCIDENTS  FROM, 


the  immediate  vicinity,  ten  years  before,  on  a  perfectly  straight 
piece  of  track,  which  is  something  pretty  hard  to  find  in  that 
locality.  These  are  the  two  most  serious  accidents  which  have 
ever  (1882)  occurred  from  this  cause  on  that  section  of  the  road. 
In  the  first  instance,  on  a  curve,  24  were  killed  and  80  injured;  in 
the  second  instance,  on  a  tangent,  only  6  killed  and  50  injured; 
but  the  difference  is  due,  not  to  the  alignment,  but  to  the  differ- 
ence in  the  height  of  the  precipice — 30  feet  in  one  case  and  80 
feet  in  the  other. 

259.  A  very  common  error  with  regard  to  broken-rail  accidents  re- 
quires correction  heg2.  There  is  not  a  particle  of  evidence — or  certainly 
none  of  much  moment  or  weight— tending  to  show  that  curvature  notice- 
ably increases  the  liability  of  breakage  or  even  the  consequences  thereof. 
As  respects  the  former,  it  is  almost  purely  a  matter  of  the  condition 
of  road-bed  and  of  chance  defects.  Thus  the  records  kept  by  the  Rail- 
road Gazette  show  that  such  accidents  are  nearly  nine  times  as  numerous 
in  the  winter  months  as  in  the  summer,  there  having  been  of  noticeable 
accidents  caused  by  broken  rails  during  the  eight  years  1873-80:  In 
January,  February,  and  March,  268 ;  in  July,  August,  and  September,  32. 
The  consequences  of  a  rough  road-bed  or  of  the  temperature  of  the 
metal,  or  both,  being  so  very  noticeable,  it  is  clearly  indicated  that  it  is 

the  hammer-like  effect  of  the  locomotive, 
rather  than  any  direct  pressure,  which 
causes  the  breakage ;  and  this  is  not  in- 
creased by  curvature :  it  is  rather  de- 
..^    creased.     On  a  tangent  a  train  impinges 
—   against  the  rails  with  a  great  deal  of  force 
from  one  side  to  the  other  alternately. 
li  \  On  a  curve  every  truck  in  the  train  tends 

Vyi  \  rather  to  hug  the  outside  rail  with  the 

\  V  front  outer  wheel — in  a  manner  shown  in 

Fig.  t7.  Fig.   1 7,  of  which  we  shall  speak  more 

fully  shortly— both  the  inner  wheels  standing  clear  of  the  rail ;  while  the 
driving  wheel-base  is  preserved  by  the  truck  from  impinging  against 
either  rail  with  anything  like  its  natural  force.  For  these  same  reasons 
a  broken  rail  on  the  inside  of  a  curve  is  noticeably  less  likely  to  cause 
a  derailment  than  if  on  a  tangent;  while  a  broken  rail  on  the  outside, 
although  it  is  of  course  greatly  more  dangerous  than  on  a  tangent,  is 
not  so  much  so  as  might  seem— for  the  reason  that,  even  on  a  tangent. 


/ 


i 


KJ 


4. — : 


257 

some  one  truck  in  the  train  is  likely  to  impinge  at  just  the  ri<.ht  s^^ 

strongly  both  to  the  imagination  and  the  judgment  curvaureUaTe  a 

vnere  is,  tne  more  dan'^'er  thfr**  Jc      tu^. i  •       . 

>i        c  ucujj,er  mere  is.      1  hose  who  mainta  n  that  it  shonlrl 

have  the  best  of  the  argument  so  long  as  it  is  confined  to  generalities 
ihe,r  case  only  becomes  weak  when'  we  consider  its  force  in  detail 

260.  The  truth  is  that  nothing  but  a  standing  miracle  keeps 

e,  her  curvature  or  any  other  of  a  dozen  causes  of  accident  from 

be..,g  a  fruttful  source  of  disaster.     The  marvellous  safety  of 

a.lvvay  travel  ,„  the  face  of  such  numberless  chances  for  dLs- 

kl  a!rf  •  ."T  impressive  triumphs  of  human  care  and 
sk.ll,  and  u  IS  th.s  fact  alone  which  gives  our  argument  any 
force  wuatever.  No  one  could  have  foreseen  it,  and  hardlt  any 
one  can  fully  realize  it;  but  the  fact  being  as  it  is,  true  wiLoI 
requ.res  that  we  should  recognize  its  consequences,  and  no^ 
.nsts  on  trusting  to  the  imagination  for  arguments  n  a  purely 
practical  question.  i^iciy 

safJH""'  ^'^'"'"l  '""  ^^"^  eff-^ctively  expressed  this  marvellous 
safety  ,„  a  puhy  sentence,  by  saying,  that  '•  the  chances  of  acci- 
dent ,n  ra.lroad  travelling  are  so  small  that  thev  are  not  materi- 

o  LeH  ""T  \  ^?  '"'°""'  °^  "■^^'^"'"S  ^^hich  can  be  accom- 
plished w.tlnn  the  hmits  of  a  human  life."  He  proceeds  with 
the  followmg  interesting  comparative  statistics: 

260<,.  "During  the  four  years   1875-8  only  i   passenger  was  killed 

"e™  Te?  d  '°"'  '."  °""  ~""°'  '"  M--'husLs.  and  o^^  .0   ^'^ 
,        •    y",.^"""g  'he  year  ,878  alone,  excluding  all  cases  of  n.ere 
injury,  of  which  no  account  was  made  no  less  thnnC  ^ 
their  death  in  Boston  alone  from  fani;g  d  w  -s  a  rs"n'd  ;Tr:Z" 

^e^  killed  by  bemg  run  over  by  teams,  and  the  pastime  of  coasting  w^ 
carried  on  at  the  cost  of  ,0  lives  more.     During  the  five  vears  "s,!^ 
here  were  more  persons  murdered  in  the  city  of  Lston  alone   hanit:! 
tneir  Ives  as  passengers  through  the  negligence  of  all  the  railroad  co 


m 


^^ 


I 


258      CHAP.   VIII.-^CURVATURE-^''  DEGREE  OF  CURVES," 

porations  in  the  whole  State  of  Massachusetts  during  the  nine  years 
1871-8  which  included  the  Revere  and  Wollaston  disasters,  in  which  50 
people' lost  their  lives.  Neither  are  the  comparative  results  here  stated 
in  any  respect  novel,  or  peculiar  to  Massachusetts  :  years  ago  it  was  offi- 
cially announced  in  France  that  people  were  less  safe  in  their  own  honies 
than  when  travelling  on  railroads ;  and,  in  support  of  this  somewhat 
startling  proposition,  statistics  were  produced  showing  14  cases  of  death 
of  persons  remaining  at  home  and  there  falling  over  carpets,  or  in  the 
case  of  females  having  their  garments  catch  fire,  to  10  deaths  on  the 
rail.     Even  the  game  of  cricket  counted  8  victims  to  the  railways   10. 

260^.  All  these  facts  agree  in  indicating  the  conclusion  that 
although  curvature  is  a  considerable  source  of  danger,  yet  it  is 
even  then  so  little  dangerous  to  life  and  property  tliat  we  are 
not  justified  in  giving  any  financial  weight  whatever  to  tins 
argument  against  it,  unless  under  peculiar  circumstances,  or  as 
a  makeweight  when  all  other  considerations  are  exactly  bal- 
anced The  case  is  entirely  different,  for  reasons  we  cannot  take 
space  to  discuss  at  length,  from  the  defects  in  operating  details 
which  people  rightly  insist  should  be  corrected  even  at  a  large 
immediate  expenditure. 

Before  proceeding  further  wilh  the  discussion  of  the  question  of  curvature 
it  may  be  well  to  explain  just  what  is  meant  by  the  term  •' the  degree  of  a 
curve."  which  we  shall  have  frequent  occasion  to  use.  for  the  benefit  of  foreign 

readers  if  for  no  others.  ,  ,        .1    j 

261.  Meaning  of  the  Term  "  Degree  of  CuRVE."-The  universal  method 
in  America  of  expressing  the  sharpness  of  curvature  is  not  by  giving  the  radius, 
but  by  the  -degree  of  the  curve"  or  number  of  degrees  of  central  angle,  sub- 
tended bv  a  chord  of  100  ft. ;  i.e..  by  the  angular  change  in  direction  of  the  curve 
in  the  distance  subtended  by  a  chord  of  100  ft.  If  the  central  angle  be  i  .  the 
radius  is  readily  computed  as  5729  65  ft-  which  is  the  radius  of  a  one-DEGREE 
CURVE,  taken  in  practical  work  as  5730  ft.  ,      ,         ,      *  .u. 

Except  as  the  length  of  the  arc  bears  a  varying  ratio  to  the  length  of  the 
subtending  chord  in  curves  of  different  radii,  it  is  readily  shown  geomeiru:allv 
that  the  radius  is  inversely  proportional  to  the  degree  of  curvature;  and  this  is 
so  nearly  true  in  fact  u?  to  the  limit  of  an  8"  curve  (within  a  small  fraction  o  a 
foot)  that  it  is  almost  universally  customary  in  the  best  practice  to  record  the 
radius  of  a  i'  curve  as  5730  ft.,  and  to  determine  the  radius  of  curves  of  otne 
••degrees"  by  the  approximate  formula, 

(To  p.  266.) 


CHAP.   VIII.— CURVATURE— AMOUNT  OF. 


259 


Table  101. 

Statistics  of  Grades  and  Curvature  on  the  Railways  op  the  North- 
eastern United  States. 
[Computed  from  the  Census  Statistics  of  1880.    Sec  note.] 
New  England. 


Namb  op  Road. 


Miles 

of 
Road. 


Curvature. 


Curves 
Per 

Mile. 


18  Roads,  A.  to  Conn., 

19  "        Conn. to  Nor. 
^o     "        Nor.  to  Sum. 


Total.  57  roads 


Single  Roads. 

Boston  &  Worcester. 
Boston  &  Albany. . . . , 
B.  &  N.  Y.  Airline.. 
Concord  &  Portsm... 
Central  Vermont 


P.  C 
Curved. 


,027 

750 

982 


1.859 


Totals  and  av. 


44 

203 

51 

40 

120 


457 


1.72 
1.89 
r.67 


1.76 


X.68 

1-55 
Z.62 
1. 41 
1.17 


1.48 


42.0 

33-3 
35-0 


Deg. 
Per 

Mile. 


36.i 


40.5 
56.0 

34-0 

37-2 
37-8 


41.1 


49- 60 
51.5° 
38.7" 


Grades. 


46.6" 


P.  C. 

Level. 


25.0" 
72 '5' 
76.0* 
93.0° 
34.5" 


60. 


0.0 

1-3 
38 


Rise 

Per 

Miie.* 


1-7 


3.8 
0.0 
6.1 
3-8 
0.9 


18.7 
24.6 
19. 5 


Rise 

and 

Fall 

Per 

Mile.* 


Ruling 
Grades. 


20.9 


X0.4 
9-3 

13  5 
19.0 

15-7 


12.2 
15.6 
10.  s 


12.8 


3. J 


13.6 


2.8 
»3-7 
»7.3 
»5.3 

8.4 


II. 5 


30 

80 

60 

80 
42 


New  York. 


Alb.  &  Susq 

Buff.,  N.  Y.  &  Phila. 

N.  Y.&Can 

Hudson  River....... 

N.  Y.  Central 

"    (Syr,  to  Roch). 


Totals  and  av. 


N.  V.  &  Harlem. 
Erie.  E.  Div.... 

Del.  Div.. 

Susq.  "   .. 

W.       "    ... 
Reps.  &  Saratoga. 


#42.5 

liD.5 

112. 9 
143-8 
296.6 
102.6 


2.36 
1. 14 

2-55 
1.68 
0.78 
o.os 


9.8.9 


Roch.  &  St;»te  Line 


atoea 
te  Lii 


Totals  and  av . . . . 

R  ,  W.  &0 

Syr.,  Bingr.  &  N.  Y. 

Syr.,  Gen.  «k  C 

l;ister&  Del 

Utica  &  B.  River.   . 
U.  Itli.  &  Elm 


Totals  and  av. 


127.0 
87  o 

»03  9 
»39-9 
129.2 

79*1 
107.7 


773-8 


1.58 


1.17 
1.67 

3-73 
1.44 

1-25 

1-37 
1.09 


36.2 
24.8 
34-6 
32.3 
19.8 
34  5 


30- 3 


1.67 


148.0 
81.0 
57-8 
73-2 
86  8 
71.0 


5x7-8 


0.63 
1.60 
1.26 
3.00 
1. 14 
1. 51 


X.53 


20.7 

29- 3 
53-8 
29.6 
28.4 
25.5 
255 


54.2' 
28. 6« 

64.7; 
28. 5» 

15.1° 
25.0° 


36. 


30- 9" 
•5' 


46.  ^» 


31-3 


»7-4 
33-8 
24.x 
41.0 
26.6 
"•5 


25.9 


88. 

32.0" 

32.4" 

28  4» 

31.5' 


ai.3 

•   •  •  • 

32.2 

75-8 

34-8 

6  8 


34.1 


4' -4' 


17.0" 
3i.6'» 

27-3* 
80. 5» 

24.0* 

21.7* 


33-7* 


II 

9 

39 

31 

12.8 

25-3 

16.8 


5-9 
3.8 
0.0 
0.0 

X.8 
09 


13.2 
9.0 
7.8 
X.6 
3-8 
90 


78-56 


2.1 


21.0 


29.4 

24.8 

17-5 
13.6 

3»-3 
7.0 


20.6 


3-» 
5-1 
4-5 
*  7 
4.3 
1.6 

5-4 
o  9 

5-7 
8.6 
24.1 
0.8 
3-2 


7-4 


8.4 
II. 8 

4-5 
I 
xo 

7 
9 


39-  43 
24-  34 
2'-  33+ 

40-  56 


7.6 


7.2 


6.8 

6-5 
8.9 

II. 6 

12.3 

II. o 


9-S 


40-  42 
30        + 
15        + 
12-  x8— 
52-  47 
53 
71-  S3 


40-  53 
52 

37-  74 
160-142 
66 
85-127 


♦  The  column     R.se  Per  Mile"  gives  the  average  excess  of  rise  over  the  fall  in  one  mile 
The  next  column  gives  the  feet  of  rise  and  fall.    Thus,  if  a  road  rose  500  it.  and  fell  «oo  in  loci 
miles.  It  would  be  given  above  as  -Rise  Per  Mile,  3.0."  "Rise  and  Fall,  a.o."    The  first 
quantity  is  an  unavoidable  necessity,  due  to  difference  of  level  of  the  termini 


26o 


CHAP.   VIIL— CURVATURE— AMOUNT  OF. 


Table  \Q\,— Continued. 
New  Jersey. 


Namb  or  Road. 


Miles 

of 
Road. 


CURVATURB. 


Morris  &.  Essex... 
Phila.  &  All.  City. 


Toials  and  av. 


Curves 
Per 

Mile. 


83.7 

54-5 
X38.2 


1. 16 
0.43 

0.79 


P.  c. 

Curved, 


34  o 
10. 5 

32.2 


Depr. 
Per 

Miie. 


Gradbs. 


44.4' 
6.3' 


25- 3' 


P.O. 

Level. 


Rise 
Per 

Mile.* 


17.8 

_24_^_ 

21.3 


Rise 

and 
Fall 
Per 

Mile.* 


Ruling 
Grades. 


2.6 
0.0 


1-3 


16.4 
10.7 


>3-5 


50 
52.8 


+ 


Pennsylvania. 


Cumb.  Valley... 
Del.,  Lack.  &  W 
Lehigh  Valley 
Lew.  &  Tyrone 

Montrose 

No.  Cent 


Totals  and  av 


Penna. 


Mid.  Uiv 

W.  Div 
P.  &  N.  Y.  Canal 
Perkiomen 

Phila.  &  Erie 

"     (Summit  Section) 

Pitts.  &  Connell 

Western  Pa 

Wilm.  &  No 
Totals  and  av 


Summary  of  North-Eastern  States. 


No  of 
Roads 

or 
Divs. 


57 
5 
6 

7 
6 

3 

6 

10 


State. 


99 


New  England. 
•t  >• 

New  York 

**        " 

•  ■  •  •  • 

New  Jersey... 
Pennsylvania., 

Totals  and  av 


Curvaturb. 


Miles 

of 
Road. 


1,859.0 

457-0 
918. Q 

773.8 
5»7-8 
1.^8.2 

705.9 
r,o»x.4 


Curves 
Per 

Mile. 


1.76 
1.48 
1.58 
1.67 
1.52 
0.79 
2.67 
2-47 


P.  C. 

Curved, 


5.372- 


.88 


36.8 

41. 1 

30 

31 

25 

22 

37-8 
45-3 


Deg. 

Per 

Mile. 


Grades. 


P.  C. 

Level. 


6» 
.,0 


35-5 


46 

60 

36.0* 

41.4" 

33-7' 

25.3' 

91.4° 

81.4" 


55-9° 


309 
13-6 
34- 1 
21.0 
20.6 

21-3 

U-5 
24.9 


Rise 
Per 

Mile.* 


33.8 


1-7 

3« 
3.1 

9.8 

7.3 

».3 
9.3 

32 


Rise 
and 
Fall 
Per 

Mile.* 


4-7 


30  9 
13.6 

7-4 

8.3 

9-5 

13-5 

12. 3 

13.0 


Compare  Summary  of  Table  102,  with  note. 


CHAP.   VIJI.— CURVATURE—AMOUNT  OF. 


261 


^ntL^rlf ''''^^''^  ^P^'^'  '"  '^''  ^"^  ^^"  ^°"°^^'"^  Tables  102,  103,  104  were  com- 
puted  by  the  writer  from  time  to  time  from  the  statistics  which  were  gathered  for  I  iZl 

IT,^  T  .       ,       '^'"^  excess  of  average  grade  in  the  prairie  States  over  what  elts 
in  the  East  is  clear  enough,  and  an  undoubted  fact. 


Table  io2. 

Statistics  op  Grades  and  Curvature  on  the  Railways  of  the  North 

Central  States. 

[Computed  from  the  Census  Statistics  of  1880.    See  note  to  Table  xoi.] 

Ohio  and  Indiana. 


Nams  of  Road. 


Cin.,  Wab.  &  Mich  ... 
C.,C.,C.&L(N.  End). 

c'       »';    (Ind.End) 

C,  H.  &  Ind 

Cid.  &  Mar 

C,  Mt.  V.  &Del...'. 
C,  Tusc.  V.  &W.... 

Dayton  &  Mich 

Evansv.  &T.  H  .... 

Ft.  W.M.&Cinc. 

Totals  and  av 


Miles 

of 
Road. 


Curvature. 


no 

138 

203 

98 

98 

»43. 

158, 

139.8 

109.0 

104.2 


Curves 

Per 

Mile. 


End) 


Ind..  D.  &S 

J.,  Mad.  &  Ind.(S 

L.  Erie&  W 

L.  S.  &M.  S 

vv    T,"     (Air-Line) 
N.  Y.,  Pa.  &0.. 

v>.  &  Miss  . . . 
P  ,  C.  &  St.  L 
T.  H.  &  S.  E 


0.56 
0.23 
o  36 
0.65 
1.90 
1.29 
2.03 
0.42 
0.60 
0.28 


P.  c. 

Curved 


Degr. 

Per 

Mile. 


t«304-5l     0.83 


152.0 

IIO.O 

353-0 

540-5 
130  8 

387 -9 
103  •  7 
338.0 
192.8 
40.0 


0.32 

0-54 
o.  19 

0.41 

o.io 

0-74 

0-33 


2-3 
8.1 

9.0 
14.3 

34-7 
28.5 

315 
7.0 

151 

5-4 


16. 


7.0 
10.4 

6. 
12. 

4- 
23- 
10. 

21. 
33- 
19- 


.6 
.0 
•9 
•7 
.6 

•7 
•7 
•4 


1.2" 

6.7» 

8.9° 

14.6° 

5.2° 
35.7° 
59  f° 

7.0° 

17.5° 
4-6° 


16. 


5  9" 
9-5° 

7-8- 
1.8° 
21.5° 
5-2» 
28.30 
46.0° 
24.0* 


15.9° 


♦See  note  to  Table  zox. 


P.  C. 
Level. 


27-4 
8.0 

8-3 

13  o 

48.6 

I5-I 
20.5 

I.O 

19.8 
15-3 


17-7 


335 
23-7 
15.4 
18.0 
190 
18.6 
11.7 


16.S 

43-2 


22.2 


Grades. 


Rise 
Per 

Mile.* 


0.7 
0.9 

2-4 
I.I 

32 

1-3 
0.7 

1-3 
0.0 

9-7 


Rise 
and 
Fall 
Per 
Mile.* 


7.8 

5-1 


1.2 


7 
13 
7 
9 
6 

3 
10.3 

6.8 


1-5 
2-3 
05 
0.1 
Z.I 

1.6 

4-4 
0.3 
0.1 
0.6 


7.8 


6.9 
5-4 
7-1 
5-2 

4-2 

11.4 

5-8 

8.8 

10.8 

10  o 


Z.3 


7-5 


Ruling- 
Grades. 


52.8  -i- 

'38-"39" 
65-65 
79-  67 
66-  66 
60-  47 
31-  25 
43-  42 
45-  50 


40- 

57-  37 
52.8 

53-  46- 
21-  27 

53-  60 

53-  57 


52.8 
52.8 


! 


i 


\n 


262 


CHAP.    VIIL—CURVATURE^AMOUNT  OF. 


Table  \02,— Continued. 
Michigan. 


Miles 

of 
Road. 

Curvature, 

Name  of  Road. 

Curves 

Per 

Mile. 

P.  C. 
Curved. 

Deif. 
Per 

Mile. 

Chicago  &G.  Trunk... 

Det.,  G.  H.  &  Mil 

1      1     A  Sat?          

330.5 
189.0 

936.0 

63.1 

103.6 

970.0 

61.1 

0.34 
0.51 
0.62 
2.14 

I.OI 

0  61 
1. 16 

6.7 
18.0 
II. 0 

43-4 
i'-3 
26.8 
24.0 

5  5: 

12.2* 
11.0° 

46. 7» 

8.2° 

i8.8» 

19- 5° 

Marq.,  H.  &  Ont 

Mich.  Air- Line  

Mirh    C           

No.  C.  Mich  

Totals  and  av 

1,253.3 

0.91 

20.2 

17-4' 

P.  c. 
Level. 


23  5 
19.0 
19.9 
25  8 
27.5 

21. 0 
30-3 


23  9 


Am.  Cent 

Belleville  &  Eld. 
C.  &  Alton 


C,  B.  &  Q 

C.  &  E.  Ill  .' 
C,  M.&St. 


Totals  and  av. 


Ch.  &  Spr 

Danv.  &«.  W 

O.  &  Miss 

III.  Central 

"        (N.  End  only) 
♦'         Branches. 


Totals  and  av. 


Burl.,  C.  R.  &N 

Burl.,&S.  W 

"       (Mo.).. 

Cent.  la 

C.  B.  C.&  W 

C,  B.&Q 

C,  M.  &St.  P 

tt  •'      

Dub.  &S.  C  .'.' 

Totals  and  av 


Illinois. 


50.6 

49-7 
243  5 
27  8 
79.8 
38.1 
203.3 

99-7 

107.5 

82.2 


982. 


o  30 

0.98 

0.27 

0.79 

0.40 

1.08 

0.38 

0.78 

039 
0.36 


II. 8 

154 
a. 7 

«5-3 

8.0 

23.0 

10.8 

144 

10.7 

9.0 


4-9" 
20.1° 

05° 

2.0» 

0.9* 
4.3» 
8.7' 

15.6° 
6.2° 

5  4° 


o  57 


III. 5 

100. 1 

228  0 

364.7 

(252-1) 

340.8 

1,1451 

0.30 
0.38 


0.21 

(0.06) 
0.38 


13  1 


5.1 

7-4 

149 

9.0 

(327) 
12.0 


6.9" 


0.32 


9.7 


4-3" 

8.4° 

11.7° 

8.3° 

(0.9°) 


10  o 

7.0 

22.0 

27.8 

6.6 

30.7 
21.3 
19.0 
14.0 
35-3 


19.4 


25.2 
21.8 


12. 1 


o 


9.0" 


42.0 

(45.7) 

30.0 


Grades. 


Rise 
Per 

Mile.* 


29.7 


Iowa. 


252.7 

59-6 

82.7 

189.0 

35-7 
280.3 

3317 
150.6 

142.7 


1,5250 


0.70 
1 .90 
1.70 

o  94 
340 
0.84 
0.51 

1-53 
0.88 


22.6 
36.0 
38.0 
20.2 
38.5 
327 
144 
23  7 
20.1 


17. 5' 
57-3° 
55  •3° 
15.6° 
81.0° 
29.2° 
10. 6° 

36 -S' 
24.8° 


1.36 


27-3 


36. 4« 


Rise 

and 

Fall 

Per 

Mile.* 


0.3 
0.0 
1.9 
0.0 

a-5 

0.0 

4-3 


1-3 


7-2 
7.8 

6.8 
93.0 

7-3 
6.5 
8.1 


9  5 


5-5 
1.8 
0.9 
0.4 
0.2 
5-2 
0.2 

3» 
0.1 

O   2 


5-3 
14.6 

6.3 

2.2 

2 


.8 


4-9 


6.4 


0.5 
2.6 

0.2 
0.9 

(0.5) 
0.4 


0.9 


91 
8.9 
9.1 
5-8 

(49) 
9.6 


8.5 


Ruling 
Grades. 


54-  51 
42        + 
52         + 
200. 

39-  45 

49-  38 
52.8 


37-  52 

100-119 

43-  80 
26-  35 
45-  61 
64-  64 

38-  55 
37-  49 
60-  33 
32-  26 


57- 
58- 


66 
58 


63-  45 
77-  86 


18.0 

2.7 

9.1 

66.0 

13.0 
12.0 

5  6 

12.6 

68  6 

2.3 

17-3 

68.6 

II. 0 

1-4 

136 

76-  73 

10.7 

5-5 

32.0 

175-160 

T3-6 

1.7 

13-6 

70-  70 

22.0 

0.8 

10.8 

58-  74 

12.0 
25.0 

4-2 
3-7 

13.0 
19.4 

6-;-  =;8 
80-  81 

153 

1       3- 

14.9 

CHAP.   VIII.— CURVATURE— A 2MO UN T  OF. 

Table  102. — Continued. 
Wisconsin,  Minnesota,  and  Dakota. 


263 


Miles 

of 
Road. 

c 

urvature. 

Grades. 

Name  of  Road. 

Curves     _    _ 
Per         P.  C 

Mile.    Curved. 

Deg. 
Per 

Mile. 

P.  c. 

Level. 

Rise 
Per 

Mile.* 

Riee 

and 

Fall 

Per 

Mile.* 

Ruling 
Grades. 

C.  M.  &St.  P 

194-4 
196.4 
192.0 
202.1 
215-4 

0.58 
0.58 
0.54 
0.70 

I.OO 

20.0 

151 

12.0 

14.8 

237 

14-9' 
13-3° 

12.8° 

13-4° 
30.2°    1 

36.0 
17.6 
26.0 
23.0 
21.0 

0.1 
0.4 
0.0 

6.5 
0.9 

5-4 

9.0 

10.5 

8.3 
II. 4 

35-  36 
50-  53 
69-  53 
74-  63 
63-  52.8 

t«             ti 

4*             »t 

M                         ii 

it                         tt 

Totals  and  av 

1,000.3 

0.68 

17.1 

16.9° 

24.7 

1.6 

8.9 

Summary  of  the  Western  States. 


No.  of 
Roads 

or 
Divs. 

State. 

Miles 

of 
Road. 

Curvature. 

Grades. 

Curves 
Per 

Mile. 

P.  C. 
Curved- 

Deg. 

Per 

Mile. 

P.  C. 

Level. 

Rise 

Per 

Mile.* 

Rise 
and 
Fall 
Per 

Mile.* 

10 
10 

7 
10 

Ohio  and  Indiana 

Michigan 

1.304  5 
2,348  7 
X.20 . 1 

0.83 
0.70 

16.3 
15.0 
90.2 
13.1 
9-7 
27-3 

16. i» 

15-9° 
i7-4» 

6    Q° 

17.7 
22.2 
23.9 

1.2 
1.2 
1.3 
1.8 
0.9 
3.1 

7.8 

7-5 
9  5 
6.4 

8.5 
14.9 

Illinois 

982.2     0.57 
1,145.1     0.32 
1,525.0     x.36 

5 

7 

4. 
Iowa 

9.0°         29.7 
36.4°    I     15.3 

49 

Totals  and  av 

8,558.8:    0.78 

16  9 

16.9°    i     21.4 

1.6 

9.1 

99 

Ditto,  Eastern  States, 
from  Table  loi.   . 

5.372.0 

1.88 

35-5 

55-9°          22.8 

4-7 

13.0 

«7 

Ditto.  South'n  States, 
from  Table  103 

3»5ii-2 

1. 10 

27.6 

3..5» 

22. 0 

1.9 

12.4 

♦  See  note  to  Table  loi. 


♦  See  note  to  Table  101. 

The  most  important  moral  to  be  drawn  from  comparison  of  this  with  the  preceding: 
table  is  in  the  last  column  of  the  table,  which  it  seemed  impossible  to  average,  viz.,  in 
the  excessive  ruling  gjades  throughout  the  West,  which  are  considerably  heavier  than 
in  the  East,  in  spite  of  the  very  much  easier  alij^nment  and  less  rise  and  fall.  In  lo- 
calities it  was  impossible  or  very  difficult  to  avoid  this,  owing  to  a  succession  of  long  low 
ridges  extending  for  great  distances  in  each  direction;  but  for  the  most  part  it  is  due  to 
bad  judgment  in  location,  in  avoiding  curvature  and  loss  of  distance  at  any  sacrifice  of 
grade,  whereas  the  reverse  should  be  the  rule.     See  Chapter  XX. 


.1'' 


264 


CHAP.   VIII.— CURVATURE— AMOUNT  OF, 


Table  103. 

Statistics  of  Grades  and  Curvature  on  the  Railways  of  the  South- 
ern States  and  Missouri. 

[Computed  from  the  Census  Statistics  of  1880.    See  Note  to  Table  101.] 

Virginia. 


Cin.  So 

Eliz  ,  Lex.  &  B. 
L.&N 


Memph  &  C. 
Mobile  &  O  . 
St.  L.  &S.  E. 


Totals  and  av . 


Miles 

of 
Road. 

Curvature. 

Grade.s. 

Name  of  Road. 

Curves 

Per 

Mile. 

P.  C. 
Curved. 

Dejr. 
Per 

Mile. 

PC. 

Level. 

Rise 
Per 

Mile.* 

Rise 

and 

Fall  Per 

Mile.* 

Ruling 
Grades. 

Atl  .  M.  &  0 

408.6 

419.6 

140.6 

8. .7 

1.6 

2-4 

1.0 

36.3 
47  0 
33-8 
27.0 

57-5° 
62.o"» 

38.0° 

30  0° 

46.9° 

^5.5 

1     13s 

]          2-7 

4-» 
1.2 
2.7 
I.I 

13-9 
135 
12.4 
10.2 

80-70  - 

Ches.  &  0 

Rich.  &  Dan .. 

R.,F.  &  Potomac 

70  ± 
60 
116-55 

Totals  and  av 

1,050.5 

1-7 

36.0 

10.6 

1 

2-3 

12.5 

North  and  South  Carolina  and  Georgia. 


Kentucky  and  Tennessee. 


335-9 
102.0 

"3-5 

71-3 

272.0 

472.0 
135  2 


1,501.9 


92 

Q3 
81 
48 
66 
80 
0.88 


1.07 


35-2 
29.5 
19.4 
14.0 
17.0 

31-3 
20.0 


23  8 


55-4- 
52  9° 
:6.9° 

13-9° 
16.6° 
20.2° 
22.9° 


28.4" 


13-4 
154 
29.0 
22.0 
15.2 
23-5 

12.5 


19.0 


0.6 
2.8 

0.3 
0.8 
0.8 
o  6 
0.2 


0.9 


15-6 
15-3 
II. I 
16.7 

12. Q 
7.2 

17s 


13-8 


Missouri. 


C,  Col.  &  Aug 

Ga.RR.&B 

Macon  &  B 

191. 0 
171. 0 
188.0 

I. OS 
0.8s 
0.33 

40.6 

33.5 
16.0 

36.0° 

31- 3" 
9.60 

9-9 
41.0 

1.8 

5-3 
2.0 

22.9 

10.5 

5-4 

60-67 

39-6 

75 

Totals  and  av 

550.0 

0.78 

30.0 

25. 6» 

254 

3.0 

12.9 

60  - 
60-66 

70-53 
70-70 
52.8 

40-30 

216-90 


Bruns  &  Chill 

Burl.  &S.  W 

CapeG.  &  St.  L 

H.&St.Jo 

79  7 

82.7 

40.0 

306.4 

0.76 
1.70 
0.20 
0.76 

14.7 
38.0 

4-5 
25.0 

22.7" 

55-3" 
4.6«» 

17. 8»   i 

t 

46.0 
12.0 
51.6 
30.0 

1-3 
2.3 
0.0 

1-7 

5.6 
17-3 

1-7 
16.9 

52.8 
68.6 
i6-ti 
80-80 

Totals  and  av 

408.8 

0.85 

20.5 

,5...  i 

3a-4 

1-3 

10.4 

. 

CHAP.   VIII— CURVATURE— AMOUNT  OF. 


26s 


Table  \^^,-^Coniinued. 
Summary  of  Southern  States. 


No.  of 
Roads 

or 
Divs. 


Statb. 


Miles 

of 
Road. 


Curvature. 


4 
3 
6 

4 


^7 


Virginia 

.V.  and  S.  C.  and  Ga 

Ky.  and  Tenn 

Missouri 


1,050.5 
550  o 

1,501.9 
408  8 


Curves 

Per 

Mile. 


3,5".2 


1.70 
0.78 
1 .07 
0.85 


no 


P. 

Cur 

C. 

kred 

36 

0 

30 

0 

23 

8 

20 

s 

Deg. 

Per 

Mile. 


Grades. 


46  90 
25. 6» 
28  4» 
25.  i» 


27.6 


31-5 


o    I 


P.  C. 
Level. 


Rise 
Per 

Mile.* 


Rise 

and 

Fail  Per 

Mile.* 


10.6 

254 
19.0 

32.4 


22.0 


2.3 
30 
0.9 

1-3 


1.9 


"5 
12.9 

13.8 
10.4 


12.4 


♦  See  Note  to  Table  loi  and  Summary  to  Table  102. 

In  Holland,  which  has  the  levellest  railways  in  Europe,  62  per  cent  is  level,  and  only 
27  miles  out  of  945  on  grades  between  0.5  and  1.5  per  cent. 

In  Germany  25  per  cent  of  the  mileage  is  between  0.5  and  1.5  per  cent,  and  a  Utile 
over  25  per  cent  curved.  ,  «^u  a  uiuc 

In  Norway  a  little  more  than  50  per  cent  is  curved,  and  37^  per  cent  has  grades  be- 
tween  0.5  and  1.5  per  cent. 


Table  104. 

Curvature  Per  Mile  on  Various  Railxvays  in  the  Rocky  Mountain 
Region  which  have  a  Great  Amount  of  Curvature. 


[Computed  from  Census  Statistics  of  1880.] 


Cent.  Pac ^ 

(from  San  Francisco 
west.) 


Average. 


Colo.  Cent     

Virg.  &  Truckee 

Utah&  No 

Union  Pac 

"       "    West  End 

Texas  Cent... 

So.  Pacific 


266  CH.  VIIL— CURVATURE— MEANING  OF  DEGREE  OF  CURVE. 


More  commonly  yet,  the  radius  is  taken  direct  from  a  table,  but  nothing  is 
ever  done  with  it  in  practical  field-work,  and  it  is  only  of  importance  for 
recording  on  maps  or  for  use  in  solving  problems. 

262i  Among  English  engineers  curves  are  usually  defined  as  of  so  many 

5729.65 
chains  (66  ft.)  radius.     The  radius  of  a  1°  curve  in  chains  is  — ^r-  —  86.813 

chains,  so  that  the  one  method  of  designation  may  be  converted  into  the  other 
by  the  formulae, 

86.813         _.      ^  86813 


R  in  chains  = 


— --,    and    D  =  -rr-. — r-^— . 
D  R  m  chams 


263.  Continental  engineers  designate  curves  by  the  radius  in  metres.     The 

radius  in  metres  of  a  i"  curve  being  -     ^'   ^  =  1746.4  metres,  we  have,  forcon- 

3.2804 

verting  the  one  method  of  designation  into  the  other,  the  similar  formulae, 

1746.4         ^      ^  1746.4 


R  in  metres  = 


V 


and    Z>  = 


R  in  metres 


264.  American  engineers,  and  those  adopting  American  practice,  when 
working  with  the  metric  system,  use,  as  the  unit  chord,  a  chain  of  20  metres 
(65.61  ft.)  divided  into  100  links  of  2  decimetres  (.656  ft.)  each.  The  radius  of 
a  curve  having  1°  of  central  angle  for  a  chord  of  100  of  any  unit  is  5730  (5729.65) 
of  that  unit,  so  that  the  radius  in  metres  of  a  1°  metric  curve  is  5729  65  X  0.2  = 
1145.93  (1146)  metres,  or  one  fifth  as  many  metres  as  there  are  feet  in  the  radius 
of  a  1°  foot  curve— as  is  natural  from  the  fact  that  there  are  only  one  fifth  as 
many  units  in  the  chord. 

265.  In  stationing  under  the  metric  system,  however,  the  best  practice  is  to 
use  lo-metre  stations,  setting  stakes  at  every  other  station  only  (or  i  chain 
apart)  on  tangents  and  easy  curves,  and  at  every  station  (or  half-chain)  on  sharp 
curves.     In  practice  this  produces  little  inconvenience. 


266.  The  radius  in  feet  of  a  i°  metric  curve  is 


65.61 
100 


of  the  radius  of  a  i' 


"  foot"  curve,  or  a  little  (li  per  cent)  less  than  f  (.667)  and  a  little  (4.6  per  cent) 
more  than  f  (62.5),  either  of  which  vulgar  fractions  may  be  used  for  approximate 
inter  conversions. 

267.  Whether  with  English  or  metric  measures,  on  sharper  curves  than  8°  or 
10°,  the  chord  becomes  so  much  shorter  than  the  subtended  arc  that  it  becomes 

inaccurate  to  assume  the  radius  as  ^-.     To  obviate  this  difficulty,  it  is  now 

becoming  usual  in  the  best  practice  to  run  in  curves  sharper  than  8°  with  half 
the  usual  unit  chord,  or  50  ft.,  and  to  run  in  curves  sharper  than  16°  with  one 
FOURTH  the  usual  unit  chord.     It  then  becomes  literally  true,  to  the  nearest  even 


CH.   VIII.— CURVATURE— MEANING  OF  DEGREE  OF  CURVE  2b J 

foot,  that  the  radius  of  all  curves,  of  whatever  degree,  is  given  by  the  formula 

p  -  5730 
R  -   --. 

It  is  expedient  for  practical  reasons  to  set  stakes  thus  frequently  on  sharp- 
curves,  so  that  this  practice  involves  no  inconvenience. 

It  is  rarely  necessary  or  expedient,  in  practical  location,  to  use  other  than 
even  degrees  (or,  at  most,  even  half-degrees)  of  curvature,  except  in  "closing 
curves,"  to  connect  with  other  lines,  and  except  that  certain  degrees  which  con- 
tain an  even  number  of  minutes  (as  50',  1°  40'  (100').  3°  20'  (200)  curves)  are, 
for  practical  convenience  in  the  transit  work,  sometimes  preferred. 

^Table  105  gives  the  radii  in  feel,  chains,  and  metres  of  all  the  curves  below 
30°  which  are  much  used  for  either  metric  or  English  measures.  We  now  re- 
sume  consideration  of  the  various  objections  to  curvature. 

Table  105, 
Radii  of  Curves  of  Various  Degrees  in  Feet,  Chains,  and  Metres, 


Degree 

of 
Curve, 


Curves  run  by  English  Measures. 


o"  30' 

0°   50' 

1° 

1°  40' 

2° 

2°    30' 

3° 

3°   20' 


5" 
6" 

8' 


8 


•a 
o 

U 


c 


Radius  in 
Feet. 


9 
10' 


11,460 
6.876 
5,730 
3.438 
2.865 
2.292 
1,910 

1. 719 
1.433 
1,146 

955 
819 
717 


Radius  in 
Chains. 


Radius  in 
Metres. 


TT° 

t-j 

•0 

c 

u 

0 

12' 

D 

0 

»n 

14° 

U 

16° 

i8» 

1 

20° 

'^J 

v 

• 

c 

k. 

\rt 

24" 

D 

0 

sz 

w 

30' 

U 

637 

573 
521 

478 
409 
358 


173.626 
100,40s 
86.813 
52.089 
43.406 
34-726 
28.938 
26 . 044 
21,704 

17-363 
14.469 

I 2 . 402 

10.852 


318 
286 

239 
191 


9.646 
8,681 
7,892 
7-236 
6,201 
5.426 


3.492  8 
2,095,7 

1,746.4 
1,047.8 

873.2 
698.6 

582,1 

523-9 
436.6 

349-3 
291. 1 

278,1 

218.3 


Curves  Run  by  Metkic  Meas- 
ures (20  M,  Chain). 


Radius  in 
Metres. 


Radius  in 
Feet. 


4.823 
4  340 
3-6x8 
2.894 


194.0 
174.6 

158.8 

145.5 
124.7 
109. 1 


2,291.86 
1. 375-12 

1.145.93 
687.56 

572.96 
458.28 
381.98 
343.78 
286.48 
229. 19 
190.99 
163.70 
143.24 


7.519-2 

4.511.5 
3759.6 
2.255,8 
1.879.8 

1.503. 8 
1.253.2 
1,127.9 

939-9 

751-9 
626.6 

537-1 
470.0 


97.0 

87.3 
72,8 
58.2 


127.33 

114.59 
104.18 

95 .  50 
81.85 
71,62 


417.7 
376.0 

341.8 

313-3 
268.5 
2350 


63,66 

57.30 

47.75 
38.20 


208.9 
188.0 
156.6 
125.3 


268 


CHAP.   VIII.^CURVATURE— MAKING   TIME, 


CHAP.   VIII.— CURVATURE— MAKING   TIME. 


26g> 


mi' 


DIFFICULTY    IN    MAKING    TIME. 

268.  It  is  beyond  dispute  that  the  addition  of  a  sufficiently 
great  amount  of  sufficiently  unfavorable  curvature  will  seriously 
cripple  any  line.  The  curvature  is  objectionable  not  alone  for 
fast  passenger  trains  but  for  freight  trains  also,  for  it  is  fully  as 
difficult  and  as  dangerous  to  run  freight  trains  over  sharp  curves 
at  25  or  30  miles  per  hour  as  passenger  trains  at  60  miles  per 
hour,  owing  to  the  difference  in  their  mechanical  construction, 
and  yet  with  each  alike  such  speeds  are  often  necessary. 

Here,  as  elsewhere,  however,  the  true  question  before  us  is 
not  "  Does  the  difficulty  exist  ?"  but  "  How  great  is  the  difficulty, 
and  what  are  its  limits  ?"  Considering  the  question  in  this  light, 
and  remembering  that  we  are  not  now  speaking  of  nor  consider- 
ing cost,  but  only  physical  possibilities,  experience  seems  to  in- 
dicate that,  up  to  reasonable  amounts  of  8°  or  even  10°  maximum 
curvature  (717  to  573  feet  radius)  this  difficulty  is  not  one  which 
results  in  very  serious  consequences;  for  lines  which  are  little 
less  than  a  succession  of  such  curves  have  as  fast  schedules  and 
make  as  good  time  and  connections  as  more  favored  lines.  On 
curvature  of  shorter  radius  the  centrifugal  force  become  so 
great  that  either  the  speed  must  be  checked,  or  the  additional 
pressure  against  the  outside  rail  becomes  objectionable. 

269.  In  the  days  of  hand-brakes  and  iron  rails  this  necessity 
of  checking  speed  on  sharp  curves  was  (or  would  have  been)  a 
serious  obstacle  to  habitual  fast  running,  but  since  the  introduc- 
tion of  air-brakes  and  steel  rails  a  train  can  be  checked  up 
slightly  with  such  a  very  trifling  loss  of  time — and  if  it  should 
chance  to  be  omitted,  the  consequences  are  so  much  less  likely  to 
be  disastrous — that,  within  the  limits  of  choice  which  are  ordi- 
narily open  to  the  engineer,  this  question  of  making  time  is  much 
less  likely  than  heretofore  to  be  seriously  affected  by  either  the 
amount  or  the  radius  of  curvature.  Since  the  introduction  of 
steel  rails,  the  question  now  chiefly  concerns  passenger  traffic, 
any  curve  of  less  than  20°  laid  with  steel   (and,  in   fact,  with 


properly  designed  engines,  much  sharper  curves)  being  safe  (we 
are  now  considering  nothing  else)  at  ordinary  freight-traia 
speed. 

270.  For  any  ordinary  differences  of  radii  the  reduction  of 
speed  necessary  to  eliminate  the  additional  centrifugal  force 
due  to  a  shorter  radius  is  not  great.  Much  misapprehension  in 
this  respect  exists,  owing  to  forgetfulness  or  ignorance  of  the 
fact  that  centrifugal  force  increases  only  as  the  degree  of  curva- 
ture, but  as  the  square  of  the  speed,  so  that  comparatively  trifling 
decrease  of  speed  will  place  very  material  differences  of  radius 
on  an  equality  in  this  respect.  Thus,  to  obviate  the  effect 
of  sharpening  a  curve  from  a  5°  to  a  io°  we  do  not  need  to 
halve  the  speed,  but  only  to  reduce  it  in  the  proportion  of  i :  i/J, 
so  that  if  a  speed  of  60  miles  per  hour  be  safe  on  a  5°  curve 

a  speed  of  42.43  miles  per  hour  [~j  is  equally  safe  on  a  10° 

curve ;  and  if  we  again  double  the  degree  of  the  curve  to  20% 
we  only  reduce  the  admissible  speed  of  equal  safety  by  1^.43' 
miles  per  hour,  or  to  30  miles  per  hour. 

This  statement  neglects  the  fact  that  the  same  excess  of  centrifugal  force  is 
more  dangerous  on  a  sharp  curve  than  on  an  easy  one;  but  the  difference  in 
that  respect,  while  it  exists,  is  small,  because  the  lateral  flange  pressure  is 
(contrary  to  a  common  misapprehension)  unaffected  by  the  degree  of  curvature. 

271,  The  precise  effect  of  curvature  on  the  admissible  speed  maybe 
determined  as  follows : 

The  centrifugal  force  Cof  any  body  of  weight  IV  moving  at  v  ft. 
per  second  in  a  circle  of  r  ft.  radius  is,  in  the  latitude  of  New  York, 


C  = 


V^v 


^^-^  (log  32.16,  1.50731). 


(i> 


To  determine  the  centrifugal  force  of  a  body  moving  at  V  miles  per 

hour  on  a  D°  curve,  we  have  v  =  ^^  =  1467  T.  and  r  =  1^30^    Sub- 

00  X  00  J} 

stituting  these  values,  we  obtain 


C=  .00001167  (log  5.06722)  V*D  X  W, 


(2> 


{i>- 


.■■;   "l 

.•  > 
> 


C2 


J-^ 


3 


II  ^^' 


270 


Cyy./ii'.   VIIL^CURVATURE— MAKING   TIME, 


Or.  for  the  centrifugal  force  in  lbs.  per  ton,  multiplying  the  second 
member  of  the  above  equation  by  2000,  we  obtain 

C=. 023:48  F'Z>  (log  8.36825) (3) 

From  this  formula  Table  106  is  calculated,  giving  the  centrifugal  force 
in  lbs.  per  ton  of  2000  lbs.  on  any  curve  at  any  speed. 


Table  106. 

Centrifugal  Force  in  Pounds  Per  Ton  of  2000  lbs.  on  Various  Curves 

AT  Various  Speeds. 

[Computed  by  Eq.  (3),  par.  271.] 


Speed 

Miles  Per 

Hour. 

Dbgrbe  op  Curve. 

i«» 

5« 

IO« 

15* 

20» 

10 
20 
30 

40 

2.33 

9-34 
21.01 

37.36 

58.37 
84.05 

114.40 

149-43 
189.12 

233.48 

11.67 

46.70 

105.07 

186.78 

291.85 
420.26 

23.35 

93-39 
210.13 

373-57 

35-02 
140.09 
315.20 

560.35 

875-55 
1.260.79 

1.706.08 

2,241.41 
2,836.78 
3,502.20 

46.70 
186.78 
420.26 

747.14 

50 
60 

5^^3-70 
840.53 

1,144.05 
1.494-27 
1. 891. 19 
2,334.80 

I. 167.40 
1,681.06 

70 
80 

90 
100 

57203 
747.14 

945.59 
1,167.40 

2,288.10 
2.988.54 
3,782.38 

4,669. bo 

The  centrifugal  force  on  any  other  curve  is  directly  as  the  degree  of  curvature. 
The  heavy  division  lines  mark  the  assumed  maximum  limit  of  speed  for  safety;— when 
the  centrifugal  force  is  J4  W. 

272.  For  the  train  to  be  overturned  it  is  essential  that  the  resultant 
of  the  centrifugal  force  and  gravity  shall  fall  without  the  base,  which  is 
upon  the  point  of  occurring,  on  a  level  track,  as  will  be  clear  from  Figs. 
J 8  and  19,  when 

W      cent.  grav.  above  track 
~C   ~  half-gauge 


CHAP.    VIII— CURVATURE— MAKING    TIME. 


2;  I 


The  height  of  the  centre  of  gravity  varies  in  different  cars  and  loco- 
motives  from    as   little   as   4^ 
to  5  ft,,  in   heavily  loaded  flat 
cars,   to  as  much  as  7  ft.  in 
some    types    of     locomotives.     •      i(....^B^*-^     . 
Assuming  it  at  6  ft.,  as  in  Fig.     j«"r":i^^vr->i 
18,  makes  some  allowance  for 
the  beneficial  effect  of  super- 
elevation ;  which  moreover,  in 
the  extreme  case  of  danger  of 
overturning,    does     not    have 
its    full    effect,   because,   long 
before   the   point  where   it   is     ;    Sjl    .°.'    '..fjg.    ; 
imminent,      centrifugal     force     ?    Hf   '"L.^r"! 
will  so  act  upon  the  springs  as     ■^"■—  -^"--' — ""'" 
to  throw  the  centre  of  gravity 


into    nearly    the    position    it  Fig.  18.  Fig.  19. 

would  occupy  if  the  cars  were  a  rigid  body  and  there  were  no  super- 
elevation. 

The  maximum  superelevation  is  about  one  seventh  the  gauge,  or 
about  eight  inches.  This  may  be  considered  as  reducing  the  centr'ifucral 
force  by  one  seventh  of  the  weight  of  the  body,  or  286  lbs.  per  ton,  barring 
the  action  of  the  springs. 

273,  We  have,  then,  assuming  the  centre  of  gravity  to  be  6  ft.  above 
the  rails,  and  half  the  gauge  (between  centres  of  rails)  to  be  2.4  +  ft., 


C 


60 
2.4 


(4) 


whence  C  =  0.4  ^  when  the  train  is  upon  the  point  of  overturning. 
But  [eq.  (2)]  we  have  also 

C  =  . 00001167  V^D  IV,      . 
and  from  eqs.  (2)  and  (4)  we  readily  obtain 


•    • 


(2) 


'=/ 


0.4 


_  185.1 


.00001 1 67Z>        j/^ 


(5) 


this  being  the   equation   of  the  maximum  velocity  in  miles  per  hour 
wiiich  a  train  can  have  without  leaving  the  rails  by  overturning, 

274.  Long  before  this  comes  the  point  of  danger,  and  long  before  that 


u 

1 


272 


C//AP.   VIII.—CURVATURE-^MAKING   TIME. 


again  comes  the  point  of  more  or  less  serious  impacts, oscillation,  and  ap- 
prehension of  danger.  The  minimum  limit  of  objectionable  speed,  below 
which  there  may  be  said  to  be  not  only  no  sensible  danger,  but  no  possibil- 
ity of  annoyance  or  apprehension  of  danger,  does  not  from  its  nature  admit 
of  exact  determination  ;  but  we  shall  obtain  a  result  corresponding  closely 
with  what  have  in  fact  proved  wholly  unobjectionable  velocities  on  various 
curves  if  we  assume  this  minimum  limit  to  be  when  the  action  of  the 
centrifugal  force  upon  the  car-body  does  not  more  than  suffice,  on  easy 
curves  having  the  usual  (but,  as  we  shall  shortly  see,  probably  too  small) 
superelevation  of  about  \  in.  per  degree,  to  throw  it  over  so  as  to 
maintain  it  level  despite  the  superelevation.  The  point  at  which  this 
occurs  may  be  determined  as  follows: 

The  springs  of  an  easy-riding  passenger  car  have  been  compressed 
through  perhaps  6  in.  by  the  weight  of  the  car-body  from  their  unloaded 
dimensions.  An  addition  of  ^V  o^  ^^e  weight  resting  on  a  spring,  con- 
sequently, will  compress  it  through  an  additional  \  in.,  and  an  addition 
of  ^i  of  the  weight  resting  on  it  will  compress  it  through  \  in.  The 
shifting  of  this  much  of  the  weight  to  the  outer  springs  involves  a  cor- 
responding decrease  of  the  compression  in  the  inner  springs ;  so  that,  as- 
suming the  leverage  of  the  centre  of  gravity  of  the  car-body  only  to  be 
equal  to  that  of  the  resisting  moment  of  the  springs,  as  it  approximately 
is  (see  Fig.  18),  a  centrifugal  force  of  ^.  or  say  o.o\W,  will  suffice  to- 
preserve  the  car-body  level.  Substituting  this  coefficient,  0.04  for  04  in 
eq.  (s),  we  obtain 

"   58.536. 


v=^ 


0.04 


.00001167/?  /^~J) 


(6) 


this  being  the  equation  of  the  inferior  limit  of  the  danjjerous  velocities ; 
i.e.,  that  at  which  the  car-body  of  the  easiest-riding  coaches  will  at  the 
most  remain  level,  and  not  have  a  cant  toward  the  outside  of  the  rail,  with 
the  smallest  usual  superelevation. 

275.  As  both  the  possible  compression  of  the  springs  and  the  amount 
of  superelevation  soon  reach  a  maximum  limit,  this  particular  criterion 
for  determining  what  is  the  inferior  limit  of  obnoxious  velocities  docs 
not  hold  precisely  and  theoretically  true  when  extended  to  the  sharper 
curves,  since  it  would  require,  for  instance,  on  a  20*'  curve,  10  in.  of 
superelevation  and  5  in.  compression  of  the  springs,  neither  of  which 
are  admissible  ;  but  it  has,  nevertheless,  the  advantage  before  mentioned 
(par.  274)  of  correspondingtolerably  closely  with  what  have  in  fact  proved 
wholly  unobjectionable  velocities  on  such  curves,  as  it  plainly  should  if  cor- 


CHAP.   VIIT.-CURVATURE-MAKING   TIME.  273 


rect  for  the  lower  curves.  This  appears  in  the  tabulation  of  eqs.  (5)  and 
(6)  given  in  Table  107,  for  curves  of  different  radii  up  to  a  60°  curve  (95 
ft.  radius),  the  latter  being  somewhat  easier  than  the  curve  of  00  feet 
radius  on  the  New  York  elevated  railways,  and  hence  to  be  regarded  as 
about  the  maximum.  The  trains  pass  around  these  curves  at  6  to  10 
miles  per  hour  without  any  disagreeable  centrifugal  force, 

(See  also  par.  S65  et  seq.) 

Table  107. 
Giving  for  Various  Curves  the  Inferior  and  Superior  Limits  of  Speed 

WITHIN    WHICH    THE   CENTRIFUGAL    FORCE   IS    MORE   OR    LeSS    OBJECTION- 
ABLE  AND   DANGEROUS.  J^v,iiuxm 

[Computed  by  Eqs.  (5)  and  (6),  par.  273.] 


Curve. 


Degree. 


Radius. 
Feet. 


4" 
6° 

8° 


10' 


2.865 

1.433 

955 

717 


Maximum  and  Minimum  Limits  of  Speed.    Miles  Per  Hour. 


Minimum.     Having  no 
Disagreeable  Effect. 


573 


12° 
14° 

18" 


20' 


478 
470 

358 

319 


41-39  Miles  per  hour. 

29.27 

23.90 

20.70 


<< 


Maximum.     On  the  Point  of 
Overturning  the  Vehicles. 


18.51  Miles  per  hour. 


286 


22" 

24° 
26°. 

28° 


30' 

40' 
50" 


261 

239 
221 

205 


16.90  Miles  per  hour. 

15.64 

14.63 

13.78 


it 
(( 
it 


130. 89  Miles  per  hour. 

92.55 

75.57 
65.44 


1 1 
tt 
it 


13.09  Miles  per  hour. 


191 


12.48  Miles  per  hour. 

"•95 
II. 61 

11.06 


58.54  Miles  per  hour. 

53.43  Miles  per  hour. 

49-47 

46.28 

43.58 


1 1 
1 1 


<  t 
t  f 


41.39  Miles  per  hour. 


t  < 
tt 
ft 


1 1 
tt 
(I 


10.69  Miles  per  hour. 


60' 


143-3 
1 14. 6 


95.5 


9.25  Miles  per  hour. 
8.28 


39-46  Miles  per  hour. 

37.78 

36.72 

34-98 


tt 


1 1 

n 
t( 


33.80  Miles  per  hour. 


7.56   Miles  per  hour. 


29.27  Miles  per  hour. 
26.18 


«< 


23.90  Miles  per  hour. 


col7„„  ^  ,         '  '""  ~'""""  ^"^  ^'  'f'""  "^  '"""  "-f^'y'  'hose  in  the  last 

TZ^^^  '^T  K  °"  "  "'  P'"^'"^  '°'"'""  *  ♦''°  "'  3.  .6.  Multiplying  or 
^mg  either  column  by  a,  3.  or  any  other  factor  whatever,  wiU  give  a  new  column  o» 
speeds  of  equal  safety.  "*"  *« 

18 


274 


CHAP.   VIIL— CURVATURE— MAKING   TIME. 


276.  These  maximum  and  minimum  limits  correspond  to  a  difference 
in  centrifugal  force  of  i  to  lo;  yet  it  will  be  seen  that  the  resulting  veloci- 
ties differ  only  as  i  to  'fio  or  i  to  3.16,  as  they  should.  It  will  also  be 
seen  that  the  permissible  speed,  by  whatever  standard,  does  not  vary 
directly  as  the  radius  or  inversely  as  the  degree,  as  may  be  over-hastily 
assumed,  but  as  the  square-root  of  the  radius  or  degree.  That  is  to  say, 
on  any  three  curves  having  radii  as 

I,    2.    3. 

the  centrifugal  force  at  any  given  velocity,  it  is  true,  is  as 

3»    2,    i; 

but  the  coefficient  of  safety  against  overturning  or  of  disagreeable  or 
obnoxious  effect  of  any  kind  admissible  under  any  circumstances  on  a 
road  operated  by  steam,  is  as 

4^     i^     V7 
or  as  I73»    1-41.    i-OO- 

277.  We  may  also  note  that  the  maximum  necessary  loss  of  time  from 
a  dead  stop,  in  passenger  service,  under  any  ordinary  circumstances,  is 
only  about  three  minutes,  and  the  loss  of  time  from  slowing  up  for  a  quarter 
of  a  mile  or  so.  under  the  quick  command  of  the  train  given  by  the  air, 
is  veiy  much  less  than  this,  while  the  steel  rail  has  materially  reduced  the 
difficulty  in  and  objection  to  making  up  for  such  delays  by  higher  speed 
at  other  points.     This  is  shown  more  fully  in  Chap.  XIX. 

For  freight  service  alternations  of  speed  by  the  use  of  brakes  are  still 
very  objectionable,  and  perhaps  will  long  continue  to  be  ;  but  ordinary  cur- 
vature does  not  require  this. 

278.  We  may,  therefore,  conclude  (in  part  on  the  author- 
ity of  the  matter  referred  to  above,  which  it  seemed  more  appro- 
priate to  postpone  to  Chap.  XIX.)  that  any  difference  within  the 
power  of  the  engineer  to  effect  is  not  likely  to  materially  affect 
the  ability  to  make  ordinary  express-train  time.  If  it  were  a 
question  between  2°  curves  or  20°,  or  between  no  curvature 
and  a  great  deal,  it  might  well  make  a  serious  difference  ;  but 
under  ordinary  circumstances  the  question  is  rather  between 
say,  6°  and  10°  curves,  or  between,  say,  10  per  cent  more  and  10 


CHAP,    VIIL--CURVATURE-SMOOTH  RIDING  OF  CARS.   275 

per  cent  less  curvature.  In  such  cases,  on  other  than  trunk 
hnes  running  fast  expresses,  the  importance  of  this  particular 
question  is  not  simply  diminished  pro  rata,  but  entirely  van- 
ishes.  "^ 

279.  The  effect  of  curvature  on  the  smooth  riding  of 
CARS  is  a  matter  of  more  serious  moment  in  not  a  few  cases  of 
lines  with  a  large  through-passenger  traffic. 

For  day  travel  it  matters  less;  but  tliere  is   no  doubt    that 
since  the  general  introduction  of  sleeping-cars  not  a  little  travel 
has  been  kept  off  the  New  York,  Lake  Erie  &  Western  Railroad 
for  example,  as  well  as  other  crooked  railways,  for  this  reason 
alone,  when  a  straighter  competing  line  existed.     On  the  other 
hand,  the  number  of  lines  to  which,  on  account  of  the  competi- 
tion  of  other.ft«d  straighter  lines,  this  ^  as  an  important  consid- 
eration  is  not  very  great ;  and  even  when  it  is  or  may  be,  this  also 
is  peculiarly  one  of  those  cases  in  which,  although  a  perfect  cure 
would  be  exceedingly  important  and  valuable,  the  partial  cure 
from  the  slight  modifications  which  are  alone  within  the  power  of 
the  engineer,  without  very  great  expenditure,  will  in  most  cases 
have  httle  value.    It  is  also  to  be  remembered  that  ifa  curve  is  in 
thoroughly  good  shape  the  motion  of  a  car  is,  after  it  has  once 
entered   the  curve,   almost  as  steady  as  on  a  tangent.     If  tlie 
centrifugal  force  and  superelevation  could  be  exactly  balanced 
the  body  of  a  traveller  cither  in    a  sleeping-car  or  day-coach 
would  be  unaffected  by  cither.     Unfortunately  this  is  out  of  the 
question;  but  the  worst  effect  usually  comes  from  entering  and 
leaving  a  curve,  and  this  again  chiefly  results  from  the  fact  that 
as  roads  are  ordinarily  located,  the  line  instantly  changes  from' 
a  tangent  to  a  sliarp  curve.     The  consequence  is,  inevitably   a 
disagreeable  lurch  and   "thud;"   which   would  be   much  worse 
than  it  is  except   that  the   trackman  with   his  bar  corrects  the 
errors  of  the  engineer  with  his  transit  by  "easing  off"  the  curve 
at  the  ends,  extending  it  a  hundred  feet  or  more  on  to  the  tanjrent, 
but  of  course  necessarily  sharpening  the  curve  not  a  little  for  a 
Short  distance  beyond  the  technical  "  P.  C."     The   latter  is  un- 
fortunate;  but  it  is  far  better  than  to  leave  the  curve  as  the  en- 


276   CHAP.   VIII.— CURVATURE— SMOOTH  RIDING  OF  CARS'. 


gineer  stakes  it  out,  and  it  never  is  so  left  on  old  and  good  tracks 
SO  far  as  the  writer  has  observed,  but  invariably  flattened  off  at 
the  ends  by  the  trackmen. 

280.  The  "  easing  off"  should,  it  need  hardly  be  said,  be  rather  done  by 
the  engineer  in  proper  form  in  ihe  first  place,  in  such  manner  as  to  avoid  alsa 
the  lesser  evil  of  a  kind  in  the  body  of  the  curve.  A  simple  and  practical 
method  for  putting  in  such  transition  curves  involving  hardly  any  extra  work 
for  this  purpose  (in  fact  rather  facilitating  the  field  work)  is  given  in  the  fieldr 
book  which  succeeds  this  volume.     See  also  close  of  Chap.  XXX. 

281i  It  may  be  added  that,  as  more  fully  pointed  out  in  the  field-book  re- 
ferred to,  the  use  of  the  parabolas  instead  of  circular  curves  for  railways,  pro- 
posed in  the  early  days  of  railway  construction  and  in  a  few  cases  used,  would 
have  no  important  effect  in  reducing  the  evil  described.  What  is  wanted  is  (i), 
to  ease  off  the  curve  by  a  rapidly  changing  radius  for  a  short  distance  at  the 
ends — a  transition  curve  ;  and  (2),  to  leave  the  great  body  of  the  curve  of 
uniform  radius.     This  the  parabola  does  not  accomplish. 

282.  The  moral  effect  of  excessive  curvature  to  deter: 
TRAVEL — or  rather,  the  moral  effect  of  known  excellence  in  that 
as  in  every  other  detail  to  encourage  travel,  is  in  not  a  few  cases,. 
— as  for  instance  the  Pennsylvania  Railroad — a  consideration  of 
more  importance  than  appears.  Advertising  is  generally  re- 
garded by  all  business  men  as  a  profitable  outlay,  even  when  it 
is  all  outlay.  When  the  advertising  is  of  such  a  nature  as  to  in 
part  pay  for  itself  by  saving  expenses,  even  if  only  to  a  limited 
extent,  it  becomes  of  course  still  more  desirable,  and  in  the  case 
of  railways  has  the  peculiar  advantage  noted  in  Chap.  III.,  that 
any  additional  sales  they  may  thus  make  cost  almost  literally 

nothing. 

In  the  case  of  some  few  roads  which  have  an  immense,  an 
almost  unlimited,  traffic  to  contend  for,  this  consideration  alone 
may  become  of  such  great  importance  as  to  justify  very  heavy 
expenditure.  Thus,  the  policy  which  the  Pennsylvania  Railroad 
has  adopted  of  polishing  and  perfecting  their  line  in  this  and  in 
various  other  almost  fanciful  ways  will  doubtless  prove  a  money- 
making  operation,  and  largely  on  this  account;  for  even  with 
their  great  traffic,  which  will  justify  almost  any  expenditure  to 
effect  a  perceptible  improvement,  it  might  perhaps  be  difficult 


CHAP.    VIII-CURVATURE-SMOOTH  RIDING  OF  CARS.    277 

ZLT'l\f'"  ^^P-^'^—  vvhich  they  have  made  to  take  out 
some  of  their  curvature  by  any  correct  estimate  of  the  direct 
saving  in  operating  expenses.  One  of  the  •'  almost  fanciful  "  ex 
penditures  referred  to  is  to  secure  absolute  perfection  of  appear- 
ance,  as  well  as  real  excellence,  in  the  track  and  riglit  of  Ty  by 
dressing  he  edges  of  the  slopes  of  the  broken  stone  ballast  to 
an  exact  line,  stone  by  stone,  and  by  elaborately  neat  and  taste 

err  dt   IsT"^"         T'''  '"'  ^'^  ^"^   "^^^  particularly  re- 
fened  to   is  the  expenditure  of  occasional   large  sums   in    bold 

lines  to  eliminate  curvature  and  trifling  amounfs  of  distance 
Rai'!!"d  fs"re"of"r"'"' •'"'  Philadelphia  the  line  of  the  Pennsvlvania 

First,  and  chiefly,  the  old  line  is  an  eyamniA  «f  u 
cu.va,ure  may  be  in'noduced  .ere,;  ^^r^:!    n       Z^r  0^:"""  "' 
ence,  „i,„o„,  .^e  .,,Htest  rea,  necessi.y.    'm  very  .any  ;:"„;:;  Z^Z 
was  no  more  expensive  than  the  old,  ^vhile  materially  better 

«ood  purpose  „hi,e  capita,  .as  scarce  andTrraTn^ra^T.^::;:!::;- "I^ 
to  throw  away  when  tWfese  conditions  had  changed  so  as  to  justify  the  t^e  v  1  ^e 

i^:^z:z:::::' '"°"  '--^^  "^  -'  ^  "-=  -^^  '■  --  -"-- 

Thirdly,  there  are  various  points  where  the  new  line,  however  more  nl,« 

would  just.fy  ,„  proportion  to  the  end  attained.    The  Pennsvlvan  Ir  i  -      , 
however,  has  not  an  ordinary  traffic.  ""nsylvanta  R.i.l.oad, 

284.  But,  afterall,  the  lines  are  few  which  have  so  la.o-e  a 
con,pet...ve  traffic  to  lose  ofgain  as  to  make  the  advertfslg  vl.i: 
«f  a  better  hne  a  consideration  of  much  moment,  and  then  it  onlv 

ous  pohcy.  W.th  the  Pennsylvania  it  is  so.  Its  track  is  well 
known  among  well-informed  railroad  men,  the  world  over,  ,0  be 
<i.stt„ctly  supenor  .n  ,ts  finish,  if  not  in  its  real  excellet^ce  to 


t 


P 


I 


278      CHAP.   Vlir.— CURVATURE  AND  HEAVY  ENGINES. 

anything  which  exists  in  any  part  of  tlie  world,  and  the  same 
spirit  pervades  most  of  the  details  of  its  management,  but  only 
when  the  competition  is  very  close,  the  traffic  very  heavy,  and 
the  amount  of  avoidable  sharp  curvature  in  question  very  large, 
could  it  do  so.  In  a  new  and  direct  trunk  line  between  Phila- 
delphia or  Cliicago  and  New  York,  for  example,  it  would  be  a 
very  important  consideration. 

285.  So  far,  the  miscellaneous  and  indeterminate  objections  to 
curvature  discussed  apply  chiefly  to  passenger  travel.  Another 
of  great  importance  applies  only  to  freight  traffic,  viz.:  The  ef- 
fect OF  CURVATURE,  and  especially  sharp  curvature,  as  an  ob- 
stacle TO  THE  USE  OF  HEAVY  AND  POWERFUL  TYPES  OF  LOCO- 
MOTIVES. Without  attempting  to  summarize  now  the  mechanical 
reasons  for  the  conclusion,  which  are  given  later  (Chap.  XI.),  it 
is  a  fcict  that,  in  spite  of  occasional  obstinate  opposition  to  cer- 
tain types  of  engines  being  used  "on  our  curves"  by  men  who 
ought  to  be  good  judges,  there  is  not  the  slighest  evidence  to 
show  that  all  the  types  now  in  use  are  not  mechanically  very 
nearly  on  a  par  as  respects  the  physical  possibility  of  being  ad- 
vantageously operated  over  any  ordinary  and  reasoucible  curva- 
ture. The  wear  and  tear  is  a  little  greater  with  heavy  engines, 
as  we  shall  see;  but  that  is  not  now  the  question  before  us. 

Certainly  up  to  the  limit  of  10°  curves  (573  feet  radius)  this 
objection  is  wholly  unfounded.  The  New  York,  Lake  Erie  & 
Western,  Baltimore  &  Ohio,  and  numerous  other  lines  (see  Table 
116)  have  curves  of  that  radius  exposed  to  tlie  heaviest  and  fast- 
est traffic,  over  which  Consolidation  engines  run  without  the 
slightest  evidence  of  peculiar  difficulty,  danger,  or  wear  and  tear. 
In  the  coal  regions  of  Pennsylvania  14°  and  16°  curves  are  not 
at  all  uncommon  on  branch  lines,  and  for  operating  such  lines 
the  Consolidation  engine  was  first  designed  and  had  its  first 
success. 

286.  The  Consolidation  engine  was  designed  by  Mr.  A.  Mitchell,  then 
Master  Mechanic  of  the  Lehigh  Valley  Railroad,  in  1872.  The  type  was 
so  novel  that  the  Baldwin  Locomotive  Works  were  reluctant  to  under- 
take its  construction.     The  Atchison,  Topeka  &  Santa  Fe  Railroad  in 


CHAP.   VIII.-CURVATURE  AND  HEAVY  ENGINES.      279 


1881  operated  16  curves  with  a  60-ton  Consolidation  locomotive  (see 
Trans.  Am.  Soc.  C  E..  1880.  Paper  No.  CLXXX).  with  the  result  that "  it 
IS  beheved  that  the  Consolidation  engine  travels  the  16°  curves  with  as 
much  ease  as  the  ordinary  'American  '  engine,  and  causes  less  wear  of 
track  and  permanent  way." 

287.  In  the  "  Seventh  Annual  Report  of  the  American  Railway  Master 

Mechanics  Assoc.ation"(i876.  p.  i3)acommitteeoffiveprominentmaster 
mechanics  and  mechanical  engineers  report  as  follows  ; 

^v.i'i't^'^''  reference  to  the  loads  hauled  by  these  heavy  engines  itmavh^ 

288.  In  the  same  report  (p.  .23)  we  have  a  report  of  experiments  at 
Renovo.  on  the  Philadelphia  &  Erie  Railroad,  to  determine  the  relaUve 

Table  108, 

Comparative  Resistance  on  Curves  of  Various  Types  of  Locomotives. 
According  to  experiments  on  the  Philadelphia  &  Erie  Railroad. 
[The  precise  results  of  this  table  cannot  be  accepted  as  accurate,  but  they  are  of  value 
as  indicating  that  there  is  at  least  no  gjeat  difference  against  the  heavier  types.] 


Kind  of  Engine. 


American  ... . 
Ten  wheel. .. 
Consolidation 


Weight. 


Drivers. 


lbs. 
48,000 
52.800 
78,500 


Truck. 


lbs. 
20.500 
22.600 
9.700 


Tender. 


Total, 


1     Diam.  of 

Drivers. 


lbs. 
32,600 
47.700 
47.700 


lbs. 
101,100 
123,100 
135.900 


ins. 
60 

55 
49 


Kind  of  Engine. 


American 

Ten- wheel 

Consolidation. 


Length  of  Wheel-base. 


Rigid. 


ft. 

7 
12 

14 


in. 
6 

5 
6^ 


Total. 


Resistance  on  40  Cukve  at  10  Miles 
Pf.r  Hour. 


Total. 


ft.     in. 

21  lof 
23     8 
21      I 


lbs. 

1.963 
1.750 
1,850 


Lbs.  Per  Ton  Lbs.  P'r  Deg. 


lbs. 

39 

28.4 

20.0 


lbs. 

9-75 

71 

5.0 


?i* 


280      CHAP.   VIII,— CUR  VAT  UJ^E  AND  HEAVY  ENGINES. 


CHAP.   VIII.— MECHANICS  OF  CURVE  RESISTANCE,      28 1 


curve  resistance  of  various  engines,  which  indicate,  so  far  as  they  go, 
that  if  we  may  estimate  relative  adaptability  to  and  danger  on  various 
curves  by  the  relative  resistance,  the  heaviest  class  of  engines  are  at 
least  as  well  adapted  to,  and  as  safe  on,  sharp  curves  as  any  other  class  of 
engines.  Table  108  gives  a  summary  of  these  experiments,  which  were 
made  by  Mr.  Isaac  Dripps,  General  Master  Mechanic  of  the  Philadelphia 
&  Erie  Railroad,  with  a  recording  dynamometer  car  which  he  guarantees 
to  have  been  correct ;  but  notwithstanding  this  guarantee,  it  seems  almost 
certain  that  there  must  have  been  some  defect  of  apparatus  which  par- 
tially vitiates  the  results,  as  they  seem  unduly  favorable  to  the  Consoli- 
dation type.  The  tests  may  be  accepted,  however,  as  indicating  quite 
strongly  that  the  difference  is  not  great  against  them.  The  speed  was 
kept  as  near  10  miles  per  hour  as  possible,  and  the  effect  of  varying 
velocity  estimated  from  the  diagram. 

289.  Mr.  Dripps  says  : 

"  The  locomotives  were  in  good  working  order,  and  were  generally 
taken  for  the  experiments  as  soon  as  detached  from  their  trains,  the  only 
preparation  necessary  being  to  disconnect  the  piston-rods  from  the  cross- 
heads  so  as  not  to  have  the  friction  of  the  piston  in  the  cylinders.  All 
the  other  connections  were  left  precisely  as  if  ruiming  by  steam,  so  tliat 
the  friction  due  to  all  the  working  parts  of  the  locomotive,  except  the  fric- 
tion of  the  piston  within  the  cylinders,  would  be  indicated.  The  loco- 
motives exj)eriniented  with  were  pulled  by  another  locomotive  and  the 
dynamometer  car.  They  would  have  been  pushed  except  for  the  danger 
of  snow  blowing  on  the  track. 

"These  experiments  prove  conclusively,  that  heavy  locomotives  prop- 
erly designed,  with  a  short-wheel  base,  and  with  as  many  bearing  points 
on  the  rails  within  such  base  as  possible, — thus  reducing  the  weight  on 
each  bearing  pcint, — will  pass  around  curves  with  less  friction,  and  be  less 
destructive  to  the  track,  than  the  ordinary  passenger  locomotive  of  much 
less  weight.  Of  course  these  heavy  locomotives  are  best  adapted  for 
slow  speeds,  and  will  show  the  greatest  economy,  and  will  work  to  the 
best  advantage  on  railroads  having  double  track,  heavy  grades,  and  a 
heavy  freight  traffic. 

"  The  effective  power  of  Consolidation  locomotives  is  5oper  cent  more 
than  the  ordinary  six-wheel  connected  freigiit  locomotive  ;  and  from 
actual  service  I  find  that  the  locomotives  of  this  class  work  up  to  their 
power  fully  as  well  as,  in  fact  better  than,  the  six-wheel  connected  locomo- 
tive. Two  locomotives  of  the  Consolidation  class  will  do  the  same  work 
— haul  as  manv  cars — as  three  of  the  six-wheel  connected  class;  and  as 
three  of  the  latter  will  cost  $10,000  more  than  two  of  the  former,  there  is 
thus  a  saving  of  $10,000  in  the  original  outlay,  and  the  saving  of  wages  of 
the  crew  of  one  locomotive  (and  train)  daily;  and  with  a  properly  con- 
structed locomotive  of  the  Consolidation  class  the  running  repairs  for 
tonnage  hauled  will  be  less  than  any  other  class  of  locomotives  now  in 


■use.  On  the  narrow-gauge  Denver  &  Rio  Grande  Railway  which  has 
many  24^^  and  30'' curves,  the  Consolidation  type  is  almost  e^cSsive^v 
usual  f^'or^SSd'.  'h '^'""'  ''"  wheel-base  being  o^Ty  a  little  shorter  thLns 
usual  for  standard  gauge,  or  m  the  proportion  of  about  12  to  15  feet." 

290.  The  preceding  facts,  taken  altogether,  seem  conclusive 
that  objections  to  the  use  of  any  reasonable  amount  or  radius  of 
curvature  whatsoever,  on  the  ground  that  it  will  be  peculiarly 
objectionable  for  the  heavier  types  of  locomotives,  finds  but  lit- 
tle warrant  in  fact.  Indeed,  it  is  noticeable  that  it  is  on  roads  of 
much  and  heavy  curvature  that  the  Consolidation  type  has  been 
most  readily  adopted  and  is  most  in  use. 

291.  We  have  now  discussed  all  the  indeterminate  and  imagin- 
ative (but  not  therefore  imaginary)  objections  to  curvature,  and 
found  that  while  all  of  them  have  a  foundation  in  fact,  and' may 
be  at  times  of  great  importance,  yet  that  on  the  contrary  some 
of  them  are  always,  and  all  of  them  are  sometimes,  of  so  little 
moment  that  for  the  most  part  they  should  have  no  appreciable 
effect   on  the  decision  as   to  what  curvature  to   use.     We  will 
therefore  return  to  the  concrete  and  definite  objections  to  curva- 
ture, viz.,  its  direct  effect  upon  operating  expenses  and  on  length 
of  trains  (the  latter  considered  in  Chaps.  XVIII.  and  XIX.).     In 
order  to  discuss  these  intelligently  we  must   first  consider  the 
abstract  question  of   the  mechanical   laws  of  curve  resistance, 
from  mistaken   notions  as  to  which  much  that  is  mistaken  may 
arise  in  practice. 

THE  MECHANICS  OF  CURVE   RESISTANCE. 

292.  Curve  resistance  has  never  yec  been  exhaustively  investigated, 
and  our  knowledge  is  in  several  respects  deficient.  The  more  essential 
facts  are  now  tolerably  well  determined ;  but  simple  as  the  subject  ap- 
pears, the  mechanics  of  a  rollingtruck  on  a  curve  is— to  determine  it  cor- 
rectly—a very  intricate  problem,  the  solution  of  which  we  must  attempt 
to  make  clear. 

293.  The  forces  arising  from  the  fact  of  curvature  are  of  three 
classes : 

I.  Forces  originating  in  and  confined  in  their  action  to  the  truck  itself, 
causing  the  slippage  of  the  wheel  on  the  rail  which  is  the  ultimate  source 


■I'  ■;. 


jj ;^-; 


282      C//AP.   VIII.— MECHANICS  OF  CURVE  RESISTANCE. 

of  all  curve  resistance.  The  following  two  classes  of  forces  can  only  act. 
by  augmenting  or  diminishing  the  former: 

2.  Centrifugal  and  centripetal  force :  acting  upon  the  car  as  a  whole, 
and  communicated  to  the  truck  through  thecentre-pin  and  side  bearings. 

3.  A  force  due  to  obliquity  of  traction  originating  within  the  train  as  a 
whole  and  communicated  to  the  car-body,  and  thence  to  the  truck. 

We  will  consider  the  nature  and  action  of  these  forces  in  their  order: 
294.  The  position  assumed  by  any  rectangular  flanged  wheel-base  in 

passing  around  a  curve  is  shown  by  ob- 
servation and  experiment  to  be  that 
shown  in  Fig.  20.*  The  front  outer 
wheel  crowds  hard  against  the  rail,  and 
the  rear  axle  then  assumes  a  radial 
position,  neither  wheel  touching  the  rail 
unless  the  gauge  is  so  tight  or  the  wheel- 
\j  I  base  so  long  as  to  bring  the  inner  rail 

\f^  \  up  to  the  flange  rather  than  the  flange 

»  ^  to  the  rail.     Fig.  20  shows  the  position 

^»G'  «*•  of    STABLE    EQUILIBRIUM    tO    which,    if 

any  force  disturb  the  position  of  the  wheels  for  a  moment,  they  promptly 
return.  Therefore,  if  any  force  is  to  permanently  change  their  position 
it  must  be  sufficient  to  slide  them  laterally  on  the  track.  Otherwise  it 
will  not  produce  motion  at  all.  To  slide  the  wheels,  as  to  lift  a  weight, 
the  TijVir  of  an  inch  requires  as  great  a  static  force  in  pounds  as  to  slide 
it  a  foot  or  a  mile.  The  power  consumed  varies  with  the  distance 
moved,  but  the  force  required  to  produce  motion  at  all  does  not  vary. 

This  position  is  likewise  shown  by  experiment  to  be  assumed  just  the 
same,  however  great  or  little  the  superelevation.  This  fact  may  be  ob- 
served by  watching  the  motion  of  cars  around  the  first  sharp  curve  in  any 
yard. 

295i  The  writer  constructed  some  heavy  models  with  both  cylindrical  and 
sharply  coned  wheels,  the  wheel-base  being  capable  of  increase  or  decrease  at  plea- 
sure, and  the  gauge  and  radius  being  likewise  adjustable  by  moving  the  rails.  The 
flanges,  however,  were  made  almost  vertical,  and  with  a  sharp  interior  fillet,  in 
order  to  give  an  exact  point  to  measure  from.     He  found  that  coning  did  not 


CHAP.    VIII.— MECHANICS  OF  CURVE  RESISTANCE.      285^ 


*  The  writer  believes  he  was  the  first  to  observe  this  fact,  and  determine  it 
experimentally.  The  general  fact  that  the  rear  flanges  stand  away  from  both 
rails  he  has  since  found  had  been  previously  observed  by  a  number  of  individ- 
uals, but  even  that  is  not  generally  known  to  this  day. 


Fig. 


21. 


exercise  the  slightest  influence  on   the  position  assumed  by  the  wheel-base, 

which   was   invariably  that  stated,    the   front 

outer  wheel  being  always  in  contact  with  the 

rail  at  b.  Figs.   20  to  23,  and   the  rear  outer 

wheel  standing  away  from  the  rail  by  a  distance 

a,  which,  so  far  as  the  writer  could  determine 

it,  was  always  precisely  equal  to  the  versed  sine 

of  a  chord  of  txvice  the  length  of  the  wheel  base 

(see    Fig.    20),    indicating   that   the  rear  axle 

was   always   radial.       In    only   one   case   did 

this  fail, — in  that  outlined  in  Figs.  21  to  23, 

and  then  only  because  it  was  impossible  for 

the  wheels  to  assume  it.     If  the  gauge  was  so 

tight,  the  wheel-base  so  long,  or  the  curve  so 

sharp  (or  any  two  or  three  of  these  together)  that  the  distance  a  by  which  the 

rear  wheels  naturally  tended  to  stand  away  from  the  outside  rail   was  greater 

than  the  play  of  the  gauge,  then  the  rear  axle  simply  moved  over  until  it  pressed 

against  the  inner  rail,  as  shown  in  Fig.  22. 

296.  With  European  rolling-stock,  having  no  truck,  this  condition  usually 
prevails,     so     that 
their     rails      wear 
quite  differently  on 
curves   from   ours, 
both  inner  and  out- 
er rail  being  ground 
by  the  flange.     On 
this  account  it  is  fre- 
quently  laid  down 
in   European   text- 
books that  the  posi- 
tion outlined  in  Fig.  22  is  the  normal  one   for  any  wheel-base   in  curves,  but 
this  error  arises  from  insufficient  investigation,  and  is  disproved  by  American 
experience  as  well  as  experiment. 

When  the  inner  rail  was  entirely  removed,  so  that  the  inner  wheels  ran.  on 
their  flanges,  the  position  and  path  of  the  wheels  was  in  no  way  affected,  show- 
ing thai  the  inner  rail  performs  no  necessary  function  in  guiding  the  trucks, 
but  merely  supports  the  wheels. 

297.  These  facts  disprove  the  old  hypothesis  that  coning  would  enable 
the  wheels  to  adapt  themselves  to  the  unequal  length  of  inner  and  outer 
rail,  and  maintain  a  radial  position.  They  can  only  do  so  when  the  axles 
individually  are  free  to  assume  a  radial  position.  Moreover,  owing 
partly  to  this  fact,  and  partly  to  the  eflfect  of  the  ordinary  wear  on  tan- 


'/rf-----^. 


K> 


\ 


Fig.  22. 


II 


'•  f'- 


di 


1284     CHAP.   VIII.— MECHANICS  OF  CURVE  RESISTANCE, 

gents,  the  tread  wears  down  near  the  flange  very  rapidly,  and  such  con- 
ing as  there  may  be  soon  disappears.  We  may  therefore  neglect  it  here- 
after, and  assume  the  wheels  to  be  cylindrical.  The  coning  now  put  in 
wheels  is  chiefly  useful  as  a  prospective  provision  for  wear;  and  experi- 
ment shows  that  whether  the  wheels  be  coned  or  not,  the  tendency  of 
any  rectangular  wheel-base  is  to  roll  very  nearly  in  a  straight  line. 

298.  As  we  have  seen  that  the  rear  axle  is  always  radial  to  the  curve, 
the  front  axle.  Figs.  20  to  23,  stands  at  an  angle  A,  Fig.  23,  to  the  rail, 
^qual  to  the  arc  subtended  by  the  length  of  the  wheel-base,  /.     With 

a  5-ft.  wheel-base  (the  usual  leng^th  for 
freight  trucks)  this  angle  would  be.  on  a  i* 
curve,  .05°  or  3',  and  proportionately  on 
other  curves;  with  a  12-ft.  wheel-base  the 
angle  is  0.12°  =  7.2'.  The  distance  by 
which  the  rear  outer  wheel.  Figs.  20  to  23, 
stands  at  a  distance  from  the  outer  rail 
(being  equal  to  the  ver.  sin  of  twice  the 
arc  subtended  by  /)  is  readily  determined 
to  be,  from  what  has  preceded, 

• 
For  a  5-ft.  wheel-base,  .0022  foot  per  degree  of  curvature. 
For  a  12-ft.  wheel-base,  0^0127  foot  per  degree  of  curvature. 

299.  The  gauge  of  a  road  is  the  exact  distance  between  inside  of  rails 
and  the  gauge  of  the  wheels  is  usually  set  so  as  to  allow  a  normal  play  of 
from  f  to  f  inch,  averaging  about  \  inch  or  .04  feet.     The  rear  inner 
wheel,  then,  of  a  5-ft.  wheel-base  will  be  close  against  the  inner  rail  on  a 





Fig.  23. 


.04 


=  17°  curve +,   and   a  12-ft.  wheel-base  on  a 


.04 


^3  curve  -h. 


.0022  .0127 

In  watching  ordinary  cars  pass  around  a  curve,  however,  there  will  be  con- 
siderable fluctuations  in  the  position  of  the  rail  owing  to  irregularities  of 
bot  h  curve  and  truck. 

300.  The  slipping  of  wheel  on  rail  on  a  curve  arises  from  two  causes: 

First.  Longitudinal  slipping,  due  to  the  difference  in  length  of  inner 

and  outer  rail.     This  difference  on  any  given  curve,  or  part  of  a  curve,  is 

equal  to  an  arc  of  a  radius  equal  to  the  gauge,  and  the  same  number  of 

degrees  long;  i.e.,  it  is,  on  any  given  distance  d,       </xC  or,  on  a 


CHAP.   VIII.-MECHANICS  OF  CURVE  RESISTANCE.      285, 


ve 


1°  curve  and  standard  gauge,  <^  x  -^  =  .00082^.    On  any  other  D^  cur 
it  will  be  o.ooo82dD. 

.t  ^^y^^- ^'"■"l 'I'PP'ns.    The  front  axle,  as  we  have  seen,  stands 
at  an  angle  A.  F.g.  23  or  a.  Fig.  24,  to  the  rail.    In  rolling  through  an. 


Fig.  24. 

infinitesimal  distance  d,  therefore,  the  wheel,  since  it  tends  of  itself  to- 
roll  straight  forward  in  the  direction  PA  must  be  slidden  laterally 
through  a  distance  AA'  =  d  sin  a.  ^ 

For  a  5-ft  truck  on  a  i«  curve AA'  =  d  sin  3'  =  .00087^. 

For  a  12-ft.  truck  on  a  1°  curve AA'  =  ./sin  7.2'  =  .0021^. 

This  lateral  slipping  takes  place  only  on  the  front  axle,  since  the  rear 
axle,  as  we  have  seen,  is  and  maintains  itself  radial  to  the  curve 

301.  On  the  front  axle  both  lateral  and  longitudinal  slipping  is  taking- 
place  simultaneously  and  continuously,  and  the  question  then  arises  how 
the  longitudinal  slipping  is  divided-whether  the  outer  wheel  slips  for 
ward  or  the  rear  wheel  backward,  or  the  total  amount  is  divided  between 
the  two.     A  single  experiment  as  to  this  point,  as  careful  as  its  delicate- 
nature  would  permit  with  ordinary  rolling-stock,  was  once  made  on  the 
Horse-shoe  cui-ve"  of  the  Pennsylvania  Railroad,  with  the  conclusion 
that  both  wheels  slipped  ;  but  it  is  impossible  that  this  condition  obtains 
generally  and  continuously,  since  that  wheel  will  slip  which  can  slip 
easiest,  and  the  slightest  variation  in  either  the  load  or  the  coefficient  of 
fnction  will  give  one  wheel  or  the  other  an  advantac^e  in  this  respect 
Either  the  superelevation  or  the  centrifugal  force  is  alone  competent  to 
produce  enough  inequality  of  load  to  effect  this,  for  one  or  the  other 
must  always  be  in  excess,  unless  by  accident.     And  furthermore,  if  one 
wheel  should  begm  to  slip  first,  it  would  certainly  continue  to  do  so  for 
the  same  reason  that  when  a  locomotive  driver  begins  to  slip,  its  ratio  of 


■2S6      CHAF.   VIJI.^MECHANICS  OF  CURVE  RESISTANCE. 


CHAP.    VIIL^MECHAmcS  OF  CURVE  RESISTANCE.      287 


^idhesion  (i.e.,  coefficient  of  friction)  is  heavily  reduced.  It  may  there- 
fore be  considered  as  certain  that  all  longitudinal 
slip  in  every  case,  unless  by  accident,  is  confined 
to  either  the  inner  or  outer  wheel  exclusively ; 
although  it  may  not  be  the  same  wheel  for  any. 
two  successive  axles,  nor  for  any  two  consecutive 
moments. 

302.  Admitting  this  to  be  true,  the  truck  in 
rolling  on  a  curve  is  rotating  about  some  one 
wheel.  A,  as  a  centre,  as  shown  in  Fig.  25  ;  and 
we  have  the  following  condition  of  things  in. 
say,  a  5-foot  truck  rolling  around  a  curve : 
p,^  (i)  One  rear  wheel,  y4,  is  not  slipping  at  all  in 

'Cither  direction. 

(2)  One  rear  wheel  is  slipping  longitudinally  at  the  rate  of  .<xio%2dD 
<in  a  i2-ft.  truck  also,  .ood^idD). 

(3)  One  front  wheel  is  ^pping  laterally  at  the  rate  of  .ooc&'jdD  (I2- 
ft.  truck,  .ooiidD). 

(4)  One  front  wheel  is  slipping  both  laterally  and  longitudinally  ai 
the  same  rates  as  in  the  above,  giving  a  combined  rate  of 


4/.00082'  +  sxx&f  dD. 

Table  109  give  the  summary  of  the  slipping  thus  indicated. 

Table  109. 

Total  Slipping  of  One  Wheel  in  Feet  that  takes  Place-  in  passing 

OVER  100  Ft.  of  Various  Curves. 


• 

5- Ft.  Truck 

;  4  Wheels. 

1 2- Ft. 

Truck;  4  W 

HEELS. 

Formula. 

i» 

5° 

io<» 

20*> 

i» 

5" 

io» 

20» 

I  rear,  wheel 

s  front    "    

.000 
<q83 

.087 

.121 

.000 
.410 

.435 
.605 

0.00 
0.82 

0.87 
1. 21 

0.00 

l.*64 

1-74 
2.42 

.000 
,083 

.210 
.235 

0.00 
0.41 
1.05 
1.13 

0.00 
0.83 
2.10 
a.  36 

0.00 
1.64 
4.20 

4  5» 

44 

V  00832  -f  0087  VA 
or  for  i2-ft.  truck, 
as  shown  in  Fig. 
27. 

Total  slip  of  one 
wheel 

.290 

1.450 

2.90 

5. So 

•517 

a.  59 

5.18 

'O  35 

Average  per  wheel 

•073 

.363 

0.73 

1-45 

1 

0.13 

.J 

0.65 

1.30 

3.60 

303.  The  formula  (4)  requires  explanation :    Since  the  wheel  is  slip- 
ping in  two  directions  at  right  angles  to  each  other,  it  will  at  each  instant 


of  time,  while  advancing  over  an  infinitesimal  distance,  d,  Fi^r  25  slip 
longitudinally  in  the  direction  ^.  and  laterally  in  the  direction/.  The 
true  direction  and  amount  of  slip- 
ping will  therefore  be— neither  a, 
nor/,  nor  both  together — but  along 
the  diagonal  d.  Figs.  26  and  27 
represent  to  scale  the  actual  con- 
ditions. 


B<ooo29 


.      .  ,       ,   „  Fig.  26.-12-FT.  TRUCK.       Fig.  27 —s-Ft.  Truck. 

iniS    IS    merely    following    the     ^^nount  and  constituent  elements  of  the  slip  of 

fundamental  law  of  the  composi-  oa'a^^xoc'tirve.^'^- ''' '°  ^"'""^  ""''"  ^  ^^^^^^""^ 
tion  of  velocities,  which  is  the  same  in  its  nature  as  the  composition  of 
torces.  It  has  been  carelessly  assumed  at  times  that  a  total*  sliding  of 
the  wheels  represented  by  the  sum  of  the  two  sides  a  and  /  rather  than 
by  the  hypothenuse  d,  measures  the  distance  through  which  the  wheel 
slides,  and  the  consequent  loss  of  foot-pounds  of  energy,  but  this  is  palp- 
ably erroneous. 

304.  It  will  be  observed  that  according  to  Table  109  the  wear  due  to 
curvature  on  the  front  wheels  is  more  than  double  (4.20  to  1.64)  that  on 
the  back  axles.     Any  check  upon  this  from  observed  wear  of  car  wheels 
IS  in  the  nature  of  things  impossible  irom  the  fact  that  the  direction  of 
motion  of  the  car  is  reversed  with  every  trip.     With  engine  and  tender 
trucks,  however,  this  is  not  the  case.     Statistics  of  tiiis  kind  likewise  are 
very  difficult  to  obtain  ;  and  the  following  little  table  (Table  no),  embrac- 
ing observations  on  the  Camden  &  Atlantic  Railroad,  is  all  of  the  kind 
which  the  author  has  ever  been  able  to  discover.     This,  however,  appears 
as  far  as  it  goes  to  strikingly  confirm  the  theory  advanced.     It  is  to  be 
observed  that  the  wear  of  tender-truck  wheels  is  1 1.2  per  cent  greater  on 
the  front  than  on  the  back  axle,  and  the  wear  of  the  engine  truck-wheels 
bered^^'  ""^"^  ^'^^'^'''    ^"  ^°^''^^^^"S  these  figures  it  is  to  be  remem- 

1.  The  Camden  &  Atlantic  has  very  little  curvature. 

2.  Curvature  is  only  one  cause  for  rail  wear,  the  others  bein^  use  of 
brakes  and  sand,  original  defects  and  regular  running  wear  on  tangents 
wh.ch  would  be,  if  not  substantially  equal  for  both   axles,  much  more 
nearly  equal  than  that  from  curvature. 

The  average  might  be  and  probably  is  somewhat  affected  bv  a  ten- 
dency-especially  on  a  small  road  where  the  engines  were  well  known-to 
condemn  two  wheels  at  once  which  had  been  running  the  same  time,  al- 
though there  might  really  be  not  a  little  difference  in  their  wear  The 
great  excess  in  the  difference  in  wear  in  the  engine  trucks  is  notable. 


288      CHAP,   VIII.— MECHANICS  OF  CURVE  RESISTANCE. 


Table  110, 

Wear   of   Leading   and   Trailing  Wheels   of   Locomotive  and  Tender 
Trucks  on  the  Camden  &  Atlantic  Railroad. 

[Compiled  from  Report  to  Am.  Ry.  M.  M.  Assoc,  on  Loc.  Wheels  and  Axles  (Rep.  1878,  p.  23), 

by  Rufus  Hill,  M.  M.] 

Engine  Trucks. 


Size. 

No.  of 
Pairs. 

Mileage. 

Relative 

Life  of 

Wheels  on 

Front  Axle. 

Back  Axle 

=  1.0. 

Remarks. 

Lead. 

Trail. 

28  in. 
26  " 

8  each. 
4  i 

28,998 
15.461 

43.024 
27,008 

.674 

•573 

Av.  all  entj.  wheels, 

28.623. 
Av.  all  tender  wheels^ 

26,821. 

Average. 

22,230 

35.016 

.624 

Tender  Trucks. 


30  in. 
28  in. 


10  each. 


27.897 
29,249 

23.419 
20,365 


25,232 


31.997 
32.736 
23,560 

25,346 


28,410 


.87 
.894 

•994 
.803 


,888 


Front  truck. 
Back  truck. 
Front  truck. 
Back  truck. 


The  table  is  stated  to  have  been  made  up  from  records  of  condemned  wheels  only,  so 
it  does  not  give  a  fair  idea  of  the  average  mileage  of  all  wheels. 

305.  It  does  not  follow  that  the  total  slippage,  and  hence  total  curve 
resistance,  of  a  six-wheel  truck  would  follow  exactly  the  same  law  as  that 
of  a  four-wheel  truck  of  the  same  length  of  wheel-base  and  carrying  the 
same  load  ;  but  it  is  useless  to  consider  that  question  for  lack  of  positive 
knowledge  as  to  the  position  naturally  assumed  by  a  six-wheel  truck.  It 
is  probably  the  same  as  if  the  middle  pair  were  omitted,  but  there  is  no 
evidence  of  that  fact. 

306.  Although  we  have  seen  that  coning,  however  much  or  little 
there  may  be,  has  no  influence  whatever  in  practice  upon  the  position 
assumed  by  the  truck,  yet  if  any  coning  exists  it  will  certainly  modify  the 
AMOUNT  of  slipping,  and  hence  the  resistance.  To  consider  how  much 
it  will  or  may  modify  it.  however,  would  lead  us  into  hopeless  and  profit- 
less intricacy,  because  there  must  be  slippage  under  any  circumstances 
with  a  rectangular  wheel-base,  which  will  speedily  wear  away  the  coning^ 
on  the  working  part  of  the  tread. 


CHAP.   Vm.-MECHANICS  OF  CURVE  RESISTANCE.      289 

It  is  probable,  however,  that  the  effect  of  the  coning  while  it  exists  is 
either  „./ or  posuively  injurious,  taking  front  and  reaf  axle  togethTfor 
the  reason  that  the  position  assumed  by  the  wheels  bears  no  rdltion  t 
tha  required  by  the  coning  and.  especially  on  the  front  outer  wheel  s 
hable  to  increase  its  diameter  unduly. 

307.  So  far,  there  is  as  little  reason  to  doubt  our  correctness  as  can 
be  expected  in  any  subject  which  has  not  been  exhaustively  and  thor- 
oughly investigated  experimentally:  and  frictional  slippage  which  hi 
been  estimated  mcludes  all  that  takes  place  between  rail  a^d  wheel  ex- 
cept (,)  that  due  to  flange  friction  and  (2)  the  possible  action  of  other 
forces  communicated  to  the  truck. 

308.  To  determine  the  resistance  arising  from  the  slippage  estimated 
the  very  delicate  question  arises  of  what  is  the  coefficient  of  slidingfric: 
tion  under  such  circumstances.  ^'luing  iric- 

The  primary  fact  to  be  remembered  in  estimating  this  is  that  the  ve 

Snih  ^r:fn"Tr  "'^°"  ^^•=''  "''^^  ■-^^ryL.^^,  as  'shin  mo^ 
fully  in  the  following  Table  ,.,,  computed  directly  from  the  preceding 

Table  m. 
VELoaxv  :«  Feht  Per  Second  with  wh.ch  the  Wheel  su.es  on  xh. 
'^AiL  ON  Various  Curves. 


Velocity  of  Train. 


10  miles  per  hour. 


\ 


30  miles  per  hour.. 


Velocitv  of  Slidinc 

; ;    Feet 

Per  Second. 



5- Foot  Truck. 

12-Foot  Truck. 

1° 

S*' 

lo" 

20° 

i» 

5« 

IO» 

20<» 

.012 
to 

.018 

.06 

to 

.09 

.12 

to 

.18 

.24 

to 

•36 

.012 
to 

•034 

.06 

to 

•17 

.12 
to 

•34 

.24 

to 

.68 

•036 

to 

•054 

.18 

to 

•  27 

.36 

to 

.54 

.72 

to 

1.08 

•  036 

to 

.102 

.18 

to 

•  51 

•36 
to 
1.02 

.72 
to 
2.04 

-ow'^vrcrs'^^-^'ri^sriE^^ 

at  ordi^a^Tn'^  ^rr^lptir:!"  "  "'"""  '^'^"^"^"'"^  ^^"^"^  '"^ 

3.  Its  maximum  at  a  velocitv  d  n_L  ;e  o^.^  .t 
motives  and  perhaps  ,  with  car^h^eutsir^i'^el  *  "''''  "^ 


290     CI/AP.   VIII.—MECHANICS  OF  CURVE  RESISTANCE. 

These  laws  were  most  authoritatively  determined  and  most  com^ 
pletely  illustrated  by  the  famous  brake  experinieiiis  of  Capt.  Douglas 
Galton  and  Mr.  George  Westinghouse,  the  general  results  of  which  are 
embodied   in  Tables  112  and  113.     We  shall  have  occasion  to  refer  to 

Table  112. 

Coefficients  of  Friction  between   Cast  iron  Brake-shoes   and  Steel- 
tired  Wheels. 

[Determined  by  Experiments  of  Capl.  Douglas  Gallon  and  Geo.  Westinghouse,  Jr. 

Trans.  Inst.  M.  E.,  1878.] 


Velocity. 

Coefficients  of  Friction. 

Miles  Per  Hour. 

At  First. 

After  5  Sec. 

After  10  Sec. 

After  15  Sec. 

After  20  Sec. 

o-f-to  I  or  2 
7i 
I3i 
17 

20i 
37 

30i 

34 

37i 

41 

48 

54 

60 

.250 
.242 
.213 
.205 
.182 

.171 

.163 

.153 
.152 
.144 
,132 
,106 
.072 

.133 
.119 
.099 

.083 

.070 

.058 

.110 
.116 
.081 

•    .•••••• 

.069 
•045 

•    •    t 

193 
157 
152 
130 
107 

, 

.099 
.072 

•    • 

•  096 

093 
.080 

.063 

While  these  results  are  unquestionably  more  nearly  correct  than  any  other  existing 
evidence,  there  is  considerable  room  for  doubt  as  to  the  exact  values  given. 

Table  113. 
Coefficients  of  Friction  of  Skidded  Wheels. 

{As  determined  in  the  Galton-Westinghouse  Experiments.    See  Table  iia.] 


Velocity. 
Miles  Per  Hour. 

Coefficient  of  Friction. 

Steel  Tire  on 
Steel  Rail. 

Steel  Tire  on 
Iron  Rail. 

0  + 

7 

13 
27i 
34 
41 
5a 

54 
60 

{ 

.242 
.088 
.072 
.070 
.065 

.057 
.040 
.038 
.027* 

.247 
.095 

.073 
.070 
.060 

♦  mean  01  tnree  tests  only. 


'-^^:l^:^:!!^z!!f5^!^!^!ff^^^^  2^. 


in  lbs.  per  ton,  ^^  "'  ^<'^"""<1  ^'°"S  the  track,  would  be 

2000  X  }  =  500  lbs. 

■oocjj'orrirnc:,  :::^;::r  :'^  -'i  ''-"^^  -  --"-  - 

between  rail  and  wheci  would  br-M""/x°'"  '"'''''  '""'°"  °"'y 

This  is  the  curve  resistance  (except  fr.^      ""'T^'  =  "'^^^  "'• 
<an  be  accounted  for  at  slow  veS//   ,7  '"'*'"  ^°'=ffi<^i<="t)   that 
•effector  shocks  and  irre.u  aSs      F  ,  ^"^  "'"^^ '^'«'°"  ='"<^ '^e 

^umn,arized   above  it  ZZT  u       ""  °^"'='"="  '"'''  °f  '""ion 

flange  friction  w'^ld  decre  1  Ji'h  l^''^''-''  """^  '"^^  ^"^^^^  -^ 

that  ,t  not  only  slides  but  revolves,  but  its  existence  can-' 
tiot  be  conceded. 

It  is  true,  as  claimed,  that  the  actual  contact  is  by  a 

surface  and  not  a  theoretical  point  or  line;  but  although  the 

>vheel.  in  moving   through  an    infinitesimal  distance  ^B    ' 

t'S:  28,  IS  actually  rotated,  yet  as  this  takes  place  simul' 

taneously  with  the  other  sliding  its'  effect  is  simply  to  de-  v,.    « 

crease  the  velocity  on  one  side  of  the  center  of  contact  bv  «  f 
creases  it  on  the  other  side.  ^^  ^'  """"^  ^^  »'  »«' 

311.  Flange  Friction.— We  have  seen  that  :^t  ^a^u  •    * 

3...n,  on  the  su^f^- '^fttir^-  t^e  2::^  i^S^-  -- 
mes      The  force  which  causes  this  rotation-the  only  force  which  e^^ts 

It  necessarily  follows  from  this  fact  that,  assuming;  that  the  coefficient 

till        al^lvTthf  sT'  ''  "'  '^'""'^  "'  '"''"^'  ^''^  P-ssure  f    ac. 
IS  always  the  same  on  curves.     For.  however  easy   the  curve,  a 


292      CHAP.   VIII.— MECHANICS  OF  CURVE  RESISTANCE. 


minute  sliding  motion  is  continuously  taking  place,  caused  by  the  reac- 
tion of  the  flange  ;  and  the  static  force  or  pressure  required  to  slide  one- 
body  on  another  through  an  infinitesimal  distance  is  sufficient,  if  con- 
tinuously applied,  to  slide  it  through  any  distance  whatsoever.  The- 
POWER  CONSUMED  varies  with  the  degree  of  curvature,  because  power  or 
energy  of  any  kind  is  measurable  only  by  a  double  unit,  the  force  applied 
X  the  distance  through  which  it  acts.  The  latter  (the  distance),  we  have 
already  seen,  varies  with  the  degree  of  curvature,  and  hence  the  power 
consumed  does  also  ;  but  the  static  force  applied  does  not  vary  with, 
the  degree  of  curvature. 

This  very  important  distinction  is  one  which  should 
be  clearly  comprehended  and  kept  in  mind.  A  very  mis- 
taken idea  is  too  prevalent  that  the  flange  pressure  as  well 
as  curve  resistance  increases  with  the  degree  of  curva- 
ture. 

An  apparent  contradiction  to  this  statement  is  the: 
well-known  excess  of  flange  wear  on  sharp  curves,  but 
this    is   rather  a    confirmation.      The    greater    distance 
elidden  through  produces  the  greater  wear,  not  greater  pressure. 

312i  The  front  outer  wheel  alone  has  its  flange  normally  in  contact  witb 

the  rail.    The  forces  acting  upon 


<^f^P^J^ni^-MECHAmcs  OF  CURVE  RESISTANCE. 


293 


Fig.  30. 


the  front  outer  wheel  are,  firsts 
the  load,  Z.,  Fig,  29,  resting  upon 
it,  acting  vertically  downward  ; 
secondly,  a  horizontal  pressure 
against  the  rail  sufficient  to  slide 
three  wheels  (see  Fig.  25,  page 
286),  each  loaded  with  L. 

Assuming  a  coefficient  of 
sliding  friction  of  0.25,  this  late- 
ral force  amounts  to  0.75  Z,  and 
the  resultant  in  magnitude  and 
direction  of  these  two  forces  is 
shown  in  Fig.  29. 

313.  The  manner  in  which 
the  various  forces  thus  meas- 
ured  will  act   is   not  doubtful 


in  theory,  and  we  have  their  footprints  on  the  rails  themselves  to  assure 
us  that  theory  and  practice  correspond.  Instead  of  the  pressure  on  the 
rail  being  vertical,  as  in  Ficr.  30.  've  have  the  conditions  and  the  relative 


I 


:  t  m 


1' 


294     C//AP.   VIIL— MECHANICS  OF  CURVE  RESISTANCE. 

position  of  rail  and  wheel  shown  in  Fig.  31.  Figs.  32  to  41  give  a  series 
of  rail  section  selected  from  a  great  number  taken  by  the  writer  on  the 
Atlantic  &  Great  Western  (now  New  York,  Pennsylvania  &  Ohio)  Rail- 
road, showing  the  wear  which  actually  results  from  the  conditions 
watched.  They  were  exact  copies  originally,  to  full  scale,  and  are  now 
reduced  one  half. 

Fig.  30  is  a  half-scale  section  of  a  new  flange  and  rail  section  of  ordi- 
nary form  (they  vary  somewhat  in  outline,  but  that  is  unimportant)  in 
their  natural  relative  position  on  a  tangent.  Fig.  31  shows  the  same  new 
Q  fiange   and    rail  section    in 

"^  (.LATERAL  THRusT.J  .  their  natural  relative  posi- 

Ifc  tion  ON  ANY  CURVE  WHAT- 

EVER, however  sharp  or  flaU 


CHAP.    VIII.-MECHANICS  OF  CURVE  RESISTANCE.      295 


Fig.  31. 


Fig.  42. 


The  tread  stands  entirely  free  of  the  top  of  the  rail,  the  surfaces  in  con- 
tact being  neither  the  horizontal  tread  nor  the  vertical  flange,  but  the 
curved  surfaces  which  are  perpendicular  to  the  resultant  shown  in  Figs. 
29  and  31.  To  understand  this,  let  the  reader  turn  Fig.  31  around  diag- 
onally until  the  diagonal  stands  in  a  vertical  position,  and  let  him  con- 
ceive it  to  represent  the  vertical  force  of  gravity  alone.  He  will  see  that 
the  wheel  would  naturally  take  this  position— as  naturally  as  a  wheel 
shjiped  like  Fig.  42  rolls  on  the  central  curved  surface  instead  of  the 
side  surfaces. 

314.  The  consequences  of  this  condition  of  things  are  these: 
First.  The  disproportion  in  the  diameter  of  the  wheels ;  hence  the 
necessary  longitudinal  slipping,  and  hence  the  curve  resistance,  is  materi- 
ally increased.     If  the  increase  of  radius  of  wheel  be  W  '"^h,  the  extra 
distance  slipped  through  per  station  of  100  feet  by  one  wheel  will  be  1.16 


feet;  which,  by  referring  to  Table  .09  on  page  286,  will  be  seen  to  be  as 

TfoIIowsT""  °l  '\  "'■'''^^  °^  '"^  ^^"  °"  ^  '''  —     This  increase 

Lh    ,    H  ^^"  P'"""'''^'^'  '^  '"'"'"'"'  '"'  =■"  <=""'es.  and  thus 

tends  to  d,sproport,onateIy  increase  the  resistance  of  easy  curves     But 

It  IS  profitless  to  inquire,  because, 

&««<//^,  The  inner  angle  of  the  wheel  and  the  outer  corner  of  the 
rail  ,s  gradually  worn  away,  the  greatest  wear  being  always  on  thi  corner 
o  the  outside  ran  and  in  the  direction  of  the  resultant  (see  fS Tto 
41).  on  curves  of  all  radii.  ^  ^     ^    ^° 

stanTlTif  f  ^  °'  "■'",  '"''"'^''  "°'  "P°"  '^'  P^^^«-«'  -hich  is  con- 
stant on  all  curves,  nor  (to  any  marked  extent)  upon  the  angle  of  wheel 

to  m,l,  but  upon  the  amount  of  sliding  which  takes  place4r  Tn  o  he ' 
words,  vanes  directly  as  the  degree  of  curvature. 

315.  Finally,  from  the  effect  of  these  causes  we  have  a  still  further 
cliange  of  conditions,  viz.:  mrther 

r/urMy.  As  the  wear  proceeds,  the  surfaces  in  contact  become  lare-er 
and  larger,  and  this  introduces  a  further  source  of  slippa<.e  ra'^wear^d 
curve  res,stance,  the  ultimate  form  of  which  is  show"!,'  in  F  g  4^  That 
particular  section  was  taken  from  a  ,6"  curve;  but  the  outer  r^il  on  aU 

theTn'd      rr""  '°"^  ■'"'!"'■  ''""'  '°  ''^'^^  P--->y  'he  same  form  i" 
the  end^   Thus  m  some  similar  sections  to  those  shown  in  Fi<.s  ,2  t^., 

on    he  Pennsylvania  Railroad,  rails  from  4"  curves  after  sustai;ing  nearly 

four  times   he  tonnage  of  the  rails  shown  in  Fig.  34,  were  in  even  worsi 

condition  than  the  rail  from  a  .6'  curve  shown  in  Fig  4, 

whirl  %r''.  "'°™  ''■'I  ^'"-  "'•  "'^  '™^  bearing  surface  on  which  the 
»heel  rolls  (compare  Fig.  3,)  is  directly  on  the  corner,  and  the  mWmt 
urfaces  above  and  below  are  revolving  in  a  circle  of  nearly  i-inch^on'ef 
radius,  the  average  of  the  whole  surface  being  nearly  if  not  quite  S 
It  necessarily  results  from  this,  that  while  fhe  wheel  is  "oiling  through 
any  distance  its  surfaces  slip  on  the  rail  through  1^1  „^  i  ^^  ^^^^ 
tance:  =  1.51  feet  in  100.  *       °° 

316.  The  coefficient  of  friction,  moreover  (as  well  as  rail  wear)  with 
such  large  surfaces  in  contact,  is  probably  considerably  larger  than  when 

he  bearing  is  on  a  mere  point,  as  in  the  unworn  rafl.  Fig  3, ^07  the 
formerly  accepted  -  law"  that  fr.ictlon  is  independent  of  the^ar'ea's  n  con! 

ated,,    f  Proven  untrue  for  lubricated  and  still  more  for  unlubri- 

cated  surfaces,  as  was  found  out  practically  long  since  with  brake-sl"oei 


■n 


u 


296      C//AP.   F///.— MECHANICS  OF  CURVE  RESISTANCE, 


The  information  on  friction  laid  down  in  most  of  the  standard  text-books 
is  very  deceptive. 

317.  This  third  source  of  extra  resistance,  due  to  badly  worn  rails,  is 
reached  in  a  much  shorter  time  on  sharp  curves,  and  as  a  rule  exists  only 
on  them  ;  but  nevertheless,  when  it  exists,  the  amount  of  the  extra  re- 
sistance caused  thereby  is  independent  of  the  radius.  If  rails  be  equally 
worn  it  will  amount  to  substantially  the  same  on  all  curves. 

When  the  wear  has  become  so  great  that  the  rail  has  the  form  of  Fig. 
41,  so  that  the  flange  bears  against  the  rail  almost  down  to  its  point,  the 
wear,  and  resistance  as  well,  is  doubtless  very  much  increased.  In  a  lot 
of  rails  which  have  been  all  exposed  to  substantially  the  same  tonnage, 
like  those  in  Figs.  32  to  41,  this  condition  will  be  likely  to  exist  only  on 
the  sharpest  curves,  and  accordingly  the  apparent  indications  of  a  test  of 
such  rails  will  be  that  rail  wear  increases  very  much  more  rapidly  than 
the  degree  of  curvature— in  fact  nearly  as  the  square  of  the  degree  of 

curvature. 

The  writer  himself  reached  this  conclusion,  from  the  only  facts  then 

before  him,  in  his  report  on  these  observations. 

318.  But  if,  on  the  contrary,  we  investigate  the  tonnage  necessary  to 
produce  the  same  wear  of  rails  on  different  curves,  we  shall  find  it  to  be 
almost  directly  as  the  degree  of  curvature,  and  this  is  undoubtedly  the 
true  law  of  rail  wear ;  from  which  it  follows  that  the  RATE  of  wear  on 
any  one  curve  increases  as  the  rails  become  more  worn,  and  this  pro- 
duces the  deceptive  appearance  of  a  rate  of  wear  varying  as  some  function 
of  the  square  of  the  degree  of  curvature. 

319.  As  to  the  wear  on  the  inner  rail,  it  is  apparent  that  the  effect  of 
the  flange  pressure  (see  Fig.  29,  page  292)  is  to  increase  by  about  one 
third  the  load  resting  on  the  front  outer  wheel.  We  might  accordingly 
expect  that  all  the  longitudinal  slipping  would  be  confined  to  the  inner 
wheel  which  runs  (see  Figs.  20  to  23)  with  its  flange  entirely  clear  of  the 
rail.  From  this  we  might  expect  (i)  that  the  wear  of  the  inner  rail  would 
be  wholly  on  top,  and  (2)  that  it  would  be  more  rapid  than  the  outer  rail. 
This  is  always  found  to  be  the  case,  as  will  be  evident  from  Figs.  32  to  41. 
The  excess  of  top  wear  on  the  inner  rail  would  undoubtedly  be  much 
more  disproportionate  than  it  is  except  for  this  fact : 

The  bulk  of  tonnage  is  slow  traffic,  and  in  such  cases  the  excess  of  the 
superelevation  over  the  very  small  amount  required  to  balance  the 
centrifugal  force  (i  inch  per  degree  at  15  miles  per  hour;  see  page  298) 
produces  a  slight  excess  of  load  on  the  inner  wheels;  not  sufficient  to 
counterbalance  the  effect  of  the  flange  pressure  on  the  front  axle,  but 


CHAP,    VIII.-MECHANICS  OF  CURVE  RESISTANCE,      297 

amply  sufficient  to  cause  the  rear  axle,  both  flanges  of  which  stand  clear 
o\  the  rail,  to  slip  entirely  on  the  outer  rail  on  slow  trains,  as  being  the 
point  of  least  resistance. 

320.  We  thus  have  this  condition  : 

(1)  The  front  outer  wheel  produces  all  the  flange  wear  and  little  or 
none  of  the  top  wear, 

(2)  The  front  inner-wheel  produces  nearly  all  the  wear  on  inner  rail 
—confined  entirely  to  top  of  rail. 

(3)  The  rear  outer  wheel  of  slow  trains  produces  nearly  all  the  top 
wear  on  outer  rail. 

(4)  The  rear  inner  wheel  produces  only  the  normal  tangent  wear. 

321.  As  respects  the  aggregate  amount  of  curve  resistance  :  From  all 
these  data  together  we  may  expect  it  to  be— 

(1)  0.37  lb.  per  ton  per  degree  of  curvature  as  a  minimum,  varying 
directly  with  the  curvature,  plus— 

(2)  Upwards  of  i  lb.  per  ton  as  a  constant  addition  due  to  flange 
friction  on  new  rails  (assuming  the  coefficient  of  friction  to  be  as  low  as 
0.25.  as  it  appears  to  be  with  car  wheels.  With  engine-drivers  it  is  about 
0.35)- 

(3)  As  rail  wear  increases  there  will  be  a  very  considerable  further 
addition  to  the"  resistance  due  to  the  flange  wear  on  worn  rails.  This 
effect  will  become  visible  very  much  sooner  on  the  sharper  curves,  but 
It  will  occur  sooner  or  later  on  all  curves  when  the  flange  has  cut  into 
the  side  of  the  rail. 

321^.  Let  us  compare  these  conclusions  with  experience : 
I.  Actual  experiment  on  the  63°  curves  (90  feet  radius)  of  the  New 
York  elevated  railroads,  conducted  by  Charles  E.  Emery,  M.  Am.  Soc. 
C.  E.,  shows  the  resistance  to  be  0.43  lb.  per  ton  per  degree  of  curva- 
ture on  new  rails  with  fixed  wheels  in  the  ordinary  mode,  and  0.33  lb. 
per  ton  with  loose  wheels.  (If  the  reader  will  refer  back  to  Table  109 
and  the  accompanying  discussion,  he  will  see  this  to  be  as  nearly  as  may 
be  what  our  theory  would  indicate.) 

2.  The  late  Benj.  H.  Latrobe  experimented  on  14°  curves,  with  new 
rails  also,  and  found  the  resistance  to  be  .40  lb.  per  ton. 

3-   French  experiments  with  about  12-ft.  wheel-bases  on  easy  curves 
show  about  1.25  lbs.  per  ton  resistance. 

4.  The  writer  made,  by  the  aid  of  very  delicate  electrical  apparatus, 
what  he  believes  to  be  the  most  accurate  experiments  on  train  resistance, 
so  far  as  they  went,  which  have  as  yet  been  made ;  and  his  conclusions! 
•so  far  as  relating  to  curve  resistance,  were  that  curve  resistance  is  much 


298      CHAP.    VIII.-^MECHANKiS  OF  CURVE  RESISTANCE. 


greater  per  degree  on  easy  curves  and  at  slow  speeds,  as  shown  in 
App.  A. 

322.  This  completes  our  analysis  of  the  forces  originating  and  acting 
within  the  truck  itself,  which  are  the  only  ones  of  importance.  Let  us 
see  what,  if  any,  effect  the  forces  acting  upon  the  car  body  and  train  as  a 
wbole  have  to  modify  this  result. 

Centrifugal  force  and  superelevation  act  upon  the  car  as  a  whole, 
and  their  effect  is  communicated  to  the  truck  through  the  centre-pin  or 
side- bearings. 

The  centrifugal  force  C  in  lbs.  per  ton  of  any  body  moving  at  V  miles 
per  hour  on  a  Z?"  curve  we  have  already  found  to  be  (eq.  (3),  par.  271),^ 

C  =  .02335   F'A (I) 

from  which  Table  106,  page  270,  was  computed. 

323.  The  superelevation  of  the  outer 
rail  creates  a  force  tending  to  draw  the 
car  inward  and  to  counteract  the  cen- 
trifugal force.  The  weight,  by  a  well- 
known  mechanical  law  (Fig.  44),  bears 
the  same  ratio  to  this  force  as  g.  Fig. 
43,  does  to  the  superelevation  e.  On  a 
4  ft.  8^  in.  gauge  (say  4  ft.  io|  in.  centre 
to  centre  of  rail)  it  amounts,  therefore,. 


Fig.  43. 


Fig.  44. 


in  lbs.  per  ton  per  inch  of  superelevation,  to  ^g-rr  x  2000  =  34.04  lbs. 

The  maximum  amount  of  elevation  which  is  ever  to  be  found  on  rail- 
ways is  about  8  inches,  creating  a  force  of  272.32  lbs.  per  ton.  Many 
roads  limit  it  to  6  inches,  or  204.24  lbs.  ;  but  we  may  for  safety  assume 
the  maximum  to  be  10  inches,  or  340.4  lbs.  per  ton. 

Comparing  this  with  Tables  106  and  107,  it  will  be  seen  to  just  about 
balance  the  centrifugal  forces  at  what  is  marked  as  the  maximum  safe 
speed,  according  to  usual  practice,  on  various  curves. 

324.  To  determine  the  effect  of  these  forces  on  curve  resistance,  let 
us  assume  the  extreme  case — that  the  maximum  superelevation  is  en* 


^A^l    ^'"—MECHANICS  O^  CURVE  RESISTANCE.      299 


tirely  unbalanced  by  centrifugal  force.     This  is  the  utmost  limit  that 

safety  permits. 

The  first  effect,  with  the  centre  of  gravity  in  the  position  sliown  in 
Fig.  43.  is.  by  well  understood  mechanical  laws,  to  throw  %  or  about  70 

outeTrail"'  Th'^'"  "''°"  ")\  '""''  '''"■  '^^"'"^  ""'^  3°  Per  cent  on  the 

H  h  I  r  !!  '""'^'  °'  ^"""^  "'"  ^°"'P''''  "'«  'P""g^  on  the  inside 
and  by  the  further  tipping  of  the  car  body  cause  the  insfde  rail  to  carr^ 
tliree  fourths  or  more  of  tlie  total  load. 

The  second  effect  is  to  confine  all  longitudinal  slipping  to  the  outside 
wheels  as  being  the  most  lightly  loaded.  This,  however,  we  have  seen  ta 
be  the  casew.th  the  front  axle  under  any  ordi„a.y  circun.stances.  The 
lateral  slip  of  the  front  axle  is  of  course  not  affected. 

The  third  effect,  resulting  from  the  combination  of  the  above  causes 


,/rz.i  .sb£.    \ 
i40     //CO 


ccoo 


/ooo 


2009 


Fig.  45  —Front  Ootbr  Whkbl. 

(I he  higher  rectangfle  shows 
the  conditions  without  supereleva- 
tion; the  smaller  recungle,  with 
superelevation.) 


I. 


i\ 


^3000 

I 


Fig.  46.— Rear  Outer  Wheel. 


;      » 


Fig.   47.— Both 
Inner  Wheels, 

is  to  change  the  magnitude  and  direction  of  the  forces  acting  on  each 
wheel  m  the   manner  shown  in   Figs.  45  to  47,  in  which  the  solid  lines 
how  the  magnitude  and  direction  of  the  forces   already  determined, 
independent  of  the  superelevation. 

»hi?h'  '"  "f'^'  ™?"^''  '^'''"^  ^'■°'"  '^^'''^  '°9'  P«g«  ^86,  the  slippage 
which^  regularly  takes  place  in  a  5-foot  wheel-base  on  a  10°  curve,  we 


Rear  inner  wheel 

"     outer      " 

Front  inner     " 

"     outer    " 

Total  amount 


Slippage  in  feet 
per  too  feet. 


0.00 
0.82 
0.89 
1.21 


Increase  of  Load. 


2.92 


50  per  cent,  increase. 
50  "   "   decrease. 
50  "   "   increase. 
39  "   "   decrease. 


New 
Slip. 


15  per  cent,  decrease. 


0.00 
0.41 

1-33 

•74 


2.4& 


■ 


'f  fRiPa 


I'i 


'1  * 


-r- 

IN 
I    N 
I 
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I 
I 
I 
I 
I 
I 
I 

I 
i 
I 
I 
I 
I 


••13000 

I 
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300      C//AP.    VIII.— MECHANICS  OF  CURVE  RESISTANCE. 

The  further  resistance  from  flange  friction  on  the  front  outer  wheel 
i(as  also  flange  rail  wear)  should  also  be  diminished  about  39  per  cent. 

325.  We  thus  see  grounds  for  believing  that  the  general  effect  of  even 
an  extreme  amount  of  unbalanced  superelevation  may  be  to  somewhat 
decrease  the  resistance,  but  not  to  any  important  extent ;  and  with  the 
ordinary  and  proper  limit  of  6  or  7  inches  superelevation,  partially 
balanced,  as  it  always  is  in  practice,  by  centrifugal  force,  the  effect  be- 
comes almost  insignificant  one  way  or  the  other,  although  still  apparently 
to  decrease  the  resistance  so  far  as  it  has  any  effect  at  all.  On  the  other 
Jiand,  a  similar  computation  to  the  above  as  to  the  effect  of  an  unbalanced 

centrifugal  force  will  indicate  that  it  has  a  very 
similar  and  equally  inconsiderable  effect  to  in- 
crease the  resistance.  Fig.  48  shows  the  most 
objectionable  effect  from  excess  of  centrifugal 
force.     (See  par.  327.) 

326.  Let  us  now  see  what  effect  such  unbal- 
anced forces  do  not  have.  They  do  not  alter  in 
any  manner  whatsoever  the  position  of  any  of  the 
wheels,  nor  can  they  by  any  possibility  do  so,  it 
would  appear,  until  the  centrifugal  or  centripetal 

^IG.     48. — EfFKCT     of    Un-      ,  ,  c  ....i^-..  1J1-J 

BALANCED     CENTRIFUGAL   force  becomes  a  force  so  great  that  it  would  slide 
Fkon?  ''ou?Eir'''w'HEEL   ^^^  whccls  laterally  on  the  track  if  the  car  were 

AGAINST  Rail.  standlncr  still  on  the  rails,  which  would  be  when 

(Compare  Fiff.  45.  show-  *^ 

•ing    effect    of    an    equal    the  superelevation  was  equal  \,o\x\t.  coeff.  fric.  X 

amount  of  unbalanced  cen-  ^  ,  u       ..  •       i. 

tripetai  force  from  super-  gauge,  OX  at,  Say,  \  gauge,  or  about  14  inches. 
fir*vHScity^n*ecSar)  "to  ^or  the  force  required  to  slide  a  rolling  wheel  on 
produce  this  amount  of  cen-   the    rail,   either    laterally    or    longitudinally,    is 

trifugal  force.  j  o  j 

neither  greater  nor  less  than  if  the  wheel  were 
standing  still  (unless  there  may  be  some  slight  and  unknown  modifica- 
tion of  the  coefficient  of  friction) ;  and  so  long  as  the  force  is  not 
FULLY  sufficient  to  do  this,  it  has  no  effect  at  all  to  move  the  body.  All 
it  can  do  is  to  increase  or  decrease  the  pressure  of  the  flange  against 
the  outside  rail,  and  this  (within  the  limits  of  safe  and  customary  prac- 
tice) only  to  a  trifling  extent.  This  results  from  an  elementary  mechani- 
cal law  which  has  been  too  readily  lost  sight  of  by  theorizers  on  this 
subject,  that  a  lifting  force  of  1999  pounds  is  as  incapable  of  lifting  a  ton 
as  a  force  of  one  pound. 

327.  The  real  objections  to  too  much  superelevation,  or  to  too  high  ve- 
locity, is  its  effect  upon  safety.  Throwing  so  much  weight  upon  one  rail 
and  one  set  of  springs,  is,  if  carried  to  excess,  highly  dangerous,  although 


5     I  ^V 


CHAP.    VIII.-MECHANICS  OF  CURVE  RESISTANCE.      30r 

the  resistance  is  not  in  any  case  very  seriously  affected.  An  excess  of 
superelevation  would  appear  to  be  the  least  evil  of  the  two,  however,  in 
a^  respects,  for  we  have  seen  (par.  324)  that  it  has  probably  some  slight 
effect  to  decrease  the  resistance  of  the  slowest  freight  train. 

328.  The  contrary  assumption   is  very  general,  but  it  is  absolutely  unsup. 
ported  by  experimental  evidence  so  far  as  the  writer  can  discover,  and  it  cer- 
tainly finds  little  defence  in  theory.     The  truth  is,  that  much  of  the  current  and 
almost  endless  discussion  of  this  topic  among  road-masters  and  even  engineers 
has  Its  root  in  insufficient  examination  of  the  mechanics  of  the  problem.     It  is 
ASSUMED  that  the  two  obtrusively  evident  forces,  centrifugal  force  and  its  oppo- 
site, are  the  only  ones  to  be  considered,  and  that  the  truck  is  thrown  against  one 
rail  or  the  other  by  these  forces  according  as  either  force  preponderates.     Yet 
one  has  only  to  watch  the  wear  of  rails  and  the  motion  of  a  truck  around  a 
curve  to  find  that  there  is  some  force  independent  of  either  (which  we  have 
analyzed  at  length)  which  presses  the  outer  wheel  against  the  rail  with  tre- 
mendous  force,  however  high  the  superelevation  ;  and  from  this  it  follows  that 
It  is  the  effect  of  the  other  two  central  forces  upon  this  force  which  is  the  real 
problem  lo  be  considered. 

329.  We  conclude,  therefore,  that  the  centrifugal  and  cen- 
tripetal forces  have  but  a  trifling  effect  on  curve  resistance,  and 
that  the  proper  rule  for  superelevation  is  to  elevate  sufficiently 
to  balance  the  centrifugal  force  of  the  fastest  trains  up  to  a 
maximum  of  six  to  eight  inches.  This  will  slightly  decrease  the 
resistance  and  danger  of  accident  to  freight  trains,  and  greatly 
improve  the  comfortable  riding  of  passenger  coaches,  provided 
always  that  some  uniform  rule  be  followed,  since  almost  any 
rule  is  better  than  none. 

330.  A  third  source  of  possible  curve  resistance,  obliquity  of  trac- 
tion, affects  the  train  as  a  whole.  The  conditions  of  the  problem  are 
presented  in  Fig.  49.  ^ 

It  may  now  be  considered  as  established  that,  despite  a  prevalent 
impression  to  the  contra- 

0 
B_ — r _  ^ 


ry  (which  many  able  engi- 
neers have  shared),  no  loss 
of  power  whatever  occurs 
from  this  cause.  Let  OA, 
f^'g-  49.  represent  the  trac- 


Fig.  49, 


tive  force  to  be  transmitted  through  the  coupling  O  to  the  car  B      As^ 
there  is  a  change  of  direction  in  the  force  at  O,  it  is  sometimes  claimed 


^^i 


■^1 


302      CHAP.   VIII.— MECHANICS  OF  CURVE  RESISTANCE. 


that  no  force  OA  can  be  caused  to  act  on  the  following  car  in  the 
changed  direction  OB  without  a  certain  loss  of  tractive  force,  and  hence 
-waste  of  energy.  This  position  is  in  both  respects  unsound.  There  is 
no  loss  of  tractive  force  at  each  car  due  to  obliquity  of  traction,  and,  even 
if  there  were,  it  would  not  necessarily  imply  any  waste  of  energy.  It  fol- 
lows that  the  method  of  analyzing  the  strains  by  which  such  position  is 
supported  (which  consists  in  making  the  angle  OCA,  Fig.  49,  a  right 
angle  and  then  taking  the  force  OB  =  AC,  or  less  than  OA)  is  incorrect. 

331.  The  correct  way  of  representing  the  action  of  the  forces  involved 

is  by  the  parallelogram  of  forces  shown 
in  Fig.  49,  which  should  be  constructed 
as  shown,  with  OB  =  OA,  the  force  OA 
being  transmitted  undiminished  through 
O  as  around  a  pulley ;  the  lateral  stress 
OC  having  no  more  effect  to  reduce  the 
force  OB  than  the  stress  OC,  Fig.  50,  has 
to  make  the  force  OB  less  than  OA.  Both 
in  Figs.  49  and  50,  if  the  stress  OC  is  suf- 
ficient to  produce  lateral  motion  in  the 
direction   OC  by  overcoming  the  static 

resistance,  it  will  or  may  consume  power,  and  the  force  OB  may  be  th*»n 
quite  different  from  AO,  but  otherwise  not. 

In  a  train  of  cars,  the  lateral  component  has  only  the  effect  to  mi- 
nutely increase  the  lateral  resultant  of  the  superelevation,  which  we  have 
just  seen  tends  to  decrease  the  resistance  (if  anything),  but  has  no  effect 
to  change  the  position  of  any  wheel,  or  to  increase  perceptibly  the  pres- 
sure of  the  wheels  against  the  rails. 

Conceive  the  track  to  be  a  complete  circle,  and  the  train  to  com- 
pletely fill  it.  Conceive  the  floor  of  the  cars  to  be  a  rigid  continuous  cir- 
cular platform.  There  would  then  nowhere  be  a  lateral  resultant  of  the 
kind  discussed,  but  no  reason  is  apparent  why  the  curve  resistance  should 

be  either  greater  or  less. 

332.  The  transmission  of  force  from  car  to  car,  through  a  train  on  a 
curve,  is  an  almost  exact  mechanical  parallel  to  the  transmission  of 
power  by  a  rope  or  chain  over  a  pulley ;  the  rope  being  the  string  of  car 
bodies,  and  the  car  wheels  the  pulleys.  The  fact  that  the  pulleys  are 
carried  by  the  rope  itself,  instead  of  in  a  block  exterior  to  it,  '\s  a  mere 
detail  not  affecting  the  mechanical  conditions.  In  either  case  the  loss 
from  such  transmission  is  simply  the  friction  of  the  pulley.  Conceive  a 
chain  made  of  successive  links,  each  carrying  a  pulley  wheel  and  being 


CHAP.    VIII.-MECHANICSOF  CURVE  RESISTANCE.      303 

dragged  over  a  large  cylinder  or  succession  of  cylinders,  large  or  small 
Conceive  furter,  the  rope  to  be  so  long  and  the  friction  of  ^he  pnhet 
so  great  that  the  whole  power  of  the  prime  mover  is  consumed  In  k  ep- 
mg  the  Cham  ,n  motion  at  uniform  speed.  We  have  here  a  perfea 
mecnamcal  parallel  to  a  train  in  motion  on  a  curve,  except  for  the  one 
nnnor  fact  that  the  resultant  of  all  the  forces  acting  on  the  wheels  does 
not,  m  case  of  a  ra.lroad  train,  lie  exactly  (althoughlt  does  nearh)  n  the 
plane  of  the  wheels  themselves,  whereas  in  the  case  of  the  pulley  wheels 
'l^o^:r:rT^r^'^  ^'^  coupling-pomts  from  .'chalget 

friction  of  the  n^  !'"    "^        '"''""'  "^  ^''""^  ""^  ^^^^  —  than%he 
fnct.on  of  the  pulleys  proper,  m  either  case.     It  is,  of  course  true  that 

the  resistance  of  the  rear  pulleys  would  tend  to  pre;s  each  puiley"    ad 

vance  more  t.ghtly  against  the  surface,  and  so  produce  greater  f rkt  on  in 

a  railroad  tram  it  is  entirely  pertinent  to  prove  that  a  lateral  centripetal 
force  is  produced  by  obliquity  of  traction,  so  that  the  resultant  of  ^ 

™r  fl\:o"  '  Th  t  ^^^7  ^^  ^'^  ^'^^^'  ^"^  ^^-  this  LXod  ce 
greater  friction.     The  latter,  however.-the  only  possibility  periinent  to 

discuss,-,s  commonly  neglected  in  discussions  wh^h  assume  th a    M 

resultants  from  obliquity  of  traction  indicate  /..;.  //..,.  Zr/^^i^^^^f. 

lc>ss  of  energy      Force,  i.e.,  static  stress,  is  one  thing,  resistInce     e 

destruction  of  dynamic  energy,  is  another  and  quite  Afferent  thing     We 

cannot  figure  away  energy  with  a  parallelogram  of  forces,  but  musf  prove 

w  en  and  how,  if  at  all.  it  is  lost  by  additional  friction.     As  a  mattero 

fact  the  e  appears  to  be  no  loss,  but  a  trifling  gain,  under  ordinary  con- 

d.fons.  from  the  fact  that  the  centripetal  tendency  is  increased.     ' 

333.  There  .s  so  much  misconception  as  to  this  matter  that  we  may  en- 

deavor  to  make  it  still  dearer.     In   Fig.  ,,  let  the  lines  OOP  represent  the 

n:.ld7  Tr7  T.^T'  ^"  ^^^'^^  '''^^'-'^  ■'  ^^'  ^'^  -'  -M^^^^ 

F'ns,  and/,,  ihecoupling-hnk.    Let 

the  lines  SS  represent  in    magni-  S»~-£t^__Js 

tude  and  direction  the  tensile  force 

acting  upon  the  link  and  tending  to 

rupture  it.     As  a  matter  of  course, 

these   forces    S  must  be  equal  to  Fig.  51. 

TctT^r'  "'T  ''"*''".  ^""^  ''"''""  "'"  ^^"^^'  ^"^  ^h^"  resolved  into  forces 
a  t  ng  ,  ,he  axes  of  the  cars  this  makes  the  latter  also  equal.     The  losses 

0    ens.,e  force  from  car  to  car  occur  at  the  centre  pins  O  of  e\ch  car,  and  no 
at  the  coupling  points  P.     The  tension  on  the  front  end  and  back  end  of  ^h. 

resistance  of  that  car  ;  but  the  longitudinal  strains,  parallel  with  the  respttive 


304      CHAP.    VIII.— MECHANICS  OF  CURVE  RESISTANCE. 


axes  of  the  cars,  on  the  rear  draw-gear  of  a  forward  car  and  the  front  draw- 
gear  of  a  rear  car,  are  always  equal  to  each  other  in  magnitude,  although  differ- 
ent in  direction  by  the  amount  of  the  angle  between  the  axes.  That  is  to  say». 
the  diminution  of  tensile  force  from  car  to  car  is  internal  to  each  car,  and  not 
at  all  at  the  coupling-point. 

334.  But  the  point  is  not  worth  disputing,  for  the  loss,  if  it  were 
granted  to  exist,  is  very  small.  Assuming  the  car  body  to  be  30  feet 
long,  the  deflection  angle  OAB,  Fig.  49.  will  evidently  be,  on  a  Z?°  curve, 
0.3Z?  or  18'  X  D,  and  of  the  tractive  force  F(  =  OA,  Fig.  49)  there  will 
be  an  assumed  loss,  which  let  =  L,  at  each  coupling,  from  obliquity  of 

traction  :  ,  ^ ,, 

/,  =  yr  (I  _  cos  18')  Z>  =  o.ooooi6Z?/^. 

The  tractive  force  of  a  Consolidation  engine  is  something  over 
20,000  lbs.  at  the  engine  and  zero  at  the  end  of  the  train,  averaging,  say^ 
10,000  lbs.    Then  the  loss  per  car  will  average,  on  a  1°  curve. 

Z  =  0.16  lb.  per  car, 
or,  on  a  10°  curve  with  a  60-car  train, 

Z,  =  96  lbs. 
Not  a  very  serious  matter,  certainly. 

336.  We  conclude,  therefore,  as  to  curve  resistance  : 

1.  Obliquity  of  traction  and  the  length  of  the  train  have  no- 
appreciable  effect  to  modify  curve  resistance. 

2.  Centrifugal  force  within  the  limits  of  practice  has  but  lit- 
tle effect  on  the  resistance,  but  that  little  is  to  increase  it. 

3.  Centripetal  force  from  superelevation  within  the  limits  of 
safe  practice  has  but  little  effect  on  the  resistance,  but  that  little 
is  to  reduce  it. 

4.  The  best  rule  for  superelevation  is  to  elevate  for  the  fast- 
est rej^ular  speed  up  to  a  maximum  limit  of  6  to  8  inches  in  all. 

5.  Rail  wear  and  curve  resistance  over  rails  in  the  same  con- 
dition are  as  nearly  as  may  be  directly  as  the  degree  of  curva- 
ture, with  some  minor  elements  which  are  independent  of  radius. 

6.  Rail  wear  and  curve  resistance  are  appreciably  less  with 
new  rails  than  with  old,  and  become  greater  as  the  outer  rail  is 
worn  away  to  the  shape  of  the  flange. 

7.  The  pressure  of  the  flanges  against  the  rail  is  the  same  on 
all  curves  independent   of    radius,  but   the    wheel   stands  at  a 


CHAR.    VIII.^MECHANICS  OF  CURVE  RESISTANCE.      305 


greater  angle  to  the  rail  as  the  curve  is  sharper,  and  likewise  is 
shdmg  faster  on  the  surface  of  the  rail,  increasing  the  danger  of 
derailment  correspondingly,  by  some  unknown  amount,  but  not 
nearly  in  proportion  to  the  degree  of  the  curve 

8  The  lowest  probable  limit  of  curve  resistance  at  ordinary 
freight  speeds  and  in  ordinary  curves  is  about  4  lb  per  ton 
per  degree  of  curve,  with  all  in  perfect  order.  With  worn  rails 
and  somewhat  rough  track  it  may  be  as  high  as  |  lb.  per  ton 

9.  While  so  obscure  a  point  cannot  be  considered  as  estab- 
lished  by  the  existing  experimental  evidence,  all  the  more  trust- 
worthy  existing  evidence  seems  to  combine  with  theory  to  indi- 
cate  that  curve  resistance  per  degree  of  curve  is  very  much 
greater  on  easy  curves  than  on  sharp  curves  ;  so  that  when  the 
resistance  is  i  lb.  per  ton,  for  example,  on  a  1°  curve,  it  may  be 
6  to  8  lbs.  per  ton  on  a  10°  curve,  and  not  more  than  15  to  18 
lbs.  per  ton  on  a  40°  to  50°  curve.     (See  Appendix  A.) 

10.  It  may  be  considered  established  that  curve  resistance  is 
affected  somewhat  by  the  speed,  and  probably  by  a  verv  consid- 
able  percentage;  so  that  if  the  curve  resistance  in  motion  be 
i  lb.  per  ton  it  may  be  as  high  as  i  lb.  per  ton  on  worn  rails 
for  speeds  of  less  than  4  or  5  miles  per  hour,  or  for  the  first 
train  length  or  thereabout  in  getting  under 
way.  As  a  stoppage  on  any  curve  is  always  ^onftfudrnafsiip. 
a  possibility,  this  contingency  should  not  be  ^'"'"''^* 
forgotten  when  reducing  grade  on  curves,  es- 
pecially near  possible  stopping  points. 

II.  The  beneficial  effect  of  the  narrower 
gauge  is  small  with  the  same  length  of  wheel- 
base.     With  a  3-ft.  gauge  as  against  a  4.7-ft.  ^,  . 
gauge,  with  a  wheel-base  of  4. 7  ft.,  it  is  about  f,c  c     f  ^ 

'         '  ^v^i^w    1*10.  52.— Effect  of  Dif- 

,  4/4    73      I        .    -a  A<.«  FERENCE     OF     GaUGR    ON 

as     (not     exactly    as)     -±Z_ll±7_  _  ^047  __  ,        Curve       Resistance, 

4/  ^3     I T  ~  77T^  ~  ff        Length  of  Wheel-base 

^3      +4-7  5-570  REMAINING  THE  SAME. 

less,  as  outlined  in  Fig.  52.    With  a  wheel-base  Pi^^'of  X'^S  ,'„"■>» 

>f"ven     distance     is    repre- 
Of  2^-  the  crai'n  i«5  onl^r  ^^"'72  ,  sented  by  thetwodiaeonals 

v'l  ig  ine  gain  is  only =12  per  cent  less    marked  n.  g.  and  sfd.  g.) 

97.36 
If,  however,  the  length  of  wheel-base  decreases  with  the  gauge 


_£^ 


iS^ 


ms 


306      CHAP.   VIII.— MECHANICS  OF  CURVE  RESISTANCE. 


CHAP.   VIII.-MECHANICS  OF  CURVE  RESISTANCE.      30/ 


■;  i 


Longifudinal  S/f'p 


the  gain  is  directly  as  the  gauge.  All  the  preceding  refers  only 
to  the  surface  friction  on  the  top  of  rail,  flange  friction  being 
much  less  affected. 

12.  Increasing  the  length  of  wheel-base, 
say,  from  gaug^  to  2  gauge  increases  curve  fric- 
tion  as   outlined  in   Fig.   53,  in   the  ratio  of 

^     =  58  per  cent. 
1.414 

336.  Perhaps  the  best  existing  experimental  confir- 
mation of  the  eleventh  conclusion  above  is  to  be  found 
in  some  delicate  experimenis  on  models  by  Mr.  Reuben 
Wells  (Rept.  Am.  Ry.  M.  M.  Assoc,  1876),  which  have  at- 
tracted far  less  attention  than  their  merit  deserves.  While 
no  one  test  of  any  kind  can  be  considered  decisive,  the  tests 
do  afford  an  indication  which  is  perhaps  more  delicate  and  re- 
liable as  a  test  of  principle  than  could  easily  be  made  with  the 
actual  rolling-stock.     With  trucks  representing  to  yV   scale  a  p,^        _  effect 

'        '-  J     .    f.     01    ;-      __         Qp     DiFFERENCB 

OF  Length  ok 
Wheel-base  on 
Curve  Resist- 
ance, Gauge 
remaining    the 

SAME. 


wheel-base  of  4  ft.  10  in.  and  gauges  of  3  ft.  and  4  ft.  8^  in.  on 
a  curve  representing  to  the  same  scale  one  of  300  ft.  radius 
and  273  ft.  long,  gravity  being  the  impelling  force,  Mr.  Wells 
found — 


Speed. 
Miles  Per  Hour. 

5-76 

7-59 
10.12 

16.70 


Resistance ;  lbs.  per  ton  (actual). 
St  G.  N.  G.  p.  c,  of  N.  G. 

46.80  39 -H  83-6 

48.96  41.66  85.1 

45.76  41 -66  91-0 

68.20  64.40  960 


By  formula  above 

|/^<TK^v*-j-  wheel  base* 

the  per  cent  of  N.  G. 

should  be,  uniformly, 

82.7  p.  c. 


If  we  consider  that  in  these  observed  resistances  the  normal  tangent  roll- 
ing friction  is  included,  whereas  in  the  formula  it  is  not,  the. two  correspond 
wonderfully  closely,  indicating,  however,  that  the  absolute  amount  of  curve 
resistance  decreases  with  the  speed-which  is  probable  from  other  reasons. 
The  tests  were  made  by  raising  the  track  to  a  grade  which  would  give  the  de- 
sired velocity  and  the  resistances  in  lbs.  per  ton  deduced  therefrom.  The  high 
absolute  amount  of  the  latter,  compared  with  normal  rolling-stock  resistance, 
should  not  be  allowed  to  convey  an  impression  that  the  models  were  rough. 
On  the  contrary,  they  show  that  it  waS  very  delicately  constructed,  as  the  re- 
sistances  per  ton  of  its  actual  weight  are  but  little  more  than  three  times  what 
might  be  expected  with  fully  loaded  cars,  which  is  even  less  than  the  probable 
difference  in  coefficient  of  friction  due  to  the  difference  of  load. 

Mr  Wells's  primary  purpose  in  undertaking  these  tests  was  to  detcrmme 
bow  much  there  might  be  in  the  alleged  theoretical  advantages  of  loose  wheels 


for  passing  curves  He  found  that  in  no  case  was  much  gained,  while  in  some 
cases  the  loose  wheels  were  a  positive  disadvantage.  The  preceding  theoreti- 
cal discussion  of  the  mechanics  of  curve  resistance  may  be  readily  shown  to 
point  directly  to  the  same  conclusion,  and  almost  to  Mr.  Wells's  identicaUg. 
"''%'-,7     r^  "T^"^^  expedient  to  extend  this  discussion  for  that  purpose. 

337.    The  late  Baron    Von    Weber,    whose  great   services  to  the  cause  of 
science  entitle  anything  vouched    for  by  him  to  a  presumption    in  its  favor 
gave  currency  to  a  very  absurd  formula  in  respect  to  curve  resistance,  which 
has  been  quite  extensively  quoted  as  trustworthy,  as  it  was  alleged  to  rest  on 
some  extensive  and  elaborate  experiments.     This  formula  gave  the  total  resist- 
ance as  a  function  of  -^__.  /,  being  the  radius  in  metres.     This  formula 
gives  resistances  increasing  much  faster  than  the  degree  of  curve,  instead  of 
slower,  as  we  have  found;  the  results  varying  from  a  resistance  of  0.8  lb   per 
^      net  ton  per  degree  for  a  curve  of  1000  metres  radius  (3310  ft.,  or  i»  44') 'to  a 
resistance  of  ^67  Ibs^per  net  ton  per  degree,  for  curves  of  100  metrer/adius 
(331  ft.,  or  17    20 ).     But  by  extending  the  formula  to  a  little  sharper  curves  its 
untrustworthy  and  absurd  nature  is  at  once  seen.     For  a  curve  of  60  metres 
radius  (197  ft.)  we  obtain  a  resistance  9.45  times  as  much  per  degree  as  on  a 
curve  of  1000  metres  radius,  and  for  a  curve  of  55  metres  radius  or  less  an  in- 
finite  resistance.     As  the  curves  of  the  New  York  elevated  railways  are  of  less 
than  30  metres  radius,  and  as  ordinary  American  engines  were  operated  over 

S.^r'lT-   r  ^^/^f  •"^^°''  ^^"^^  ''"^^  ^»^hout  accident  or  delay,  on  the  United 
Stales  Military  Railroads  in  the  late  war.  this  is  hardly  a  rational  result 

338.  A  new  and  dangerous  doctrine  has  lately  been  advanced,  in  a  semi- 
official  manner   which  has   given    it  wide   currency   as   a  conclusion   of    the 
Master  Car-Builders'  Association,  al- 
though  it  was  in  no  sense  such  in  fact, 
viz.,   that  the  corners  of  rails  should 
be  rolled  to  a  larger  radius  (f  inch)  so 
as  to  exactly  fit  the  radius  of  the  fillet 
or  interior  corner  of  the  flange,  instead 
of  the  two   being  of  quite   dissimilar 
radius,  as  in  Fig.  31,  which  shows  the 
more  usual  and  the  only  proper  prac- 
tice. 

These  conclusions  were  expressed 
in  an  otherwise  able  paper,  by  M.  N.  Fig.  54. 

Forney,  Secretary  of  the  Association  ^'TyS'^^\^?.J'^\  '-3  .^  ^'■-  Forney's  paper, 
(R.P..M.C.B.  Assoc,  ,885),-  and  , he  ^^^^^^^ ^^^'iSS^.r.^.':^^,^^^. 
Iheory  was  based  upon  the  claim  that  SLs.)  "''  "  ^='"«'  "'"■  »  «""  <"  «  i"=h 
the  usual  form  of  rail  an.l  flange,  such  as  is  shown  in  Figs.  30  and  3,  causes 
sharp  flanges,  producing  wear  such  as  .s  outlined  in  Fig.  5^4  ;  the  corner  of  the 


308      CHAP,  VIII.— MECHANICS  OF  CURVE  RESISTANCE. 


rail  wearing  to  a  larger  radius,  and  the  fillet  of  the  flange  to  a  smaller  radius^ 
thus  producing  sharp  flanges. 
The  facts  are: 

1.  (See  Table  114.)  Only  a  very  small  percentage  of  wheels  ever  get  sharp 
flanges,  and  there  are  never  two  sharp  flanges  on  one  axle;  showing  that  some 
mechanical  defect  of  wheel  or  truck  (usually  the  latter)  is  the  chief  cause  of 
sharp  flanges,  and  not  some  general  cause  acting  upon  all  wheels  alike. 

2.  Except  in  the  one  case  of  the  outside  rail  on  curves,  rails  invariably  wear 
, to  a  much  smaller  corner,  radius,  as  in  Fig.  55,  re- 
produced from  an  example  of  wear  in  Mr.  Forney's 
paper  (see  also  Figs.  32  to  41),  and  never  in  the 
manner  outlined  in  Fig.  54. 

3.   In  the  one  case  of  the  outside  rail  on  curves 
the  rails  do  finally  wear  away  in  something  like  the 
Fig.  55.  manner  outlined  in  Fig.  54,  until  the  side  of  the  rail 

takes  almost  the  exact  form  of  the  flange,  as  in  Fig.  41,  but  there  is  then  much 
more  friction,  more  rapid  wear,  and  more  danger  of  derailment  than  when  the 
rails  are  new,  as  in  Figs.  31  or  54  ;  because,  although  the  bearing  surface  is 
small  in  the  latter  case,  it  is  subjected  to  only  rolling  wear,  whereas  if  the 
flange  fits  all  around  the  rail  corner  the  additional  bearing  surface  is  exposed 
to  rubbing  friction.     (See  par.  313  etseq.) 

339.  Imagine  a  heavy  sphere  rolling  down  a  plank,  as  in  Fig.  56.     It  has  a 

very  small  bearing  surface,  yet 
any  additional  bearing  surface 
which  might  be  gained  by  turn- 
ing the  plank  into  a  troughs 
"exactly    fitting"     the    sphere- 

Fig.  56.  would    plainly    produce    more 

friction  and  more  wear,  rather  than  less.  The  same  conditions  obtain  in  Fig. 
54,  where  the  material  outside  the  dotted  lines,  which  it  is  proposed  to  remove 
in  first  manufacture,  is  really  "  precious  metal,"  serving  to  long  postpone  the 
day  when  the  rail  and  flange  fit  as  Fig.  41,  and  a  very  rapid  rate  of  wear  begins. 
The  metal  outside  the  dotted  lines  in  Fig.  54  will  require  at  le&st /our /imes  as 
great  a  tonnage  to  wear  it  away  as  will  be  required  to  wear  away  an  equal 
weight  of  metal  after  it  is  gone.  Moreover,  the  wear  of  flange  outlined  in  Fig. 
54  never  takes  place  at  all  except  in  a  very  small  percentage  of  the  wheels 
(2  to  6  per  cent),  indicating  that  it  is  not  due,  when  it  does  take  place,  to  the 
form  of  the  rail. 

340.  What  sound  practice  would  seem  to  require,  therefore,  is : 

I.  The  tread  of  the  wheel  should  have  something  the  form  of  Fig.  57,  witfr 
a  fillet  radius  of  at  least  fin.,  instead  of  the  i-in.  radius  which  Mr.  Forney 


f^:!fi^:fffzf^^  309 


i  J-^-:  "^^^"^^  ^^^"^^  '^'''^'  ^'  '^^  -^^  ^^ould  be  little  if  any  greater  than 

thaf :^;  init':;;^ i::n:^r-;^^^^^   -^  r^i  of  ^g.  ..us 

flange   pressure    arises    from  c>  "^      '"''  "  ^'^^  '''     ^^^^  -^  ^^^eral 

the    passage    of    a    curve    or      Weral  thrust  ? 

other    cause,   instead    of    the 

bearing  surfaces    being  able 

to   still   maintain   the  merely 

Tolling   contact    of   minimum 

wear,  as  outlined  in  Figs.  31 

and  59,  we  have  the  ruddui^ 

side  contact  shown  in  Fig.  53) 

sure    to    produce   rapid   side 

wear,  in  addition  to  the  usual 

top  sliding  and  wear.      This 

has     actually     resulted    with 

rails  of  such  form.      On  the 

Lehigh    Valley    and    on    the 

parts  of  the  Pennsylvania  laid 

with  its  new  rail  section  of  ^ 

in.  corner  radius,  both  rails 

results,  however  old  or  worn  the  roii;  .  "^'   '°™    ""'^   ""« 

34?    «     ,  °' "°™  "■"^'''' ^^^P'on  the  outside  rail  of  curves. 

best  ex;sUng"vide„?;::''to:h'e'':;^r?'°"^  '""""  '°  ''-■  "«>•  S^-^  ">« 
having  parallel  axles  He  ex oenle  ,  °,  T'"^  °"  '"=  """'"'  P^"  "'  "-ks 
."  Fig.  60.  To  dete™"  ^Z7^  ZZ'"""'  '"''  ^^  '''  ^'"'"" 
has  since  constructed  and  tested mV.,  ""'  ""^"'  ""'  "■•'■'" 

similar  results.  '"°''''  °'  """"^  '^'«"«"'  f"™  "i*  closely 

Of  u.. =\T,  r2';,rr":e  "xh:  Tr  '--'•  --  --"^  •"  ^  -■= 

-i«d   wheels   of  34i  and  3  i   "or  a  diff  °"  ,"'""''  «P-sented  full, 

radii  of  the  actual  ptth  Of  th^ln^ddUhwtr^efaf  '"■  '"  T"'""'     '"'' 

-te  that  a  sin.i  p.r  of  ^^^'o!:i:'z:^:z:t:s::::-::z  ;:: 


I 


3IO      CHAP.   VIII.— MECHANICS  OF  CURVE  RESISTANCE. 


Fia  57. 


CHAP.   VIII.-MECHANICS  OF  CURVE  RESISTANCE.      311 

in  their  diameters,  will  roll  in  a  curve  of  53i  Ti.  radius.  Two  pairs  of  such 
wheels,  If  the  axles  are  held  parallel,  as  in  the  model,  would  roll  in  the 
following  curves: 

Axles  3  ft.  apart  will  roll  in  a  curve  of    67  ft.  radius. 


«< 

4 

i( 

(( 

5 

•< 

«< 

6 

<( 

«t 

7 

(t 

« 

8 

« 

•( 

9 

(( 

*( 

10 

(C 

(i 
« 
<< 
<c 
•< 

M 


<  < 
(( 
(( 
« 

« 
«« 


91^ 

I74i 
251 

337f 

479 

643i 


Fig.  58.— Rail  Section  and  Wheel-tread,  Lehigh  Valley  Railroad. 
(Showing  effect  of  having  corner  of  rail  of  larger  radius  than  fillet  of  flange.) 


Fig.  60.-M0DEL  t;sED   bv  Mr.  M.  N.  Forkhv   kor   I.vhstioatino  thk  Epfect  or  C<m,«o 

ON  the  Path  of  Rectangular  Wheel-bases. 

v,^J^Z  "''T  r'"^  "'Z"  '"■  '"  ""  ''"«"•  °f  ">*  ""d,  and  an  average 
play  m  the  gauge  of  J  ,n.,  we  find  abom  A  in.  to  be  the  difference  of  diameter 
«h,ch  ordmary  coned  car  wheels  can  have,  assuming  that  both  wheels  stood 


312      CHAP.   VIII.— MECHANICS  OF  CURVE  RESISTANCE. 

close  to  the  outside  rail,  which  they  do  not  (see  Fig.  20  and  par.  294).     This 
would  correspond  to  results  in  actual  practice  as  follows  : 


Axles  3  ft.  apart 

will  roll  in  a  curve 

of  J 

2.572  ft.  radius. 

..      ^ 

•< 

3.513 

i 

'•      5 

(< 

5.107 

/ 

"     6 

(« 

6,700 

/ 

•'      7 

« 

9.638 

/ 

f 

"      8            •• 

« 

12,969          " 

/ 

-     9 

<« 

18,393 

\ 

/ 

"    10            •• 

M 

24,700 

/ 

^ 

A 

/ 

1 

y 

8 

jj 

/ 

j> 

^ 

< 

/^ 

it 

s 

^ 

e 

y^ 

Si 

S 

-»^-.^-"?^^• 

§ 

"tfl 

it^ 

9 

«p 

S 

0. 

iW         2»         2V»' 

3          d»/a'      ♦' 

4V«' 

._.  ji 

Gauge,  2.35  in. 

Fig.  6i. — Radius  of  Path  of  Wheel-base  shown  in  Fig.  60.  with  Wheels  set  at  Various 

Distances  apart,  as  shown  along  the  Base-line. 

These  figures  indicate  that  even  under  the  most  favorable  possible  circum- 
stances coning  can  have  little  effect  to  facilitate  the  passage  of  curves. 

343.  Having  now  investigated  the  nature  of  rail  wear  on 
curves  and  the  causes  of  curve  resistance,  we  are  better  prepared 
to  take  up  and  estimate  at  their  true  worth  the  positive  objec- 
tions to  curvature,  as  summarized  at  the  beginning  of  this  chap- 
ter, whicb  are  : 

1.  The  direct  cost  of  curvature  of  various  radii;  that  is 
to  say,  the  greater  wear  and  tear  of  road-bed  and  rolling-stock, 
and  the  greater  consumption  of  fuel. 

2.  The  limiting  effect  of  curvature  on  the  weight  and 
length  of  trains. 

A  moment's  consideration  will  show  that  these  two  causes 
of  expense  are  sharply  defined  from  each  other.  For  every 
curve,  whether  sharp  or  flat,  and  wherever  situated,  must  cause 
a  certain  amount  of  wear  and  tear  and  waste  of  power,  although 


CffAP.  Vm.-CURVATURE-EFFECT  ON  EXPENSES.     313 

it  may  not  cause  any  shorter  trains  to  be  hauled,^;i;i;ir771^ 
DIRECT  effect  on  expenses;  but  if  the  curvature  be  very  sha  p  o 
very  unfavorably  situated,  or  if  the  line  be  very  nearlv  level  so 
that  there  are  no  heavy  grades  to  li^it  trains  in'^advance  of  cur! 
vature,  there  w.ll  finally  come  a  point  where  too  much  or  too 
sharp  curvature  will  not  only  cause  wear  and  tear,  but  likewise 
cause  the  length  of  trains  to  be  cut  down.     In  that  case  the  di- 

iue     '^T"\       '''"  '"'■^''"'"'  '"^  ^"^^  ^'"^   '-^  ->d  waste  of 
fuel,  w.l   continue  on  as   before,  but  there  will  now  be  a  new 

r;  d- tiLTirn:^^ '''-' "  '^^'  ^'^^^'^  -^^'^  -  ^"  ---  -■^^^■ 

We  for  the  present  (until  Chaps.  XVIII.  and  XIX.)  consider 
only  these  DIRECT  sources  of  expense  which  are  common  to  aU 
curva  ure  wherever  situated,  assuming  that  it  does  not  require 

run  them."  ""'  ''"'  '"'"^  """^  "  '""''^  ^"P^"^-^  '° 

THE  EFFECT  OF  CURVATURE  ON  OPERATING  EXPENSES. 

of  ^^^'Jrij'^^  '"'?  ''^'^^^  '^^"  ^P^---  '86)  that  about  33  per  cent 
of  the  cost  of  fuel  goes  for  getting  up  steam,  kindling  fires  runninrto 
and  from  trams,  stopping  and  starting  trains,  standingldle  et  e"c  and 
IS  hence  a  constant  wastage,  independent  of  the  distance  run  AU  f 
th,s  may  be  considered  as  likewise  unaffected  by  cuV^lture  "d  in  aL 
uon  thereto  there  is  another  and  important  sou'ceTf    ^s"'  Z      "nden" 

and  hence  with  the  distance  run,  but  is  inappreciably  affected  bv  the 
po  ver  developed  per  hour.  Every  part  of  a  locomoti  ve,^eve„  the  liein^ 
IS  hot  enough  to  burn  the  hand  in  the  coldest  weather  '''^'^^Sing. 

whilh  if  ^'H°^;'  k'"""^  '"''  ^""■■<=ly<=^Posed  (by  a  mi;taken  negligence 
«h,ch  IS  gradually  being  corrected  in  some  few  instances  as  onfhL  1 1 
Shore  &  Michigan  Southern   Railway,  on  which  Si  th^firA 
agged*),  and  the  ends  of  the  cyli„d';rs  are  pL    t  d  on  ;brmetl! 

wt^er  is  shotn  brr'n"'  ""  ■'''"'''  ^"'°""'  »'  '-'   consl^d    „ 
cergrler  than  •  ''"'"'"'  '°  "^  "^^^  ""'f"™'^  -bout  20  per 

o  t  mperatu  e  ^""""^^' ^-^ '"^^^  "  P—«  for  each  Jf.  difference 


-^^s^^C:— ::-rirry".r;^^^^-^^ 


314     CHAP.   VIIL—CURVATURE^EFFECT  ON  EXPENSES. 


•< 


345.  To  appreciate  the  full  force  of  this  fact,  we  must  remember  that 
the  hottest  summer  day  is  cold  to  the  cylinders  and  boiler.  The  temper- 
ature within  the  boiler  is  about  350''  F.;  and  hence  whether  the  temper- 
ature outside  be  o''  F.  or  100°  F.  makes  little  proportionate  difference. 

Let  us  suppose  the  average  fuel  consumption  in  July,  with  an  average 
temperature  of  if  F.,  to  be  60  lbs.  per  mile.  In  January,  with  an  aver- 
age temperature  of  37"  F.,  experience  shows  that  the  consumption  will 
be  some  20  per  cent  greater.    Then  we  have  : 


Tbmpbratvkk. 


Lbs.  Coal 


July, 

January, 


Interior. 

350° 
350'' 


Exterior. 

.u 


Difference.    Burned  Per  Mile. 


Increase  p.  c, 


IT 
If 


40" 


273 
313' 


60 
72 


14.6  p.  c.         20  p.  c 


The  cause  of  this  enormous  effect  of  difference  of  temperature  is  very 
obscure,  and  it  would  lead  us  too  far  to  discuss  it  in  detail.  The  matter 
has  attracted  far  less  attention  than  it  should,  and  even  the  facts  from 
which  any  discussion  of  causes  must  start  are  but  little  known  to  railroad 
men.  It  will  be  seen  that,  superficially  considered,  the  facts  seem  to  in- 
dicate that  a  very  large  proportion  of  the  fuel  consumption  is  due  to  the 
effects  of  exterior  temperature  ;  for  if  a  decrease  of  40°  F.  or  li  per  cent 
in  the  difference  between  the  temperature  within  and  without  the  boiler 
saves  20  per  cent  of  the  fuel,  it  would  seem  as  if  we  had  only  to  decrease 
the  difference  a  little  farther  to  save  half  or  three  quarters  of  it. 

This  conclusion  would  be  absurd,  but  all  that  it  is  desired  here  to 
show  is  that  exterior  radiation  is  a  very  serious  matter.  The  chief  causes 
for  the  great  difference  in  winter  and  summer  fuel  consumption  are  prob- 
ably these : 

I.  Tl?e  rolling  friction  is  considerably  higher.  Most  of  the  energy 
destroyed  by  friction  must  take  the  form  of  heat,  and  as  the  journals 
speedily  attain  about  the  same  temperature  in  both  winter  and  summer 
(moderately  warm  to  the  touch)  the  difference  in  temperature  of  the 
journals  and  the  external  air  is  much  greater  in  winter,  and  this  means 
so  much  more  journal  friction. 

This  theoretical  deduction  lacks,  as  yet.  direct  experimental  evidence,  pend- 
ing which  it  must  be  regarded  as  doubtful.  By  some  strange  omission,  the 
comparative  winter  and  summer  train  resistance  has  not  been  the  subject  of  di- 
rect investigation,  so  far  as  the  writer  is  aware;  but  that  there  is  considerable 
difference  appears  to  be  indicated  by  the  fact  that  it  is  found  necessary  in  prac- 


CHAP.   VIII.-CURVATURE-EFFECT  ON  EXPENSES.     315. 

tical  operation  to  cut  down  trains  in  winter  by  about  10  per  cent  (say  from  20- 

cars  to  18.  or  from  40  cars  to  36),  for  which  it  is  riiffirnit  \r.  •        •         ''"""^^^ 

,„,. ,         ,         .  ^        J  /•  ^wi  wiucn  It  IS  dilticult  to  imagine  any  other 

rafonal  exp.anafon.      The   popular  explanations  are :       (,)    That  the   wind 
ravels  n,ore  m.les  ,„  winter  than  in  summer,  which  is  no    true:  and  wTa" 
the  track  .s  m  worse  condition,  .vhich  is  unquestionably  true  to    ome  extend 
but  there  are  very  few  days  when  snow  and  ice  cause  much  trouble  on  the  sur-' 

and  the  effect  of  heav.ng  of  the  road-bed  on  train  resistance,  although  impor 
tant.  can  hardly  account  for  the  difference  which  exists 

,.  ,f  *■  \"'^;"^'/«'^'«i°"  ^'so.  from  the  hot  stean,,  when  first  admitted 
to  the  cylinder  mto  the  interior  walls  thereof,-whence  itisalmos  tn- 
stantly  returned  again  into  the  exhaust  steam,  as  the  temperature  alls 
from  reducfon  of  pressure,  without  having  done  anv  work.-is  admitted 
to  be  a  very  great  source  of  waste,  but  is  entirely  distinct  from  the  exter- 
nal  rad.at.on,  for  .t  is  not  appreciably  affected  by  the  external  tempera- 
ture and  does  vary  with  the  power  demanded,  and  inversely  with  the 
speed  ;  .„  all  of  whtch  details  it  differs  from  external  radiation 

It  IS  true  that  a  locomotive  standing  still  and  not  using  steam  loses 
but  a  trtfl.ng  amount  from  radiation  (about  30  lbs.  per  ifour),  bu  the 
cond,t.ons  are  vastly  different  when  working  against  a  fierce  wind  w  th 

t     Lr.  o°thef    f        •  ""i  "  '^  '"''=""  *°"^'^'  the  evidence  that 
at  least  ,  of  the  fuel  consumed  goes  to  replace  radiated  heat.     If  so  as 

33i  per  cent  goes  for  other  causes  of  wastage,  we  have  50  per  cent  of  ihe 
Pot  M  "".  ^"^'..P""'"" -hich  varies  directly  with  the  power  detnanded. 
Possibly  It  IS  siill  less,  but  it  can  hardly  be  much  more 

The  correctness  of  this  conclusion  is  indicated,  in  a  measure,  by  the  coal 
buned  by  engines  running  light.  An  engine  which  will  burn  60  .0  80  lbs.  per 
mile  with  Its  full  train,  will  burn  20  to  30  lbs.  per  mile  only  ,0  run  itself. 

J17.  Assuming  curve  resistance  to  average  about  i  lb.  per  ton    it  is 
perhaps  as  correct  an  average  as   possible  to  say  that  a  continuous 
M   20  curve  causes  an  average  additional  train  resistance  of  about  6  lbs 
per  ton,  or  about  doubles  the  resistance  of  a  train  on  a  level.     A  mile  in 
length  of  such  a  curve  contains  600°  of  curvature. 

We  may  say,  therefore,  that  600-  of  curvature  will  waste  about  50  per 
eent  as  much  fuel  as  the  average  burned  per  mile  run 

348.  Repairs  of  ENCINES.-Referring  to  Table  85,  page  20,  it  will 
b  seen  that  the  proportion  of  this  item  assignable  to  the  avera^;  effect 

wear  Tr  r*^  r^''  ''  ^''°"'  '9  ^"  ""'•  """"^y  ^"  °f  "  "'^"g  f'om 
wear  of  wheels  and  tires.     Experimental  data  as  to  the  actual  effect  of 

em  er  grades  or  curvature  on  locomotive  or  car  repairs  are  very  few 

statistics  of  actual  expenditures  for  such  purposes  on  lines  differing  con- 


3l6    CHAP.   VIII.— CURVATURE— EFFECT  ON  EXPENSES. 


CHAP. 


VIII.— CUP  VA  TUPE— EFFECT  ON  EXPENSES.      3 1  / 


siderably  in  grades  and  curvature  afford  no  assistance,  except  to  drive 
us  to  the  conclusion  that  curvature  has  little  or  no  effect,  as  we  have  al- 
ready seen  (par.  164). 

349.  We  may  get  at  the  probable  effect  of  curvature  on  engine  re- 
pairs little  more  definitely,  at  least  to  the  extent  of  checking  any  error  of 
consequence,  as  follows  : 

The  ways  in  which  engine  repairs  are  affected  by  curvature  are  two: 
First, — and  more   important,— by  the  additional  wear  of  tires  and 

wheels. 

Secondly,  by  the  effect  on  wear  and  tear  of  the  additional  power  de- 
manded. 

The  last  is  an  inconsiderable  element,  because  the  additional  power 
demanded  by  the  curvature,  even  in  extreme  cases,  is  inconsiderable 
when  measured  in  foot-pounds.  Thus,  if  there  be  300°  in  a  mile, — which 
by  turning  to  Tables  loi  to  104,  page  259,  will  be  seen  to  be  a  very  large 
allowance, — this  amounts  to  less  than  a  continuous  6"  curve,  or  3  lbs.  per 
ton  continuous  addition  to  the  train  resistance.  On  descending  grades 
this  is  rather  a  help,  saving  the  use  of  brakes.  On  ascending  grades  of 
say  I  per  cent  the  normal  train  resistance  is  some  26  lbs.  per  ton,  and  3 
lbs.  per  ton  resistance  adds  but  12  per  cent  to  this.  As,  then,  only  31 
per  cent  of  the  cost  of  engine  repairs  (exclusive  of  running-gear)  varies 
directly  with  the  distance  run  on  tangent,  the  increase,  if  in  direct  pro- 
portion, would  be  only  0.12  x  0.31  =  3.7  per  cent  for  300°,  or  say  7.5  per 
cent  for  600°  of  curvature,  so  far  as  this  cause  alone  is  concerned. 

The  maintenance  of  running-gear  (including  frames,  which  is  a  very 
small  item)  amounts  to  30  per  cent  of  the  total  cost  of  engine  repairs, 
but  of  this,  only  one  third,  or  10  per  cent,  can  properly  be  assigned  to 
the  effect  of  curvature  and  grades.  We  may  assume  that  two  thirds  of 
this,  or  6.7  per  cent  of  the  total  cost  of  engine  repairs,  is  due  to  curva- 
ture. By  turning  to  Table  104.  we  shall  find  that  the  average  amount 
of  curvature  on  an  average  railway  is  some  30°  per  mile.  On  a  contin- 
uous 11°  20' curve,  containing  600°  per  mile,  the  curvature  is  20  times 
this  amount;  and  hence  on  such  a  mile  the  extra  cost  due  to  the  curva- 
ture would  be  6  X  20  =  120  per  cent  of  the  average  cost  of  engine  repairs 
per  mile.  This  seems  to  be,  and  is,  a  rude  process ;  but  it  may  be  further 
checked  as  follows : 

350.  The  cost  of  maintaining  tires  average  on  trunk  lines,  like  the 
Erie  or  Pennsylvania,  about  i^  cts.  per  mile  run,  with  an  average  cost  o 


engme  repairs  of  some  6  cts.  as  a  minimum.  Their  average  curvature 
per  mile  is  some  5o^  The  above  allowance  (of  ,20  per  cent  addition  to 
the  total  cost  of  engine  repairs  by  600"  of  curvature)  is  equivalent  to  al- 
lowing  that  with  continuous  11°  20'  curves  the  total  cost  of  running-gear 
maintenance  would  be  7.2  cts.  per  train-mile,  or  six  times  greater  than  it 
is  now,  on  an  average,  with  twelve  times  as  much  curvature.  While 
this  may  not  be  much  too  large,  it  is  certainly  ample.  See  also  the  fol- 
lowing  data  (Table  114)  as  to  the  wheel  wear  of  cars  and  the  causes 
thereof. 


Table  114. 

Percentages  of  Wheels  removed  in  1884  on  the  New  York.  Lake  Erie 
&  Western  Railroad  for  Various  Causes  of  Each  One  of  Twenty- 
four  Different  Makes. 

(Out  of  a  total  of  some  300,000  wheels  and  18,000  removals.) 

Class  i.-Six  Best  Makers-aggregating  78.2  Per  Cent,  of  All  Wheels  in 

Service. 


Makers. 

Cracked  and  Broken. 

Shelled 
Out. 

Sharp 
Flange. 

Slid 

Flat. 

Worn 

Flat& 

Worn 

Out. 

Total. 

p.  C.  of 

Removals 

to  No.  in 

Service. 

Broken. 

Crack'd 

Total. 

1 

2 

1.3 

a. 7 

5-3 
2.0 

30 

7.2 
6.8 

14.9 
10  I 
23.2 
20.8 

8.4 

9-5 

15-4 

25.2 

23  8 

0.3 

1-7 
0.6 
0.7 
0.6 
0.0 

4.8 
1.9 
1.6 
4-8 
2.6 

1.2 

9.6 
32.9 

259 
29.7 

350 

"•3 

76.9 
64.0 
56.6 

49-4 
36.6 
63.7 

ICO. 

100. 

lOO. 

100. 
100. 
100. 

385 
369 
7.40 

3 

4 

5 

^.00 

6 

2.28 

8  97 

Average 

2.0 

12. 2 

14-4 

07            2-7          22.3 

60.1 

100. 

4-39 

Class  2.~Six  Next  Best  Makers-aggregating  17.2  Per  Cent  of  Wheels  in 

Service. 


7 

a-4 

8.8 

«-3 
31 

17.0 
12.2 
30.8 
37.9 

9-7 
138 

19.4 
147 
33-6 
29.4 
II. 0 
16.9 

0.0 
0.1 
0.1 
0.1 
0.3 
0.0 

6.9 
i6.i 

6.4 

2.9 
23.2 

6.1 

20.8 
20.4 
21.0 
18.8 
33-2 
40.1 

52.9 
48.7 

38.9 
48.8 

323 
36.9 

100. 
100. 
100. 
100. 
100. 
100. 

— 

8 

8.21 

9 

14.63 

9.26 

10.88 

10 "■ 

11 

*I2 

22.5 
8  23 

Average .... 

3.3 

93.7 

25-9 

0.1 

8.3 

2Z.I 

44-7 

100. 

1 

TO.  94 

\h 


m 


318      C//AP.   VIII.— CURVATURE— EFFECT  ON  EXPENSES, 


Table  114. — Continued. 

Class  3.— Twelve  Worst  Makers— aggregating  only  4.6  Per  Cent  op 

Wheels  in  Service. 


Ta        

•9 

3-4 
10.4 
0.0 
6.3 
4-9 

16 
6.0 
0.2 
5.8 
7-5 

71.9 

59-3 

19.0 

0.0 

21.9 

14-5 
8.6 
22.9 
36.2 
88.8 
26.4 
4-5 

72.8 
62.7 
30.0 
0.0 
28.2 

19-4 
,6.5 

24.5 
42.2 
90.0 
32.2 
12.0 

0.0 
0.0 

03 
0.0 
0.0 
0.0 
0.0 
0.0 
0.5 
0.0 
0.0 
0.0 

0.0 
0.0 

54-6 
21.8 
24.1 
9-3 
4.9 
4-6 
I  6 

1.1 

22.3 

83-7 
II. 9 

45-4 
17.8 

15.6 
17.4 

49.6 
44-7 

4-9 
13.6 
43-6 

0.0 
40.6 
38.7 
59-9 
55  0 
35-3 

14 
14.9 

34.4 

100. 
100. 
100. 
100. 
100. 
100. 
100. 
100. 
100. 
100. 
100. 
100. 

14.40 

*J 

T^ ••.. 

3-76 

••  5                ... 

90  5 

♦i.:: 

35-7 

♦♦•17  

12.62 

**i8 

10. 1 

♦♦10 

76.9 

♦20 

14. X 

♦21 

28.9 

22 

25.2 

23 .,., •....• 

5  00 

♦♦♦24 

2.29 

Average  — 

4-4 

37.2 

41.6 

0.0 

12.4 

20.3 

25.7 

100. 

20.l6 

Bold/ace  numbers  represent  makers  having  from  20,000  to  50,000  wheels  each  in  service. 
Starred  numbers  indicate  the  smaller  makers,  viz.,  *  Lets  than  1000  in  service;  •♦  less  than 
500  in  service;  ♦•♦  less  than  300  in  service. 

Summary. 


Ter  cent  of  whole  number  in  service. 

Broken 

■Cracked 


Broken  and  cracked.. 

Shelled  out 

Sharp  flange 

Slid  flat  

Worn  flat  and  worn  out. 


Total  removed 

Per  cent  of  number  in  service  removed. 


Six  Best 
Makers. 


78.2 

a.o 
12.2 


14.2 

0.7 

a  7 

•a. 3 

60.1 


100. o 
4-39 


Six  Next 

Best. 


17.2 

a. 2 

»3.7 


a5.9 

0.1 

8.2 

21. t 

44.7 


100. o 
10.94 


Twelve 

Worst 

Makers. 


4-6 

4-4 
37a 


41.6 
0.0 

12. 4 
20.3 
25.7 


100. 0 

20.16 


Av.  of  all 
on  Road. 


xoo.o 

8-4 

19.4 


21.8 

0.4 

58 

21.7 

50.3 


100. o 

6. 21 


percentage  of  total  number  in  service  removed  for  each  cause. 


Per  cent  of  whole  number  in  service 

Broken 

Cracked 

Broken  and  cracked 

Shelled  out 

Sharp  flange 

Slid  flat 

Worn  flat  and  worn  out 

Toul  removed 


Six  Best 
Makers. 


78.2 

0.09 
0.54 


0.63 
0.03 
0.12 
0.98 
2.63 


4-39 


Six  Next 
Best. 


17.2 

0.23 
2.60 


2  83 
o  01 
0.89 
2. 31 
4.90 


10.94 


Twelve 
Worst. 


4.6 

0.88 
7.50 


8.38 
0.00 
3.50 
4.10 
5.18 


20.16 


Total. 


100. o 

0.15 
i.ao 


I.15 
0.02 
0.36 
1-35 
3»3 


6.31 


CHAP.    VIII,— CURVATURE— EFFECT  ON  EXPENSES.      319 


While  the  above  table  gives  valuable  and  trustworthy  indications  of  the  relative  quali- 
ties of  different  makers,  it  gives  an  entirely  false  idea  0/  the  absolute  qualities  0/ 
American  chilled  car  wheels,  unless  a  large  allowance  is  made  for  the  fact  that  it  is 
modified  immensely  by  the  constant  annual  additions  of  new  stock.  This  is  immediately 
evident  in  the  total  number  removed  for  all  causes,  which  is  only  6.21  per  cent  of  those  in 
service,  indicating  on  its  face  an  average  life  0/  sixteen  years,  which  is  certainly  more 
than  twice  the  actual  average  life  of  wheels  on  the  road  in  question,  and  would  be  much 
more  than  twice  or  even  tliree  times  the  average  life  in  years,  except  that  the  average 
mileage  per  car  p)er  year  has  recently  been  very  low. 

An  average  life  of  eight  years  for  car  wheels  would  require  12)^  per  cent  per  year  aver- 
age renewals,  against  only  6.21  per  cent  actual  renewals— a  discrepancy  of  over  one  half. 
The  constant  additions  of  new  rolling-stock  which  are  known  to  have  been  made  on  the 
road  are  the  only  apparent  cause  for  this  effect.  With  such  an  abnormal  proportion  of 
new  wheels,  the  proportion  of  failures  from  "old  age"  will  be  decreased,  and  hence  that 
the  proportion  of  failures  from  acute  diseases,  such  as  cracked  or  broken,  will  be  abnor- 
mally increased ;  since  in  a  large  proportion  of  the  wheels  these  are  the  only  failures  which 
are  occurring. 

This  table  sheds  especially  valuable  light  on  the  cause  of  sharp  flanges.  It  will  be 
seen  that  there  is  twenty  times  as  large  a  proportion  of  wheels  removed  because  of  sharp 
flanges  among  bad  wheels  as  good  ones,  and  that  with  good  makers  the  proportion  of 
wheels  removed  for  sharp  flanges  (2.7  per  cent,  and  that  on  a  very  crooked  road)  is  so 
small  as  to  indicate  that  bad  quality  of  the  wheel  itself  is  the  leading  cause  of  sharp  flanges. 

Of  broken  or  cracked  wheels,  only  about  one  quarter  break  in  the  flange  or  tread,  and 
nearly  two  thirds  of  the  fractures  arise  from  the  bursting  strains  produced  by  forcing  the 
wheels  on  the  axles. 


351.  Repairs  of  Cars.— In  Table  86,  page  203,  the  proportion  of  the 
cost  of  this  item  assignable  to  the  effect  of  grades  and  curvature  is  given 
as  some  23  per  cent.  Of  this  at  least  three  fourths  would  ordinarily  be 
assignable  to  the  effect  of  grades  and  only  one  fourth  to  curvature. 
Then,  proceeding  exactly  as  in  the  case  of  engine  repairs,  we  have  6  x  20 
=  120  per  cent  of  the  average  total  cost  of  car  repairs  per  mile  as  the  extra 
cost  due  to  600°  of  curvature.  This  estimate  is  certainly  large  enough, 
and  probably  considerably  too  large. 

An  exact  distribution  of  the  cost  of  rolling-stock  repairs  to  its  various 
causes  is  very  difficult,  because  the  expenses  are  not  ordinarily  kept  by 
Items,  but  only  by  aggregates.  Some  recent  statistics  as  to  wheel  wear, 
however  (the  chief  and  almost  the  only  item  of  car  repairs  affected  by 
curvature),  given  in  Table  1 14,  afford  some  valuable  insight  into  the  causes 
which  destroy  them  most,  and  indicate  that  the  wear  from  curvature  is 
a  comparatively  minor  element. 

362.  Wear  of  Rails.— We  may  take  the  wear  of  good    rails  on 
curves,  as  an  average  of  their  whole  life,  at  about  \  lb.  per  10,000.000  tons 


, 


i: 


320     CI/AF.   VIII.— CURVATURE—EFFECT  ON  EXPENSES, 


per  degree  of  curve,  or  certainly  not  more  than  this.  Observations  by 
the  writer  on  the  railroads  of  the  New  York,  Pennsylvania  &  Ohio  Rail- 
road, and  some  more  elaborate  investigations  on  the  Pennsylvania  Rail- 
road by  Dr.  Charles  B.  Dudley,  agree  in  indicating  this,  when  allowance 
is  made  for  the  fact  that  the  wear  is  not  at  a  uniform  rate  during  the 
whole  life  of  the  rail  (par.  ix-^^et  seq.\  but  is  perhaps,  rudely  speaking, 
only  one  fourth  of  the  total  during  the  first  half  of  its  life  and  three 
fourths  during  the  latter  half.  As  a  consequence,  as  already  pointed  out 
(par.  315).  the  wear  shown  by  an  investigation  of  a  lot  of  rails  of  the 
same  absolute  age  on  different  curves  will  apparently  indicate  a  very  much 
greater  wear  on  sharp  curves;  but  this  appearance  is  deceptive. 

The  wear  in  tangents,  then,  being  (as  it  is)  about  i  lb.  per  10,000,000 
tons  duty,  the  wear  on  a  continuous  11*  20'  curve  will  be  i  lb.  x  ii^  = 
5f  lbs.  per  mile  of  curve,  or  be  increased  567  per  cent  over  the  tangent 
wear.  But  this  is  assuming  that  the  tangent  rails  are  so  good  that  they 
will  need  renewals  only  from  the  effect  of  abrasion,  in  which  case  rails 
will  cost  only  about  ict.  per  train-mile. 

With  inferior  steel  rails,  as  formerly  with  iron  rails,  the  proportionate 
increase  of  wear  is  very  much  less  than  this,  owing  simply  to  the  fact 
that  the  tangent  wear  is  so  very  much  greater.  The  additional  rail 
wear  on  curves  was  estimated  by  the  writer  in  the  first  edition  of  this 
treatise— and,  so  far  as  he  can  now  judge,  with  very  close  correctness— 
at  100  per  cent  increase  over  the  tangent  wear  on  an  11°  20'  curve.  The 
absolute  rate  of  abrasion  is  much  the  same  with  all  rails,  iron  or  steel, 
good  or  bad.  With  rails  that  fail  only  by  abrasion,  therefore,  the  curve 
wear  adds  a  large  percentage  to  a  very  small  total  cost.  With  rails 
that  mash  or  split  in  service,  the  curve  wear  becomes  a  much  smaller 
percentage  of  a  much  larger  total. 

353.  Cross-ties.— The  effect  of  curvature  on  ties  has  been  much  de- 
creased by  the  introduction  of  steel  rails,  and  will  be  still  further  and  very 
largely  decreased  by  the  introduction  of  creosoted  ties.  Still  its  effect 
on  the  life  of  ties  is  considerable.  Several  years  of  the  tie's  life  must  be 
sacrificed  on  sharp  curves  because  the  holding  power  of  the  spike  be- 
comes too  little.  The  so-called  "  cutting"  of  ties  (par.  121)  isalso«ireater 
on  curves,  and  mainly  on  the  outside  of  the  rail.  As  the  rail  wears  by 
flange  cutting,  moreover,  it  is  necessary  either  to  renew  the  rails  prema- 
turely or  to  throw  them  in  to  gauge.  The  effect  of  all  these  causes  to- 
gether to  shorten  the  life  of  ties  is  a  pure  matter  of  fact;  and  considerable 
observation  of  and  inquiry  as  to  practice  in  this  respect  indicates  that 
the  following  comes  very  near  to  the  average  life  of  white-oak  ties  oR 


CHAP.   VIII.-CURVATURE-EFFECT  ON  EXPENSES.      32 1 

'  I . 

sand  or  gravel   ballast,  imperfectly  drained-the    life  given   on  cui-ves 
bemg,  if  anything,  too  short : 

On  a  tangent, 


On  a  2°  curve,  ,  , 
On  a  6°  curve,  .  , 
On  a  10°  curve,  .  . 
On  a  14°  to"  16*'  curve 


9  years. 
8 

7 
6 

5 


«< 


From  this  we  may  conclude  that  the  cost  for  ties  on  an  i,°  20'  curve 
(600  per  nnle)  IS  about  50  per  cent  greater  than  on  a  tangent,  and  t^t 
the  mcrease  is  directly  as  the  degree  of  curvature  on  any  gfven  distance' 
or,  in  other  words,  is  uniform  per  degree,  whatever  the  radius"  ' 

354.  Track  Labor  is,  as  a  matter  of  fact,  but  little  affected  bv 
curvacure.  It  is  an  unusual  thing  to  see  sections  made  shorter  thai 
others  on  th.s  account.  If  two  contiguous  sectionsare  noticeably  differ^ 
ent  in  this  respect  it  is  not  unusual  to  take  a  quarter  or  half  a  mile  off 
one  and  add  it  to  the  other,  but  any  greater  difference  than  this  is  un- 
likely. Yet  comparing  the  conditions  which  would  exist  on  a  mile  of 
tangent  and  a  mile  of  11°  20'  curve,  it  might  not  unfairly  be  claimed  that 
there  would  be  a  difference  of  50  per  cent  in  the  cost  of  track  labor;  and  to 
avoid  that  very  objectionable  result,  an  underestimate  of  the  disadvan- 
tages  of  curvature,  we  may  assume  this,  which  will  amply  cover  the  facts. 

355.  Summing  up  the  various  Items  affected  by  Curva- 
ture,  we  obtain  the  following  Table  115,  giving  the  assumed 
eflect  on  expenses  of  600°  of  curvature. 

The  total  cost  per  year  per  daily  train  of  1°  of  curvature  given 
below,  Table  115  (43.3  cts.),  divided  by  the  rate  of  interest  on 
capital,  will  give  the  justifiable  expenditure  to  save  1°  of  curva- 
ture estimated  per  daily  train,  viz.: 

At    5  per  cent, %^AZZ 


At   8  per  cent,  . 


0.05 

.0-433 
0.8 


At  10  per  cent, ^-^33      _ 


o.  10 


541. 
4-33- 


And  similarly  for  any  other  rate  of  interest;  this  being  assumed 
as  heretofore,  not  to  be  a  precisely  accurate  result,  but  one  as 
exact  as  is  either  practicable  or  necessary  to  avoid  serious  errors- 

21  * 


, 


\ 


322      CHAP,   VIII.^CURVATURE^EFFECT  ON  EXPENSES. 

Table  115. 
Estimated  Average  Cost  Per  Train-Mile  of  600"  of  Curvature. 

[Being  equivalent  to  a  continuous  ii*  ao'  curve,  one  mile  long,  assumed  to  double  the 

average  train  resistance  in  lbs.  per  tons.] 

(Cost  of  train-mile  assumed  at  fi.oo.)  


Item. 
(As  per  Table  80.) 


Average 

Cost  of  liem. 

Cts.  or  Per 

Cent. 


Ftrel 

Water 

Oil  and  waste 

Repairs,  engines • .  • 

Switching-engines  service. 
Train  wages  and  supplies 

Repairs,  cars 

Car  mileage 

Rail  renewals 

Adjusting  track 

Renewing  ties 

Earthwork,  ballast,  etc., 

Yards  and  structures 

Station  and  general 


Total  cost  per  train-mile  of  600' 
of  curvature  (cts.  or  per  cent). 


7.6 
0.4 
0.8 
5.6 
5-a 
15.4 
10. o 
2.0 
2.0 
6.0 
30 
4.0 
8.0 
30.0 


Per  Cent  added  by 

6oo»  of  Curvature, 

as  above. 


Cost  due  to 
Curvature. 


lOO.O 


50  per  cent. 

3.8 

25    "       •* 

0.1 

25    "       " 

0.2 

125    "       " 

7.0 

Unaffected. 

•  •  •   1  •  •  • 

120  per  cent. 

12.0 

Unaffected. 

300  per  cent. 

6.0 

50    -       " 

30 

50    "       •• 

1.5 

50    "       " 

2.0 

Unaffected. 

35.6  per  cent. 


35-6 


35* 


=     -0593  <*• 


Total  cost  per  train-mile  per  degree,  -^ 

of  !•  of  curvature  per  year  per  daUy  train  (.0593  ct.  x  3*5  X  2)  =  43-3     ^s. 


Total  cost 


ed 


356.  The  similar  estimate  which  the  writer  made  in  the  first 
ition  of  this  treatise  gave  a  smaller  estimate  for  the  value  o 
curvature  than  this,  viz..  ».s  cts.  instead  of  35-6  fo-"  the  cost 
cer  train-mile  of  600°  of  curvature-a  difference  of  over  50  per 
cent-  and  this  in  spite  of  the  fact  that  the  former  estimate  was 
for  the  most  part  on  an  iron-rail  basis.  The  only  positive  reason 
for  this  difference  is  that  the  writer  has  seen  reason  to  increase 
the  estimate  of  the  effect  of  curvatur-^  on  rolling-stock  repairs,  al- 
though a  chief  reason  has  been  to  ensure  that  the  estimate  was 
Urge  enough.  According  to  the  above  estimate,  the  total  cost 
of  atrain-m.leshould  be  10  per  cent  greater  on  a  road  having  100 
aiore  curvature,  whicli  is  the  most  that  the  evidence  warrants. 


CHAP.  VIII—CURVATURE-EFFECT  ON  EXPENSES.      323 

397.  To  illustrate  how  very  little  difference  any  probable  error 
m  the  above  estimate  can  make  in  the  justifiable  expenditure  to 
avoid  curvature:  Assuming  the  case  of  a  road  running  .0  dailv 
trains  each  way,  the  justifiable  expenditure  to  save  1°  of  curva- 
ture, at  8  per  cent,  is  $54.  ,0,  and  to  save  20°,  $1082.00;  a  sum  which 
will  warrant  no  very  large  amount  of  work  to  avoid  it.     The 

ANNUAL   LOSS  TO   REVENUE   IF  IT   BE   NOT   AVOIDED  will  be 

43-3  cts.  X  10  trains  X  20°  =  $86.60; 

a  sum  sufficient  to  pay  for  perhaps  two  extra  trains  over  the  road 
dunng  the  year  or  for  running  7302  trains  instead  of  7300  When 
the  effect  of  the  most  trifling  difference  of  grade  is  compared  with 
this  It  becomes  slight  indeed. 

388.  This  example  is  for  a  considerable  traffic  and  for  a  con- 
siderable amount  of  curvature,  to  save  at  one  point.     As  such 
It  well  Illustrates  the  principal  purpose  of  such  estimates  as  we 
have  just  made.     It  is  not  to  avoid  errors  of  10,  20,  or  even  50  or 
100  per  cent  in  the  sums  spent  to  save  curvature;  for  we  cannot 
go  far  wrong   if   we  assume   either  $700  or  $800  or  $1200  or 
$.500  as  our  standard  value  for  such  an  amount  of  curvature 
instead  of  $,058.    But  its  principal  purpose  is  to  save  us  from  the 
manifold  greater  errors  which  may  so  easily  result  from  follow- 
ing mere  guesswork  and  "judgment:"  from  spending  $cooo  or 
$.0,000  to  gain  something  whose  true  value  lies  between  $'700 
and  $,soo,  as  has  been  done  in  many  cases  on  heavy  work*  or 
from  the  corresponding  error  of  introducing  10°  or  20°  of  curva- 
ture recklessly,  which  might  be  saved  at  trifling  cost,  or  perhaos 
at  no  cost  at  all,  by  a  little  more  care. 

359.  All  the  preceding  estimate  of  the  direct  cost  of  curvature 
has  been  based  upon  the  assumption  that  the  cost  per  degree 
was  for  the  most  part  uniform  for  all  curves,  independenf  of 
radius;  i.e.,  that  the  cost  of  the  curvature  in  100  stations  of  .• 
curve  was  essentially  the  same  as  that  in  10  stations  of  .0°  curve 
This  assumption  appears  to  be  unquestionably  justified  bv  the 
facts,  but  the  reasons  why  it  is  so  are  considered  later,  in  Chap. 
AlX.,  page  638.  ^ 


if 


lii 


m 


324      CI/AF.   VIIL-CURVATURE-EFFECT  ON  EXPENSES, 

360.  A  particular  form  of  bad  practice  in  respect  to  curva- 
ture and  one  of  the  most  prevalent  and  indefensible  of  the  minor 
errors  of  location,  is  a  weakness  for  very  long  tangents  and  a 
readiness  to  spend  money  to  secure  them.     A  reasonably  long 
tangent,  say  not  less  than  400  feet,  is  always  very  desirable,  if  not 
absolutely  essential,  in  order  to  taper  out  the  superelevation  and 
afford  room  for  proper  transition  curves;  but  beyond  this  there 
is  no  justification,  theoretical  or  practical,  for  expending  more 
than  a  very  small  sum  to  avoid  any  number  of  short  and  gentle 
curves     The  difference  in  distance  resulting  from  even  very  con- 
siderable  and  frequent  breaks  in  a  tangent  is  too  trivial  to  be  a 
serious  consideration  on  lines  of  small  traffic  (although  it  may 
look  as  if  it  were  considerable,  especially  on   the  ground;   see 
Chap    XXVIII.),  and    the  same  is  at  least  equally  true  of  the 
curvature.     Thus  let  us  suppose  that  there  is  a  section  of  a  mile 
and  a  half  out  of  one  of  those  four-  or  five-mile   tangents,  in 
moderately   difficult    country,   for  which    the   following   curved, 
alignment  may  be  substituted  with  some  economy  in  first  cosU 


CURVBS. 


1°  Z    for  300  ft. 


2' 

2' 

2* 


•  L 
'°  R 

'"  L 


«< 


600 

600  " 

500  •• 

200  •• 


Central 
Angle. 


12° 

10° 


Total. 


38' 


Toul  Length  of 

Tan>;ents  between 

Intersections. 


2,500  ft. 

2.500  •• 

2,000  " 

1,100  " 


8,100  ft. 


Such  an  alternate  alignment  would  perhaps  have  the  effect  of 
reducing  a  succession  of  considerable  cuts  and  fills  materially. 
How  much  does  it  damage  the  operating  value  of  the  line  ? 

The  difference  in  distance  is  as  nearly  as  may  be  23  f eet  m 
about  8350.  The  amount  of  curvature  introduced  is  38  •  Then 
to  an  hypothetical  line  running  10  trains  per  day  each  way  and 


CHAP.   VIII.— CURVATURE— EFFECT  ON  EXPENSES.      325 

paying  8  per  cent  for  capital  the  value  of  the  difference  would 
be — 

23  feet  distance  at  (possibly)  0.30  cts.  X  10,     $69  00 
38    curvature  at  $5.41  x  10, 2,055   80 

^°^^^» $2,124  80 

Many  a  tangent  has  been  broken  up  improperly  to  effect  less 
saving  than  this;  but,  on  the  other  hand,  a  saving  of  8000  to 
10,000  cubic  yards  of  excavation  is  enough  to  balance  it;  and  if 
we  reduce  the  estimated  traffic  by  two  thirds  or  three  quarters, 
in  all  ordinary  country  the  saving  by  breaking  up  tlie  tangent 
would  far  more  than  justify  doing  so,  even  in  light  work,  for  the 
above  figures  fully  represent  every  measurable  disadvantage 
from  a  moderately  curved  line  of  that  character. 

Especially  if  the  general  character  of  the  work  is  heavy,  the 
caution  of  par.  14  becomes  of  vital  moment  on  such  alignment 
if  the  most  careful  engineer  would  avoid  error. 

Table  116. 
Sharpest  Curves  in  Regular  Use  on  Standard-Guage  Roads. 

(Chiefly  from  a  list  published  in  the  Railroad  Gazette  of  Oct.  4,  1878.) 


N.  Y.,  New  Haven  &  Hartford. 
Lehigh  &  Susquehanna 


<( 


14 


Baltimore  &  Ohio. 


M 
ii 


Oroya  Railroad. 
Virginia  Central 


Pennsylvania  Railroad  tracks 

Pittsburg,  Fort  Wayne  &  Chicago 

Canarsie  &  Rockaway 

Brooklyn,  Bath  &  Coney  Island..  , 

Manhattan  Elevated 

Petersburg,  Va 


Springfield,  Mass 

Upper  Divisions 

Stony  Creek 

Butler  Branch 

Harper's  Ferry,  Md.  side.... 

Ilchester 

Harper's  Ferry,  Va.  side 

Y  for  Consolidation  Engines. 

In  Peru 

Over  Rockfish  Gap  Tunnel... 


Centennial  Grounds. 

Pittsburg 

Brooklyn 


New  York  City 

U.  S.  Military  Railway. 


410 

383 
320 
310 
400 

375 
300 

136 

395 
300 
238 
300 
246 

175 
55  to  125 

90,  loo,  103.5, 
125,  150 

50 


15" 
i8« 

18°  32' 
14°  22' 
15°  20' 
19°  lO* 
43* 

14°  32' 
19"  i</ 
24»  15' 
19°  ic/ 

23*30' 

33°  15* 


}   63" 


!i'; 


326      CHAP.   VIIL^CURVATURE— EFFECT  ON  EXPENSES. 

The  curve  last  given  was  thus  described  in  a  discussion,  by  Mr.  C.  L.  McAlpine,  of  a 
paper  by  Mr.  C.  Whinery  (Trans.  Am.  Soc.  C.  E.,  1876),  and  is  one  of  the  most  remark- 
able on  record : 

"  Petersburg  and  Richmond,  Virginia,  fell  into  the  hands  of  the  Federal  troops  near  the 
close  of  the  war.  The  base  of  the  latier  for  many  months  had  rfeen  at  City  Point,  on  the  James 

"  Early  one  morning  imperative  orders  were  received  to  run  the  trains  of  the  United  State* 
Miliury  Railways  into  Petersburg  with  the  least  possible  delay.  This  was  done  by  noon  of 
the  same  day,  under  circumstances  that  would  be  most  interesting,  but  foreign  to  the  subject 
under  discussion. 

'•  This  order  was  followed  up  by  another— that  railroad  communication  with  Richmond 

should  be  effected  at  once. 

"  The  railroad  bridge  at  Petersburg,  over  the  Appomattox,  had  been  burned.  No  connec- 
tion at  that  place  had  ever  been  made  in  peace  limes,  and  the  tirst  examinations  showed  that 
heavy  excavations,  etc.,  requiring  time  (for  which  the  department  never  made  allowance), 
must  be  made,  before  any  reasonable  connection  with  the  Richmond  line  could  be  effected. 
This  drove  the  engineer  in  charge  into  the  apparently  inadmissible  curve  adopted. 

"  Contrary  to  the  advice  of  trackman  and  bridge-builders,  a  sharp  curve  was  laid  out,  of 
more  than  one  hundred  dc-rccs,  with  a  radius  of  fifty  feet,  on  what  was  to  become  the  mam 
line  The  curve  was  on  trestle-work,  and  the  outside  posts  were  framed  eight  inches  longer 
than  the  inner  ones.  The  lies  were  of  sound  white  pine,  three  inches  in  thickness,  and  the 
rails  were  double  spiked.     Two  guard  rails  were  used,  also  double  spiked. 

"  The  locomotive  engineers  generally  condemned  the  bridge  and  curve  at  first  sight  after 
completion,  and  a  strong  prejudice  was  created  against  it.  But  the  writer  selected  the  worst 
curve-following  engine  in  the  service,  the  '  Government.'  and  ordered  her  to  make  the  first 

"*'  Walking  backwards,  and  in  front,  as  this  engine  slowly  made  its  way,  it  was  easy  to  per- 
ceive her  action  on  this  sharp  curve.  .      ,    ..  ,         ^ 
"  A  little  pressure  on  the  outer  rail  seemed  to  drive  the  wheels  (both  of  the  trucks  and 
drivers)  down  on  to  the  inner  rail,  and  demonstrated  practically  what  had  been  intended,  that 
the  trains  must  be  passed  through  the  curve  at  greater  speed. 

"  Thereafter,  when  the  locomotive  men  became  accustomed  to  the  curve,  the  speed  through 
it  was  usually  from  eight  to  ten  miles  an  hour.  ....  •        * 

"  A  very  large  traffic  passed  over  this  curve  for  months  afterwards,  supplying  the  armies  of 
occupation  in  Richmond,  and  at  other  points  to  the  southward,  and  no  accident  or  trouble- 
whatever  was  experienced  at  the  place  in  question." 

On  the  4  per  cent  grades  of  the  Mexican  Railway,  reversed  curves  of  150  ft.  radius  on 
temporary  track  around  tunnels  were  operated  by  ordinary  locomotives  for  a  year  or 
more  at  its  first  opening,  and  many  other  cases  of  such  temporary  use  of  very  sharp 
curves  might  be  adduced.  All  of  the  above  curves,  however,  are  in  permanent  track,  al- 
though  most  of  them  are  in  localities  where  it  is  convenient  to  operate  them  at  very  slow 
speeds.     The  sharpest  curves  on  the  open  road  of  three  of  the  trunk  lines  are  : 

New  York,  Lake  Erie  &  Western, 10° 

Pennsylvania ^ 

Baltimore  &  Ohio 9^ 

The  first  of  these  curves  is  a  reversed  curve  at  Passaic,  a  few  miles  out  of  New  York., 
and  an  enormous  traffic  passes  over  it.  It  could  be  taken  out  at  very  moderate  expense, 
but  has  not  proved  sufficiently  objectionable  to  make  this  appear  worth  while.  The  New 
York  Central  has  one  very  sharp  curve  of  about  i4»  on  its  main  line,  but  in  a  yard 

where  speed  is  slow.  .     ,  ♦i,^ 

Narrow-gauge  roads  have  rarely  used  sharper  than  24'  curv-es  in  any  part  of  the 
world,  although  a  few  as  sharp  as  30"  are  in  use  in  Colorado  and  elsewhere. 


CHAP.    IX.— RISE  AND  FALL. 


Z^7 


CHAPTER   IX. 


RISE    AND    FALL. 


361.  The  expense  of  gradients,  as  we  saw  in  part  in  Chapter 
VI.,  arises  from  two  causes,  which  are  totally  distinct  and  must 
be  kept  so  to  form  any  correct  estimate  of  their  cost  or  of  their 
proper  adjustment.  The  association  between  them  is  accidental. 
The  distinction  between  them  is  vital  and  fundamental. 

The  FIRST  of  these  causes  is  the  direct  cost,  for  wear  and  tear 
and  fuel,  of  ascending  to  and  descending  from  any  given  eleva- 
tion, instead  of  running  on  a  level;  in  other  words,  the  cost  of 
RISE  AND  FALL.  This  is  the  branch  of  the  subject  that  we  pro- 
pose now  to  consider. 

The  second  objection  to  gradients  is  the  effect  which  the 
maximum  or  rather  ruling  grade  (since  the  ruling  grade  may, 
owing  to  the  effect  of  variations  of  velocity,  be  either  greater  or 
less  than  the  nominal  maximum  of  the  profile)  has  to  increase 
the  cost  of  operating  the  entire  line,  however  short  the  ruling 
grade  itself  may  be,  not  by  increasing  the  direct  expense  per 
train-mile,  but  by  limiting  the  number  of  cars  to  a  train. 

362.  This  latter  objection  to  gradients  (i.e.,  to  one  particular 
gradient,  the  worst  one  on  the  line)  is  greatly  more  important 
than  the  former,  but  it  has  no  real  connection  with  it  whatever, 
being  different  both  in  its  nature  and  in  its  effect  in  detail  on  the 
operating  expenses. 

In  fact,  it  is  not,  properly  speaking,  an  attribute  of  gradients 
at  all,  except  that,  owing  to  the  limitations  of  the  locomotive 
engine,  gradients  happen  to  be  the  most  usual  cause  which 
limits  the  weight  of  trains.  But  this  is  not  invariably  so.  Some- 
times curvature,  and  not  gradients,  is  the  limiting  agent.  For 
example,  the  Hudson  River  Railroad  probably  approaches  the 


i* 

■ ), 


328 


CHAP.   IX.— RISE  AND  FALL, 


CHAP.   IX.— RISE  AND  FALL. 


329 


:i 


= 


nearest  to  being  on  a  direct  level  throughout  of  any  line  of  its 
length  in  the  world,  yet  in  laying  out  that  line  the  locating  en- 
gineer has  freely  introduced,  upon  slight  occasion,  short  gra- 
dients of  0.3  to  0.5  per  cent  (15  to  25  ft.  per  mile),  which  could 
have  been  avoided  at  slight  expense  ;  and  wisely  so,  because  the 
unavoidably  sharp  curvature  of  the  line  effectually  limits  the 
weight  of  trains  to  such  as  is  easily  hauled  on  a  considerable 
gradient.  Up  to  a  certain  grade,  therefore,  curvature  takes  on 
this  line  the  place  of  gradients  as  a  limiting  agent.  Had  the 
topography  of  the  Hudson  River  permitted  such  an  alignment  as 
that  of  the  Canada  Southern  Railway,  for  example,  which  has 
no  curvature  to  speak  of,  a  very  great  expenditure  might  have 
been  justifiable  to  eliminate  these  same  gradients  which  have 
tiius  been  freelv  and  wiselv  introduced. 

363.  And  if  at  some  time  in  the  future  the  locomotive  engine 
should  be  so  improved,  or  such  new  motor  discovered,  as  to  be  able 
to  exert  an  indefinitely  varying  power  according  to  the  need  at 
various  points  on  the  line  (even  if  the  cost  for  power  were  no 
less  per  foot-pound  than  now),  all  objections  to  both  grades  and 
curvature  except  such  as  is  inherent  in  them — the  resulting 
wear  and  tear  and  waste  of  fuel — would  disappear,  and  they 
might  be  introduced  with  great  freedom  ;  for  neither  of  them 
would  then  have  in  addition  to  their  own  inherent  disadvantages 
the  further  effect  of  limiting  the  weight  of  trains. 

The  strength  of  couplings  would  then,  perhaps,  become  the 
limiting  agent,  and  all  that  great  value  which  now  attaches  to  the 
reduction  of  the  rate  of  grades  would  be  taken  bodily  from  it 
and  transferred  to  securing  the  strongest  possible  coupling.  The 
direct  cost  of  the  rise  and  fall  on  those  gradients,  however  (its 
effect  to  cause  wear  and  waste  power),  might  remain  entirely  un- 
affected. 

Some  radical  change  of  this  kind  seems  possible— it  might  almost  be 
said  imminent— from  the  development  of  electricity  as  a  motive-power. 
An  electric  motor  so  simple  that  it  could  be  applied  to  each  axle  of  every 
car  would  revolutionize  the  art  of  laying  out  and  operating  railways. 

364.  To  put  into  technical  terms  the  whole  distinction  between  rise  and 
fall  proper  and  limiting  effect  on  trains.  The  cost  of  rise  and  fall  bears  a 


closely  approximate  ratio  to  the  foot-pounds  of  work  required  to  lift  a 
train  a  feet  high,  which  is  independent  of  the  rate  of  the  grade.  Any  new 
electrical  or  other  motor  might  and  probably  would  leave  the  cost  of 
power  per  foot-pound— which  is  a  small  matter  as  it  is— entirely  unaf- 
fected. But  the  great  objection  to  heavy  gradients  on  railways  as  at 
present  operated  lies,  not  in  their  effect  to  increase  the  foot-pounds  of 
work  to  be  performed,  but  in  the  increase  which  they  cause  in  Xh^ pounds 
of  tension  which  the  locomotive  is  required  to  exert  while  on  them.  The 
pounds  of  tension  which  the  locomotive  can  exert  being,  from  its  con- 
struction, strictly  limited,  we  are  obliged  to  increase  Wi^feet  passed  over 
in  surmounting  elevations  (i.e..  to  reduce  the  rate  of  grade)  by  every  pos- 
sible device,  and  at  large  expense,  in  order  to  enable  the  locomotive  to 
pull  large  trains. 

This  lack  of  adaptability  in  the  locomotive,  i.e.,  inability  to  exert  any 
pull  whatever  if  the  speed  be  reduced  enough,  or  to  give  any  speed  what- 
ever if  the  resistance  be  reduced  enough,  is  its  greatest  mechanical  defect. 
A  partial  remedy  lias  been  found  in  rack  railways,  etc.,  as  noted  in 
Chap.  XI. 

365.  It  therefore  results  that  the  cost  of  a  ruling  grade  is 
directly  as  the  rate  of  grade  and  independent  of  its  length  or  of 
the  elevation  surmounted,  while,  per  contra,  the  cost  of  rise  and 
fall  is  directly  as  the  elevation  surmounted,  and  (within  moder- 
ate limits)  independent  of  the  rate. 

366.  This  contrast  alone  is  enough  to  show  the  radical  dis- 
tinction between  them ;  but  while  the  distinction  is  readily 
enough  admitted  in  the  abstract,  it  is  frequently  confused  in 
practice,  and  such  a  practical  confusion  of  these  two  wholly  dis- 
tinct objections  to  gradients  destroys  the  value  of  any  discus- 
sion or  estimate  of  either,  and  forbids  any  clear  understanding 
of  the  proper  adjustment  of  grades  ;  leading,  on  the  one  hand, 
to  very  erroneous  theories  that  "undulating  gradients"  (in  other 
words,  mere  surface  roads  on  any  convenient  grade)  are  not 
seriously  objectionable,-— which  in  some  cases,  on  some  parts  of 
a  line,  may  be  very  nearly  the  case,— and,  on  the  other  hand,  to 
equally  mistaken  expenditures  to  introduce  as  long  and  as 
nearly  level  grades  as  possible  at  all  points  of  the  line  indiscrim- 
inately.    The  latter  is  a  particularly  dangerous  and  common 


330 


CHAP.    IX.— RISE  AND  FALL. 


CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY,     331 


illi 


II 


error.  By  trusting  chiefly  to  one's  impressions  or  "  experience"* 
in  such  matters,  habit  may  make  it  a  second  nature  to  reduce  all 
grades  as  much  and  as  speedily  as  possible,  and  to  stretch  out 
the  longest  piece  of  thread  which  can  be  made  to  lie  on  the  pro- 
file in  fixing  the  grades.  A  thousand  feet  further  is  not  far  on 
the  profile,  but  it  often  entails  a  considerable  expense  for  con- 
struction to  no  purpose  whatever.  On  the  other  hand,  the  con- 
trary error — an  undiscriminating  readiness  to  use  "  undulating 
grades" — has  seriously  reduced  the  value  of  more  miles  of  railway 
in  the  Western  United  States,  perhaps,  than  all  the  other  causes 
combined  ;  because,  unfortunately,  nature  has  left  it  possible  in 
that  region  to  run  almost  from  anywhere  to  anywhere  in  very 
nearly  an  air-line  if  we  are  willing  to  accept  what  are  euphem- 
istically called  *'  moderate"  grades  of  25  to  75  feet  per  mile ;  in- 
stead of  the  dead  level,  or  nearly  that,  which  in  many  cases  was 
equally  easy  to  obtain  by  moderate  deviations  from  some  "  50- 
mile  tangent." 

367.  To  some  extent  the  cost  of  rise  and  fall,  as  well  as  the 
limiting  effect  of  gradients,  depends  upon  the  rate  of  grade,  for 
it  must  be  divided,  as  respects  cost  and  disadvantages,  into  three 
quite  distinct  classes,  according  to  the  grades  on  which  it 
occurs. 

These  classes  are : 

A.  Rise  and  fall  on  grades  so  light  or  so  situated  as  never  to 
require  the  use  of  brakes  nor  variations  in  the  power  of  the 
engine. 

B.  Rise  and  fall  on  grades  heavy  enough  to  require  the 
slight  use  of  brakes  or  shutting  off  steam,  or  both,  in  descend- 
ing, but  not  such  as  to  be  a  serious  tax  upon  the  engme  in 
ascending. 

C.  Rise  and  fall  on  maximum  grades,  requiring  the  full  power 
of  the  engine  m  ascending,  with  more  or  less  use  of  sand,  danger 
of  slipping  drivers,  and  the  use  of  brakes  in  descending. 

To  which  one  of  these  classes  any  given  grade  will  belong,. 
will  depend  in  good  part  upon  the  general  character  of  the  line  r 


but  as   between  the  classes   themselves   there  is   a  marked  and 
decided  difference  in  cost,  in  passing  from  one  to  the  other. 

In  order  to  determine  the  method  by  which  they  may  be  cor- 
rectly distinguished  from  each  other,  it  will  be  necessary  to 
consider  now  one  of  the  most  important  departments  of  the 
subject  of  ruling  or  limiting  gradients,  as  well  as  of  rise  and 
fall,  viz.: 

THE  LAWS  OF  ACCELERATED  AND  RETARDED  MOTION,  AND  THE 
EFFECT  THEREOF  ON  THE  MOVEMENT  OF  TRAINS. 

368.  We  cannot  go  into  the  general  theory  of  this  question  as  fully  as 
might  be  desirable,  because  the  final  results  of  such  a  discussion,  which  we  shall 
need  to  use,  will  be  in  so  simple  a  form  that  any  one  can  use  them  almost  me- 
chanically. The  student  is  urgently  recommended,  if  not  already  familiar  with 
the  general  laws  of  mechanics,  to  study  and  master  the  elementary  principles  at 
least  of  theoretical  mechanics,  which  it  requires  no  great  labor  to  do.  Almost 
any  treatise,  thoroughly  mastered,  will  suffice,  but  Todhunter's  "Mechanics 
for  Beginners"  (the  title  being  somewhat  misleading)  is  particularly  useful  for 
those  who  desire  to  go  thoroughly  into  the  subject,  and  test  their  knowledge  by 
example.  In  this  respect  Todhunter's  entire  mathematical  series  are  quite  un- 
equalled. A  fair  but  in  some  r^pects  deficient  general  idea  can  be  obtained 
from  Trautwine's  **  Pocket-Book,"  which  may  be  assumed  to  be  in  the  hands  of 
every  engineer.  The  writer  knows  of  no  treatise  in  which  the  important  prac- 
tical applications  of  these  general  principles  which  we  are  about  to  discuss  are 
more  than  obscurely  hinted  at. 

369.  A  railway  train,  or  any  other  body,  acted  upon  by  any  force  or 
any  number  of  forces,  as  gravity,  the  tractive  power  of  the  locomotive, 
friction,  etc.,  which  are  for  the  time  being  uniform  in  their  action  and 
yet  do  not  exactly  balance  and  destroy  each  other,  is  under  the  condition 
technically  known  as  uniformly  accelerated  or  retarded  motion,  the  laws 
of  which  are  the  same  as  for  a  body  falling  freely  in  a  vacuum,  acted  upon 
by  gravity  alone.  Rather,  the  latter  also  is  but  one  particular  case  of  a 
general  law. 

When  one  of  the  forces,  as  train  resistance  or  air  resistance,  is  not 
constant,  but  increases  or  decreases  with  the  velocity,  the  body  will  not 
be  governed  by  the  laws  of  uniformly  accelerated  motion,  but  by  laws 
much  more  complicated.  Within  moderate  limits,  however,  and  within 
limits  sufficiently  broad  for  our  present  purposes,  the  motion  may  be  as- 
sumed to  be  uniformly  accelerated  or  retarded  without  sensible  error,. 
and  we  shall  so  consider  it,  except  where  otherwise  explicitly  stated. 


1^ 

I 


w 


332     CHAP,  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY. 

370.  All  energy  or  work  communicated  to  any  body  must  be  em- 
ployed either  (i)  in  overcoming  frictional  or  other  resistances,  or  (2) 
stored  up,  so  to  speak,  within  the  body,  in  the  form  of  an  increase  of 
velocity.  The  energy  so  stored  up  is  reconvertible  into  work  at  any 
time  without  loss,  and  its  amount,  for  any  given  velocity,  may  be  very 
simply  determined  by  formula,  or  instantly  from  a  table  (Tables  117  and 
118). 

371.  To  determine  by  formula  the  work  represented  by  a  given  ve- 
locity, or  the  velocity  attainable  by  a  given  amount  of  work:  It  was 
found  experimentally  long  since— by  Galileo,  at  the  leaning  tower  of 
Pisa — that  a  body  falling  freely  toward  the  earth,  with  no  opposing  re- 
sistances to  impede  its  motion  (in  other  words,  a  body  continually  acted 
upon  by  a  force  equal  to  what  we  term  its  weight),  will  fall  through  16.08 
feet  in  one  second  of  time  (in  the  latitude  of  Italy  or  New  York,  16.04  at 
the  equator,  16.095  at  London,  si**  31'  N.;  16.127  at  80°  N.),  and  will  then 
be  moving  with  a  velocity  of  twice  its  average  velocity,  or  32.16  feet  per 
second.  In  the  second  second  the  velocity  previously  acquired  will  carry 
it  through  32,16  feet,  and  the  continuous  action  of  the  original  force  will 
•carry  it  through  an  additional  distance  of  16.08  feet,  and  communicate  an 
additional  velocity  of  32.16  feet  per  second,  making  the  total  distance 
fallen  through  in  the  second  second  48.24,  and  the  final  velocity  acquired 
•64.32  feet  per  second.  By  this  process,  which  can  be  varied  in  many 
ways,  and  which  was  in  the  beginning  purely  empirical,  the  general  laws 
have  been  determined  which  may  be  summarized  thus: 

The  total  time  being  as  i,  2,  3,  4,  etc.,  the  velocity,  either  average  or 
final,  will  be  as  i,  2,  3,  4,  etc.  The  total  spaces  passed  through  will  be  as 
the  square  of  the  velocities,  or  1,4,  9.  16,  etc.,  and  the  spaces  for  each 
time  as  I,  3,  5,  7,  9,  etc.  The  final  velocity  is  always  twice  the  average 
velocity. 

The  height,  =  h,  through  which  a  body  must  fall  to  acquire  a  velocity 
of  V  feet  per  second  is 


V" 


h  =  —  = 


2g         64.32' 

•or  to  acquire  a  velocity  of  V  miles  per  hour ;  since  v  = 


5280 
60  X  60 


V, 


h  = 


/_52_8o_\   ^,. 
\6o  X  60/ 


64.32 


=  0.033445  F*. 


CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY.    333 

372.  Why  the  constant  32.16  above  noted  should  be  preci.sely 
what  it  is,  instead  of  22.16  or  42.16,  is  unknown,  and  science  does  not 
even  tend  to  determine  it;  but  it  is  known  that  this  constant,  which  is 
called  the  acceleration  of  gravity,  will  vary  directly  with  the  forcCr 
if  the  latter  be  greater  or  less  than  gravity;  so  that  with  this  change^ 
made,  the  formula  is  of  general  application  to  a  body  acted  on  by  any 
uniformly  accelerating  force  whatever. 

373.  From  this  formula  Table  117  is  calculated.  It  gives  at  once  the 
velocity  in  miles  per  hour  which  will  be  acquired  by  a  train  (or  any  other 
body)  falling  without  frictional  resistance  through  a  given  vertical  dis- 
tance (acted  on  by  a  force  equal  to  its  weight  for  a  given  distance)  and 
hence,  conversely,  the  vertical  distance  through  which  momentum  alone 
will  lift  the  train  moving  at  any  given  velocity  against  the  force  of  grav- 
ity. Nothing  more  than  this  table  and  a  general  understanding  of  the 
subject  is  needed  to  solve  all  ordinary  problems  connected  with  location 
arising  from  variations  of  velocity,  except  for  one  detail,  which  makes 
Table  1 18  the  better  one  to  use. 

t 

Table  117. 

Height  in  Vertical  Feet  through  which  a  Body  must  Fall  to  acquire 

A  Given  Velocity  in  Miles  Per  Hour, 

Or  the  height  through  which  the  energ>'  due  to  that  velocity  will  lift  the  body  against 

gravity  only  before  it  comes  to  rest. 

Miles 
Per  0.  I.  2.  3.  4.  5.  6.  7.  8.  9. 

Hour. 


to , 

20 

30 

40 

5o«  >  • '  •  • 


0. 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

0.00 

0.03 

0.13 

0.30 

0.54 

0.84 

1 .20 

1.64 

2.14 

3-34 

4  05 

482 

5.65 

6.55 

7-52 

8.56 

9.67 

10.84 

»3-38 

«4-75 

16.19 

17.69 

19.26 

20.90 

22.61 

24-38 

26.22 

30.10 

32.14 

34-25 

36.42 

38.66 

40.97 

43  34 

45-78 

48.29 

53 -si 

56.22 

58  99 

61.84 

64-75 

67.72 

70.77 

.73-88 

77-05 

83.61. 

.86.99 

9043 

93-94 

97-52 

101.17 

104.88 

108.66 

112.50 

2.71 
12.07 

28.13 

50.87 

80.30 
116.42 


Formula :  h  = 


\6o  x6o/ 


•  (in  miles  per  hour) 


0-033445  ^•. 


64.32 

For  computations  connected  with  the  movement  of  trains  the  following  Table  1 19 
should  be  used. 

374.  The  formula  of  par.  371  assumes  that  the  body  is  in  motion  as 
a  whole,  but  that  its  parts  are  at  rest  relatively  to  each  other.     In  a  mov- 


334     CI/AP.  IX.-^RISE  AND  FALL— EFFECT  OF  VELOCITY, 

ing  train  this  is  not  so ;  for  the  wheels  and  axles,  in  addition  to  their  for- 
ward motion,  are  in  rapid  rotation,  so  that  additional  energy  is  stored  up 
within  them  as  in  so  manyfly-wlieels.  To  put  the  same  truth  in  another 
way :  Each  particle  in  the  wheels  and  axles  (except  on  the  axisj  moves 
more  feet  per  second  through  space  (albeit  in  a  curved  path)  than  the 
train  as  a  whole,  so  that  they  necessarily  have  more  energy  stored  within 
them. 

The  energy  due  to  the  rotation  of  the  wheels  and  stored  up  in  them 
as  in  a  fiy-wheel  is  usually  computed  separately  from  that  which  they 
have  in  common  with  the  rest  of  the  train,  when  it  is  computed  at  all; 
but  for  all  purposes  in  connection  with  the  motion  of  trains  for  which 
the  one  is  required  to  be  known,  the  other  may  be  said  to  be  also,  and  in 
Table  1 18  the  two  are  included  together.  If  the  wheels  were  not  in  con- 
tact with  the  rails,  but  were  mounted  like  fly-wheels  within  the  car,  they 
would  exercise  no  effect  upon  the  forward  motion  of  the  train.  After 
the  train  had  been  brought  to  a  stop  they  would  continue  to  spin  around 
indefinitely  until  stopped  by  their  own  friction ;  but,  being  in  contact 
with  the  rails  (or  if  mounted  on  the  body  of  the  car  and  connected  with 
the  wheels  by  gearing),  they  act  very  eflfectually  to  carry  the  train  along 
just  so  much  farther,  in  the  same  way  as  the  rotating  fly-wheel  on  the 
little  toy  locomotives,  which  almost  every  one  has  seen,  causes  the  latter 
to  move,  being  in  that  case  the  only  motive-power. 

375.  The  amount  of  energy  in  any  rotating  body  is  determined,  as  may  be 
seen  in  any  treatise  on  mechanics,  by  determining  the  position  and  velocity  of 
a  point  called  the  centre  of  gyration,  which  is  the  point  at  which,  if  the  whole 
mass  of  the  rotating  body  were  concentrated,  any  given  force  would  communi- 
cate the  same  velocity  of  rotation  as  it  does  to  the  acutal  body.  Motion  in  a 
circular  or  other  curved  path  at  any  given  linear  velocity  means  the  accumula- 
tion of  the  same  amount  of  energy  as  if  the  body,  as  a  whole,  were  moving  in  a 
right  line  at  the  same  velocity,  and  if  the  body  be  both  revolving  and  moving 
forward,  like  the  wheels,  the  two  are  separate  and  in  addition  to  each  other. 

376.  The  manner  of  determining  this  radius  of  gyration  it  is  needless  to  go 
into  deuil.  According  to  the  pattern  of  wheel,  it  will  vary  between  0.7  and  0.8 
of  the  actual  radius,  being  in  car  wheels  nearer  0.7  and  in  locomotive  drivers 
fully  0.8.  Assuming  a  minimum  radius  of  0.7,  it  will  be  plain  that  points  on 
that  circle  are  rotating  with  a  linear  velocity  of  0.7  times  the  velocity  of  the 
train,  and  hence  that  the  rotative  energy  only  of  the  wheels  will  be  0.7'  or  0.49 

in  round  numbers  one  half  that  due  to  the  forward  motion  of  the  wheels  in 

common  with  the  rest  of  the  train.  Really  it  should  be  a  little  more  than  this 
even  figure  for  ordinary  patterns  of  wheels,  and  in  locomotives  it  is  fully  six- 
tenths. 


CHAP.  IX.-^RISE  AND  FALL— EFFECT  OF  VELOCITY.     335 

Estimating  ordinary  car  wheels  to  weigh  2^  tons  per  8- wheeled  car,  or  561 
pounds  per  wheel,  the  ratio  of  the  weight  of  the  wheels  to  the  total  weight  will 
be  about — 


Weighing 

Per  cent  of  weight  of  wheels 

Making  an  addition   to  the  total 
energy  of  the  train  of  about 


In  a  Passcng-er 

or  Loaded 

Freight  Car. 


2.2\  tons. 
10  p.  C. 

5  p.  c. 


In  an  Empty 
Freight  Car. 


9  tons. 
25    p.  c. 

12\  p.  c. 


In  Locomotive  and 
Tender. 


ID  to  12^  p.  C 
6  to    7i  p.  C 


We  may  say,  therefore,  that  the  rotative  energy  of  the  wheels  will  add 
about  6  per  cent  as  a  mmimum  to  the  accumulated  energy  or  "velocity  head  " 
of  the  train  as  a  whole,  in  the  case  of  ordinary  passenger  or  loaded  freight 
trains,  which  with  very  heavily  loaded  cars  may  be  a  little  less,  but  in  the  case 
of  long  trains  of  empty  cars  may  be  some  4  or  5  per  cent  higher.  Under  this 
assumption,  assuming  6.14  per  cent  for  ease  of  computation,  Table  118  was 
computed,  which  is  the  proper  one  for  use  in  all  computations  concerning  the 
energy  stored  in  trains  at  various  velocities. 

Table  118. 

Total  Emergy  of  Potential  Lift  in  Vertical  Feet  (or  Velocity  Head) 
IN  Trains  moving  at  Various  Velocities. 

Including  the  Effect  of  the  Rotative  Energy  of  the  Wheels  for  Passenger  or  Loaded 
Freight  Trains^  assumed  at  6.14  per  cent  of  the  total  enei^y.  For  trains  of  empty 
flat  or  coal  cars  add  about  4  per  cent  to  the  quantities  below,  and  proportionately  for 
mixed  trains. 


MiLBS 

Per 
Hour. 

0. 

1. 

2. 

8. 

4. 

5. 

6. 

7. 

8. 

9. 

Vel.  ft.. 

0.00 

0.04 

0.14 

0.3a 

0.57 

0,89 

X.28 

'•74 

«.27 

3.88 

MiLBS 

Per 
Hour. 

.0 

.1 

.2 

.3 

.4 

.5 

.8 

.7 

.8 

.9 

10 

3.55 

3.62 

369 

3-77 

3.84 

3-92 

3-99 

4.07 

4  »5 

4.3a 

II 

la 

»3 

430 
5 II 
6.00 

438 
519 
6.09 

4.46 

5.2« 

6.19 

4-54 
5-37 
6.28 

4.62 
546 
6.38 

4.70 

5-55 
6.47 

479 
5  64 
6-57 

4-87 
5.73 
6.67 

4-95 
5.82 

6.76 

5-03 
5-01 
6.86 

14 

15 

t6 

6.96 

7-99 
9.09 

7.06 
8.10 
9.21 

7.16 

8.31 

9-3» 

7.27 
8.32 
9-44 

8.43 

9-55 

7  47 
8.54 
9.67 

7-57 
8  65 

9.79 

7.68 
8.76 
9-90 

7-78 

8.87 

10  02 

7-89 

8.98 

jo.  14 

57 

18 

»Q 

20....: 

10.26 
IX. 50 
12. 8a 

10.39 
11.63 
12.96 

10.51 
11.76 
n.09 

10.64 
11.90 
13-23 

10.76 
12.03 

1337 

10.88 
12. 16 

13-51 

II. 01 

12    20 

13-64 

11  13 

"43 

13-78 

TI.26 
12.56 
13  92 

11.38 
12.69 
14.06 

14.20 

14-34 

14-49 

14  64 

14.78 

14-93 

15.08 

15-23 

15-38 

15.5a 

336    CHAP,  IX,— RISE  AND  FALL—EFFJiCT  OF  VELOCITY. 


CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY,     337 


Table  118. — Continued. 


Miles 

Per 

Hour. 

Vel.  ft.. 

0. 
0.00 

1. 

0.04 

2. 

0.14 

8. 
0.33 

4. 
0.57 

6. 

0.89 

6. 
Z.38 

7. 
x-74 

8. 

3.27 

9. 

3.88 

Miles 

Per 

Hour. 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

20    ... 

14.20 

14-34 

14  49 

14.64 

14.78 

14.93 

15  08 

15-23 

15  38 

15-52 

ai 

aa 

as 

a4 

«5 

36 

a? 

38 . . .   . . 

a9 

15  67 
17.19 
18.79 

20.46 
22.20 
34.00 

25.88 

27-83 
29.86 

15.82 

1735 
18.95 

20.63 

22    38 
24.18 

26.07 
28.03 
30.06 

15-97 
i7-5» 
19.11 

20.80 
22.56 
24-37 

36,27 
28.23 
30.27 

16.13 
17.67 
19.27 

20.98 
22.74 
24.56 

36.46 

28.43 
30.48 

16.28 
17-83 
19-44 

31.16 

22.92 
34.75 

26.66 
28.64 
30.69 

16.43 
17.99 
19.61 

21.34 
23.10 

24  93 

36  85 
28.84 
30.90 

16.58 
18.15 
19.78 

31.51 

23-38 
25.12 

37.05 
29.05 
31.11 

16.73 
18.31 

19.95 

21.68 
23.46 
25.31 

27.24 
29.25 
31-32 

16.88 

18.47 
20.12 

21.84 
23  64 
25.50 

27-44 
29.46 

31-53 

17,04 
18.63 
20.39 

31. 03 
23.82 
25.69 

37.63 

29.66 

3'-74 

30 

3»-95 

33.16 

32.18 

32.60 

32.81 

3303 

33.25 

33.47 
35.68 
37.97 
40.32 

42 -75 
45.26 
47.82 

50.47 
53-18 
55.96 

33-69 

33  90 

3»  

3a 

33 

34 

11:::::: 
%::■:. 

39 

3412 

36-35 
38.66 

41.04 

43  49 
46.01 

48  60 
51.26 
54.00 

56.80 

34-34 
36.58 
38.90 

41.28 

43-74 
46.26 

48.87 

51-53 
54.28 

34-57 
36.81 

39-13 

41.53 
44.00 

46.5a 

49  13 
51-80 

54-56 

34-79 
37  04 
39-37 

41-77 
44  25 
46.78 

49-39 
52.08 
54  84 

35-01 

37-27 
39.61 

42.03 
44-50 
47.04 
49.66 
52-36 
55-12 

35  24 
37.50 
39.85 
42.26 

44-75 
47.30 

49.93 
52.63 
55-40 

35.46 

37.74 
40.08 

42.51 
45.00 

47.56 
50.20 

52.91 

55.68 

35.91 
38.20 

40.56 

4300 

45-51 
48.03 

50.73 
53.46 
56.24 

36.13 

38-43 
40.80 

4324 
45-76 
48.34 
51.00 

53-73 
56.52 

40.  ... 

57-09 

57-37 

57.66 

57-95 

58.24  1     58.52 

58.81 

.sgio 

59-39 

41 

4a 

43 

44 

Jl:::::: 
%■■:::. 

49 

59  68 
62.62 
65.64 

68.73 
71.89 
75-12 

78.42 

81.79 
85.24 

59-97 
62.93 
65.94 

69.05 
72.21 

75-45 

78.75 
82.13 

85-59 

60.27 
63.23 
66.25 

69.36 
72.54 
75-78 

79.09 
82  48 
85  94 

60.56 

63-53 
66.56 

69.68 
72.86 
76.11 

79-43 
82.82 
86.29 

60.86 
6383 
66.87 

70.02 
73.18 
76.44 
79.76 

83-17 
86.64 

61.15 

64.13 
67.18 

70.34 
73-50 
76.77 

80.10 

83.51 
86.99 

61.4s 
64 -43 
67.69 

70.65 
73.82 
77.10 

80.44 
83-85 
87.34 

61.74 
64.73 
67.80 

70.97 
74-15 
77.43 

80.77 
84.20 
87.69 

62.04 

65-03 
68.11 

71.28 

74-47 
77.76 

8t.ii 

84  55 
88.04 

60.33 
65-34 
68.42 

71.6a. 

74.79 
78.09 

81.4s 
84.89 
88.39 

50.   ... 

Diffs... 

60 

Diffs  .. 

70 

Diffs... 

88.75 

3-59 

127.80 

4-30 

173-95 
5-01 

92-34 
3.6s 

133.10 
4-36 

178.96 
5.07 

95-99 
3-73 

136.46 
4-44 

184.03 
5»5 

99.72 
3.80 

140,90 

4-51 

189.18 
5.33 

103.52 
3.87 

145.41 
458 

194.40 
5.29 

107.39 
3.94 

149.99 
4.65 

199  69 
5-36 

111.33 
4.01 

154-64 
4.7a 

205  05 
5.43 

115. 34 
4.08 

159-36 
4-79 

310.48 
5.50 

119.42 
4.16 

164.15 
4-87 

215.98 
5-58 

123.58 
4.22 

169.03 
4-93 

221.56 
564 

•H         ,      ,T  ,  «.     J      I'* 'n  ft.  per  sec.       1.467"  F«  (m  miles  per  hour)  .,. 

Formula :  Vel.  head  = 2—^ =  — ^-^ —2 ' =  0.033445  F» 

64.32  04.32 

To  which  add  6.14  per  cent  for  rotative  energy  of  the  wheels  =  0.002055  V* 
Giving  as  the  final  formula,  by  which  the  table  is  computed,  Vel.  head  =  0.035500  ^'' 

The  above  table  is  exact  for  the  even  miles.  The  heights  for  tenths  of  a  mile  per  hour 
were  filled  in  by  interpolation,  and  the  last  digit  may  be  in  error. 

The  process  of  computing  the  result  of  a  brake-test  by  the  aid  of  this  table,  which  may 
be  useful  for  reference  in  connection  with  it,  is  as  follows  : 


FIELD   NOTES   REQUIRED   FOR  COMPUTING   BRAKE  TESTS. 

1.  Speed  in  miles  per  hour  at  instant  of  applying  brakes. 
3.  Distance  run  after  applying  brakes,  in  feet. 

3.  Jiate  0/ grade,  ascending  or  descending,  in  per  cent,  i.e.,  feet  per  station  of  100  ft. 

4.  Proportion  0/ the  total  weight  0/  the  train  to  which  brakes  were  applied.  (Except 
as  necessary  to  determine  this  proportion,  the  total  weight  of  the  train,  or  the  total  weight 
on  braked  or  unbraked  wheels,  is  unessential,  and  does  not  witer  into  the  computation.) 

To  these  essential  notes  should  preferably  be  added  : 

5.  Time  0/ stop  in  seconds  (best  taken  with  a  stop-watch). 

PROCESS  OF  COMPUTATION. 

1.  Take  from  the  table  the  height  in  vertical  feet  corresponding  to  its  speed,  i.e.,  the 
••  Vel.  head."  Divide  it  by  the  length  of  the  stop  in  stations  of  100  ft.  The  quotient 
(which  will  in  all  ordinaVy  cases  be  between  the  extreme  limits  of  2.00  and  20.00)  is  the 
equivalent  grade  0/  retardation  for  a  stop  on  a  level  grade. 

2.  To  this  quotient  add  the  actual  rate  of  grade,  if  descending,  or  subtract  it  if  ascend- 
ing. Subtract  also  the  grade  representing  the  average  train  resistance  during  the  entire 
Stop,  which  may  be  approximately  assumed  as  follows : 

Miles  per  hour. 


Initial  speed, 25       30 

and  less. 


40 


50        55 
Pounds  per  ton  (2000  lbs.). 


60 


Average  resistance  during  stop, 


Equivalent  grade, . 


8         9       10       12        14 
Per  cent  (or  feet  per  100). 


16 


0.4      0.45      0.5       0.6       0.7      0.8 


3.  The  resulting  sum  or  difference  is  the  actual  equivalent  grade  0/ retardation,  in  feet 
per  100 :  or  the  effect  of  the  brakes  as  a  whole  on  the  train  as  a  whole.  The  figures  ex- 
pressing this  grade,  as  5.00,  8.50,  12.45,  express  also  the  efficiency  of  the  brakes  upon  the 
train  as  a  whole,  in  percentages  of  the  total  weight  0/  the  train. 

4.  Divide  this  grade  or  percentage  by  the  per  cent  0/  the  total  weight  of  the  train 
upofi  which  brakes  acted  or  were  adapted,  intended,  or  expected  to  act.  The  quotient  is 
the  actual  efficiency  of  the  brakes  upon  the  load  carried  by  the  braked  wheels,  or  upon 
that  portion  thereof  which  it  was  intended  to  rely  upon  in  proportioning  the  brakes. 
This  quotient  will  always  lie  between  the  extreme  limits  of  25.00  and  i.oo,  usually  be- 
tween 3.00  and  14.00,  and  is  the  only  one  by  which  comparisons  with  different  trains 
having  differently  distributed  brakes  can  properly  be  made. 

By  formula :  Grade  of  retardation  =  Yfl-J^i^  j  +  rate  of  descending  grade,  or  )    _ 

Distance  I  —  ascending        "  J 

^   .      ,      «.       t  '  ^'  J  Grade  of  retardation 

grade  of  rolhng  friction  ;  and 7 ; : =  Efficiencv  of 

p.  c.  of  wt.  of  train  on  which  brakes  acted       ^"^^^^^ncy  01 

brakes  in  per  cent  of  weight  on  which  they  acted. 

EXAMPLES. 

I.  Train  with  9^  (75  per  cent)  of  weight  braked;  20  miles  per  hour;  284  ft.  (2.84 
stations),  distance  run  ;  grade,  52.8  ft.  per  mile  (i.o  per  cent)  descending. 
22 


■' ( 


338     CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY. 


Assumed  average  grade  of  rolling  friction,  as  above,  =  0.4.    Then 
14.20  (from  table) 


2.84 


=  5.00  +  i.oo  -  0.4  =  S.6  +  0.7s  =  7.47, 


being  the  percentage  of  the  efficiency  of  the  brakes  or  rate  of  an  equivalent  grade ;  and 
grade  of  7.47  X  20  =  159.4  Jbs.  per  ton  retarding  force  from  brakes. 

2.  Train  90  per  cent  braked  ;  60  miles  per  hour ;  1014  ft.  length  of  stop  ;  grade,  26.4 
ft.  per  mile  (0.5  per  cent)  ascending. 

Assumed  average  grade  of  rolling  friction,  as  above,  =  0.8. 


127.80  (from  table) 
10.14 


=  12.60-0.50  —  0.8=  11.30 -»•  0.90=  12.56. 


377.  The  magnitude  of  any  force  is  expressed  (in  English)  in  pounds 

or  some  multiple. 

The  work  done  (or  which  has  been  or  can  be  done)  by  the  continued 
application  of  any  force  is  expressed  in  foot-pounds,  i.e.,  by  the  force  in 
pounds  multiplied  by  the  distance  in  feet  through  which  it  acts  or  has 
acted  or  can  act.  A  Consolidation  locomotive  has  a  tractive  force  of,  say, 
20,000  lbs.  The  work  done  by  such  an  engine  in  runnin;?  a  mile  is 
20,000  X  5280  =  105,600,000  foot-pounds.  A  HORSE-POWER  is  33.000 
foot-pounds  per  minute.     If,  therefore,  such  an  engine  run  a  mile  in  4 

105,600,000  „  ,  T,.^  ., 

minutes  its  horsepower  is  ———--=  800  horse-power.  If  it  run  a  mile 

33>ooo  X  4 

105.600.000      ,      , 
in  5  minutes  it  is  exerting  a  force  of  only  — ;^^^^  =  ^4©  horse-power. 

If  a  train  at  a  certain  velocity  has  an  average  resistance  of  10  pounds 
per  ton,  the  power  consumed  by  it  will  be  10  foot-pounds  per  ton  per 
foot,  or  52.800  foot-pounds  per  ton  per  mile.  If,  again,  the  resistance  of 
brakes  be  added,  assuming  the  total  pressure  on  the  brake  blocks  to  be 
equal  to  half  the  weight  of  train  or  1000  lbs.  per  ton,  and  assuming  the 
coefficient  of  friction  to  be  at  0.16  (it  is  in  reality  very  variable),  the  re- 
tarding force  of  the  brakes  will  be  1000  x  0.16  =  160  lbs  per  ton.  and 
the  work  done  per  ton  by  the  brakes  (in  dissipating  energy)  will  be  160 
foot-pounds  per  foot  through  which  the  brakes  act. 

378.  The  same  amount  of  energy  (in  excess  of  all  retarding  forces) 
communicated  from  any  source  to  any  body  moving  in  any  direction 
will  cause  that  body  to  move  through  space  with  the  same  velocity. 
The  direction  of  the  motion  may  vary.  The  velocity  of  motion  will 
not  vary,  and  will  always  be  equal  to  that  required  to  lift  the  body 
through  the  vertical  height  through  which  the  body  would  have  to  fall 
freely  in  a  vacuum  to  acquire  that  velocity. 


CHAP.  IX.— RISE  AND  FALI^EFFECT  OF  VELOCITY. 


339 


379.  From  the  above  it  necessarily  results  that  it  is  a  general  law  of 
motion  on  inclined  planes 
that  a    body  descending 
freely  along    any  incline, 
regular    or    irregular,   as 
AC,  AD,  AE,  or  AF,  Fig. 
()2,  under   the   action    of 
the  same  vertical  force,  as 
gravity,  will     be   moving 
through  space  at  any  point,  C,  D,  E,  or  F,  which  lies  at  the  same  verti- 
cal distance  below  A,  with  the  same  velocitv  as  it  would  have  at  B  if  it 
had  fallen  vertically  through  AB.     The  direction  of  motion  will  varv 
in  each  case.     The  time  of  descending  to  the  line  bd  will  also  varv  in 
each  case,  but  the  velocity  with  which  the  bodv  is  moving  through  space 
as  It  passes  any  given  level  db  will  always  be  the  same,  by  whatever  path 
It  has  reached  that  level,  and  always  that  "due"  to  the  vertical h^\8,hx.  of 
the  plane  (less  the  loss  by  friction),  this  being  the  necessary  result  of 
the  fact  that  the  same  number  of  foot-pounds  of  work  have  been  com- 
municated to  the  body  in  either  case. 

380.  The  time  occupied  in  the  descent,  if  it  be  a  regular  plane,  will 
be  greater  than  that  "  due"  to  the  vertical  fall  in  the  ratio  of  the  len^rth 
of  the  plane  to  its  height.  If  it  be  a  curved  or  broken  surface,  the  time 
of  descent  will  bear  no  such  constant  ratio,  but  the  final  velocity  at  a 
given  vertical  distance  below  A  will  in  all  cases  be  the  same. 

381.  Conversely,  the  accelerating  or  retarding  effect  of  gravity  on 
any  incline,  and  in  the  direction  thereof,  as  on  a  railway  grade,  Fig.  63 
is  less  than  the  weight  of  the  body  in  the  same  ratio  as  the  height  ab 
of  the  plane  is  less  than  its  length 
ac;  that  is  to  say,  the   force    IV, 
Fig.     63,    which     represents    the 
weight  of  the  body  O  acting  verti- 
cally downward,  may  be  resolved 
— or    rather  resolves    itself — into 
the  force/ acting  parallel  with  the 
plane  and  tending  to  produce  mo- 
tion down  it,  and  the  force  W — (al- 
ways less  than  W^)— acting  in  the 
direction  /?,   perpendicular  to  the 


Fig.  63. 


rail,  ac  representing  the  actual  pressure  of  the  wheel  thereon.     It  is  geo- 
metrically evident  from  Fig.  63  (on  account  of  the  similarity  of  triangles) 


340     CHAP.  JX.—RISE  AND  FALL— EFFECT  OF  VELOCITY. 


CHAP.  IX.-RISE  AND  FALL-EFFECT  OF  VELOCITY.     341 


^1^ 


that  the  force  /  (technically  known  as  the  grade  resistance,  although  in 
descending  it  is  not  a  resistance  but  an  accelerating  force)  bears  the  same 
ratio  to  the  weight  that  the  rise  in  any  distance  does  to  the  length  ac, 
measured  on  the  slope,  and  not  horizontally.  Practically,  however,  on  any 
ordinary  railway  grade  the  horizontal  distance  be  is  not  sensibly  differ- 
ent from  the  length  measured  along  the  surface  of  the  rails  ac,  and  hence 
it  is  customary  and  proper  to  assume  dc  =  ac  \  whence  we  have,  approxi- 
mately, 

W~  be' 

or,  if  we  let  the  horizontal  distance  be  =  loo,  and  the  height  ab  =  r  = 
rate  of  grade  or  rise  in  loo  (whether  feet  or  other  horizontal  unit,  if  we 
use  the  same  for  both  vertical  and  horizontal),  then  we  have 

/_r_  lVr_ 

W  100  *^^ -^  "  loo* 

382.  If,  in  this  equation,  we  let  W^  2000  =  the  number  of  pounds  in. 

a  ton,  we  have 

/=2or. 

or.  The  grade  resistance  in  lbs.  per  ton  =  rate  of  grade  per 
CENT  X  20.  This  rule  should  be  memorized  by  every  railroad  engineer, 
preferably  in  the  still  simpler  form  :  "  Rate  of  grade  in  tenths  x  2."  E.  g. 
on  a  I  per  cent  or  i.o  grade  the  grade  resistance  is  20  lbs.  per  ton  ;  on  a 
0.4  grade,  8  lbs.  per  ton. 

For  the  long  ton  of  2240  lbs.  it  is  only  necessary  to  increase  the  re- 
sult by  12  per  cent.  The  rule  amounts  to  no  more  than  saying  that  if 
the  rate  of  grade  be  xb*  the  resistance  per  ton  will  be  ^-^  ton,  which  is 

20  lbs. 

383.  The  trifling  importance  of  the  error  in  assuming  in  Fig  63,  that,  for 
all  practical  purposes,  the  hypothenuse  ac  and  the  base  ab  may  be  assumed 
equal,  when  computing  grade  resistance,  is  shown  by  Table  119. 

On  a  4  per  cent  grade,  which  may  be  considered  the  utmost  limit  of  ordi- 
nary practice,  the  error  in  the  computed  resistance  is  only  o.cooS,  or  less  than 
one  tenth  of  i  per  cent.  On  the  heaviest  grade  on  which  the  locomotive  has 
ever  worked,  10  per  cent,  the  error  is  only  one  half  of  one  per  cent. 

The  error  can  be  avoided  by  substituting  for  the  actual  weight.  W,  Fig.  63, 
the  value  of  the  component  W  at  right  angles  to  the  plane;  but  for  any  grade 
less  than  the  most  extreme  this  is  unnecessary  trouble,  as  the  error,  what  there- 
is  of  it,  tends  to  safety  by  exaggerating  the  grade  resistance. 


Table  119. 

<5.v.ng:  also  the  percentage  of  excess  in  the  comDuted  ^.A.       ■  . 

ine  computed  grade  resistance  under  the  rule 
/  =  2or  of  par.  382. 


Rise  in  loo. 

(«^,  Fig.  63.) 

(=  rale  of  grade 

per  cent.) 


I 
2. 

3. 

4 

5. 
6. 


.00 
.00 
.00 
.00 
.00 
.00 
7.00 
8.00 
9.00 
10.00 


Length  on  Slope 

(«<^) 

for  Horizontal  Distance 

i^c)  of  100, 

100.005 

100.020 

100 . 045 

100.080 

100.125 

100.180 

100.245 

100.319 

100.404 

100.499 


NOTE.-This  table  likewise  affords 
a  good  opportunity  for  testing  the 
convenient  rule  elsewhere  given  for 
solving  right  -  angled  triangles  of 
small  altitude,  viz. :  B  ^^    01 

I^iff.  between  hyp.  and  base  =  ht « 

iTnown'j:   ^^^'   ""  ^""'^  (whichever  is 

It  will  be  seen  to  be  correct  with 
these  triangles  to  within  a  very  mi- 
nute percentage.  ^ 


carat  any  given  veocitys  called  ^h    T^  '°  "''  "'°'""«  '""■•°""  °f  ^"e 

being  thLVade  on  wh'i  h       a  cl/or  t'"'  °'  'T'"  '°^  '''''  ^'"'^^y- 
erating  force  of  gravity  wou  d  t«  h T  "^'"^"^  descending,  the  accei- 

hence  enable  it  to  ^tC t'^^r^lTei:  Itt:":"  '°  ""f  °"'  ^"^ 
gaining  nor  losmcr  velocity   «rhi.i,   •    .^^''^f  ^*  *''^  ^^^e  speed,  neither 

bodies  to  which  a  given  vlUtv  t-=  o  '"'k"""^"''^^'  ^""^ition   of  all 
ing  to  Newtons  firs'  Zl  of  moUon  "  '""  communicated,  accord- 

■ootion  when  a  train  was  once  movinrwL  t  """"  """  ■•«'■««"«  of 

-  "ate  of  rest.  I„  reality  a  grTse;elT,  1"°"^''  '°  ^'^"  ^  ■"'"  f™™ 
'a.ter  grade  only  can  propcrfy  be  a  led  a  "T  .7  "  "'"''"'■  """  '"is 
chosen  tern,  is  still  the  coLon  one  LI  ..5'''  °'/«=P°^^"  But  the  ill. 
■dea  in  which  it  originated    Other»i«         ut  '  """"^PPily.  *«  erroneous 

on  limiting  grades.  ''  ^'"^^"'y-  """^  """'d  be  fewer  station, 

.■O 


■m^ 


^  ♦, 

•I 

H 

4 


342     C//AP.  IX.— RISE  AND  FALI^EFFECT  OF  VELOCITY. 

387.  When  a  railway  train  descending  a  grade,  or  any  other  falling 
body,  is  acted  upon  by  an  accelerating  force  which  remains  uniform, — 
like  the  traction  of  a  locomotive  or  gravity, — in  opposition  to  a  retarding 
force  which  increases  with  the  velocity, — like  the  resistance  of  a  train, — 
the  velocity  of  motion  will  continue  to  increase  until  the  retarding  force 
becomes  equal  to  the  accelerating,  and  thereafter  the  body  will  continue 
in  motion  indefinitely  at  a  uniform  velocity.  The  net  resultant  of  all 
the  forces  acting  is  then  zero,  and  consequently  the  body  continues 
indefinitely  in  motion  at  an  unvarying  velocity,  as  theory  requires. 

388.  This  statement  should  be  read  over  until  its  meaning  is  fully 
grasped.  A  railway  train  in  motion  at  a  uniform  velocity  is  acted  on  in 
one  sense  by  two  forces,  but  in  a  truer  sense  by  no  force.  The  frictional 
and  other  resistances  and  the  traction  of  the  locomotive  act  upon  and 
destroy  each  other  within  the  body,  without  either  acting  upon  the  body 
itself,  except  to  produce  internal  stress.  Such  a  body  is  therefore  one  of 
the  nearest  examples  in  practical  mechanics  of  Newton's  abstract  con- 
ception of  a  body  moving  on  indefinitely  in  vacuo  from  original  impulse, 
without  gain  or  loss  of  energy,  as  do  the  heavenly  bodies. 

389.  Under  such  conditions  any  new  force— whether  accelerating 
or  retarding,  like  a  change  in  the  rate  of  grade  or  in  the  tractive  force  of 
the  locomotive — will  act  upon  the  body  precisely  as  if  no  other  forces 
existed  to  act  upon  it;  i.e.,  the  whole  of  the  new  force,  undiminished 
by  frictional  or  other  losses,  will  act  upon  the  body  to  vary  its  velocity, 
and  will  vary  it  precisely  as  theory  requires.  This  fact  bears  with  it  im- 
portant consequences. 

To  illustrate  this  interconvertibility  of  work  and  velocity  :  Let  us  assume 
any  body,  as  a  car,  weighing  20,000  pounds  to  have  fallen  freely  (i.e.,  without, 
or  in  excess  of,  the  loss  by  friction)  16.08  feet.  It  would  then  have  20,000  X 
16.08  =  321,600  foot-pounds  of  work  stored  up  in  it,  and  would  be  moving 
through  space  with  the  precise  velocity  of  32.16  feet  per  second  or  about  21 
miles  per  hour. 

If,  instead  of  having  fallen  vertically,  either  gravity,  or  the  tension  on  the 

draw-bar,  or  any  other  force,  had  been  communicating  to  that  same  car  body 

continuously  a  force  of  20  pounds  (or  one  pound  per  ton  in  excess  of  all 

321,600 
resistance),  the  car  would  have  to  move  through  a  distance  of 


CHAP.  IX.-RISE  AND  FALL— EFFECT  OF  VELOCITY.    343 


20 


16,080 


feet  to  store  up  within  itself  321,600  foot  pounds,  and  hence  to  acquire  the  same 
velocity  that  it  acquires  when  falling  freely  through  space,  or,  when  acted  upon 
(in  any  direction)  by  a  force  equal  to  its  weight,  in  16  08  ft. 

390.  This  velocity  once  acquired,  the  corresponding  amount  of  energy  stored 
in  the  car  may  be  expended  in  any  one  of  the  following  ways : 

First.   It  may  (theoretically)  by  proper  mechanical  appliances  be  made  to  lift 


the  body  vertically  through  a  height  of  16.08  feet,  which  it  will  do  in  one  second 
of  time,  and  bring  it  to  a  stale  of  rest. 

391.   Secondly.   It  may  be  made  to  lift  the  body  up  an  inclined  plane  A,  A\ 
A",  A",  Fig.  64,  as  on  a  grade  of  any  rate,  against  the  action  of  gravity.'    Iil 


Fig.  64. 
this  case,  if  there  be  no  other  resisting  force  but  gravity,  the  body  will  rise 
through  the  same  vertical  height  in  all  cases  before  coming  to  rest.  The  dis- 
tance run  and  the  time  occupied  in  the  ascent  will  alone  vary.  The  vertical 
elevation  surmounted  will  not  vary.  But  as  there  is  a  resisting  force  (rolling 
friction)  which  is  so  much  per  foot  run,  these  conditions  do  not  precisely  obtain 
in  practice. 

392.  Thirdly.  It  may  be  made  to  propel  the  body  on  a  level  against  the 
resistance  of  axle  and  rolling  friction.  If  the  natural  resistance  to  motion  be 
7  lbs.  per  ton,  or  70  lbs.  for  the  car,  its  accumulated  energy  of  321,600  foot- 
pounds will  continue  it  in  motion  for  a  distance  of  ^li:^  ^  ^5^^  ^^^^  ^^^^^^  .^ 
comes  to  a  state  of  rest. 

This  "rolling  friction,"  so  called,  of  7  or  a  pounds  per  ton  of  2000  pounds  is 
precisely  equivalent  in  its  mechanical  effects  to  a  grade  rising  7  or  a  feet  in 
2000,  or  to  the  "grade  of  repose"  before  explained  (par.  384). 

It  follows,  therefore,  that  any  given  grade  other  than  a  level  is  equivalent  in 
Its  mechanical  effect  upon  the  train,  if  it  be  an  ascending  grade,  to  the  actual 
rate  of  grade  plus  the  grade  of  repose;  and  if  it  be  a  descending  grade,  to  the 
actual  rate  minus  the  grade  of  repose. 

393.  Fourthly.  The  accumulated  energy  of  the  car  may  be  sooner  exhausted 
by  calling  in  the  action  of  brakes  in  addition  to  the  resistances  of  gravity  and 
rolling  friction.  If  there  be  brake-blocks  on  half  the  wheels  only  (which  has 
until  recently  been  the  general  custom  for  freight  service),  and  the  pressure  on 
them  be  equal  to  the  load  on  the  wheel,  which  is  somewhat  more  than  that 
which  the  ordinary  brake  leverage  is  intended  to  give  (modern  experiments 
indicate  that  not  more  than  two  thirds  of  the  load  on  the  wheels  is  a  safe 
pressure),  and  if  the  coefficient  of  friction  between  brake  and  wheel  be  \  which 
's  about  an  average  (it  varies  in  reality  from  i  to  i)  then  the  retarding  forces 
on  the  car  will  be— 


o    ,        20.000 
Brakes,  X  i  X  i 

Normal  rolling  friction  as  above  = 
Resistance  of  grade  if  on  a  level  = 


=  1,667  lbs. 


70 
o 


<< 


<< 


Total  resistances  on  a  level  =  1,737  lbs.  or  173.7  lbs.  per 


ir'H^ 


--"^^pfi- 


344    CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY, 

ton  of  2000  lbs.     The  car  will,  consequently,  come  to  a  state  of  rest  on  a  level 

,     .  ,.  ,  321.600  ft. -lbs.         „      ,  .         .      L     1  .- 

grade  in  a  distance  of -^ =  185    feet,  supposing  the  brakes  to  be 

^  1737  lbs. 

instantly  applied  and  with  their  full  force,  neither  of  which  is  very  likely  to  be 
the  case. 

If  the  car  be  on  an  ascending  or  descending  grade  instead  of  on  a  level  the 
-|-  or  —  resistance  of  the  grade  is  to  be  included  among  the  resistances.     If  the 


car  stood  on  a  descending  grade  of 


173-7 
2000 


=  8.69  per  cent,  or  458  ft.  per  mile,  it 


would  continue  in  motion  forever  at  the  same  velocity  even  with  brakes  set. 
This  has  repeatedly  been  proven  practically  on  8  and  10  per  cent  grades. 

If  there  were  10  cars  in  the  train,  moving  at  the  velocity  of  32.16  feet  per 
second,  and  only  one  of  them,  as  above,  had  brakes  set,  then  we  should  have — 


Brake  resistance, 
Rolling  friction  70  X  10, 


1,667  lbs. 
700    " 


3.216,000  ft. -lbs. 


Total  resistances  on  a  level.  2,367  lbs. 

=  1359  feet,  as  the  distance  in  which  the  train  would  come 


and  ,    ,. 

2,367  lbs. 

to  a  state  of  rest.* 

394.  Fifthly.  The  accumulated  energy  of  the  car  may  be  made  to  act  con- 
jointly with  the  full  power  of  the  loco- 
motive to  carry  it  over  a  particularly 
difficult  gradient.  If  the  full  power 
of  the  locomotive  is  just  sufficient  to 
carry  the  car  or  train  over  any  grade 
of  a  per  cent,  Figs.  65  to  67,  the  en- 
ergy of  momentum  will  carry  the  car 
or  train  up  a  grade  which  rises  in  all 
16.08  feet  higher;  whether  that  rise 
be  by  a  uniform  excess  of  rate,  as  in  Fig.  65,  or  in  a  local  excess  at  certain 
points,  as  in  Figs.  66  and  67. 

In  this  case  the  office  of  the  locomotive  is  simply  to  neutralize  all  grades 
and  rolling  resistances  due  to  the  a  per  cent  grade.  All  extraneous  forces  thus 
neutralizing  and  destroying  each  other,  the  vis  viva  of  the  body  lifts  it  through 
the  additional  rise  of  16.08  feet,  precisely  as,  and  to  the  full  extent  that,  theory 
requires;  but  if  the  power  of  the  locomotive  is  completely  used  up  on  the  a  per 


Fig.  65. 


♦  This  calculation  is  not  quite  correct,  because  the  wheels,  in  addition  to  their  linear 
velocity  in  common  with  the  remainder  of  the  car,  have  an  energy  of  rotation  which  adds 
some  6  per  cent  to  the  total  vis  viva  of  the  car,  as  noted  in  par.  374  et  seq.  Nor  should 
computations  of  this  kind  be  ordinarily  made  as  above,  but  by  the  *'  velocity-heads" 
given  in  Table  118,  which  include  the  rotative  energy  of  the  wheels. 


CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY. 


345 


cent  grade,  the  tram  will  come  to  a  state  of  rest  at  the  summit,  which  is  16.08 
feet  higher,  m  spite  of  the  exertion  of  the  full  power  of  the  locomotive  and  the 
aid  of  the  stored  energy  jointly.     Grades  so  operated  are  called  momentum 

.GRADES. 


Fig.  67. 

395.  Sixthly.  The  accumulated  energy  in  the  car  may.  in  theory,  be  made 

ofherTnd'T     "r^:'''"" ^^^  ^^  ^°"^P^^^^  ^  ^P""^'  ^"^  ^  P>^e.  -  ^o  any 
other  kind  of  work  whatsoever  capable  of  measurement  in  foot-pounds      If  \ 

spring  required  a  force  of  xo.ooo  pounds  to  compress  it  one  inch  and  its 
resistance  contmued  uniform,  then  the  energy  of  the  car  body  would  compress 
'^"^  ^P""^  1^:;^-  =  32. 16  inches.  A  perfectly  elastic  body,  to  which  a  spring 
approximates  would  immediately  give  back  this  energy  to  the  car  and  repel  it 
with  equal  velocity.  A  perfectly  inelastic  body,  such  as  a  bank  of  earth  which 
required  a  pressure  of  10.000  pounds  to  enable  a  body  of  the  size  of  the  car  to 
penetrate  It  one  inch,  would  (if  the  resistance  continued  uniform)  be  likewise 
penetrated  32.16  inches,  and  would  not  repel  the  bodv.  The  energy  would  be 
converted  into  heat. 

A  pile  which  apposed  astatic  resistance  to  motion  of  100,000  pounds  would 
in  theory  be  driven  |^i^  =  3.21  feet,  or  322  similar  piles  would  be  driven 
0.01  feet,  if  the  resistance  to  motion  were  uniform,  which  it  is  not. 

396.  A  rod  of  iron  of  one  square  inch  section,  which  would  require  a  load 
of  26.000,000  pounds  to  extend  it  to  double  its  length  if  its  resistance  to 
extension  continued  uniform.-i.e.,  whose  modulus  of  elasticity  was  26  000  000 
-would  sustain  a  force  of  only  some  50.000  pounds  without  rupture,'  and  say 
25.000  pounds  without  producing  a  permanent  set.  Therefore,  if  those  effects 
are  to  be  avoided,  the  stress  on  the  rod  must  at  no  time  exceed  that  limit-  and 

"k""V  /u^  ^^'  ''  '°  ^^  "'"'PP^'^  ^y  '^^  '■°^'  321.600  foot-pounds  are  to  be 
absorbed  by  reaction  against  a  force  beginning  at  zero  (since  the  slightest 
force  will  extend  the  bar  somewhat)  and  gradually  increasing  to  50.000  or  25  000 
pounds  respectively,  we  have  »       ^  »  a. 

321.600  ^  ^    , 

-— =  128.64  feet 

50,000  -*-  2  ^ 

as  the  length  which  the  rod  would  have  to  stretch  to  avoid  the  rupture,  and 

321.600 


25,000  -i-  2 


=  257.28  feet 


% 


i  ':\ 


ii 


1l 


346    CHAP.  IX.--RISE  AND  FALL-EFFECT  OF  VELOCITY. 

as  the  length  which  the  rod  would  have  to  stretch  to  avoid  exceeding  the  elastic 
limit.     But  (assuming  uniformity  of  elasticity)  the  rod  can  only  stretch  in  any 

case  the  -i°°^     part  of  its  length  (— ^\  without  rupture,  and  only  half  that 

26,000,000  \i,3oo/ 

without  permanent  set. 

Therefore,  to  avoid  these  efifects  and  yet  enable  the  bar  to  do  (or  use  up)  the 
requisite  amount  of  work  in  slopping  the  car,  it  would  have  to  be 

128.64  X  1300  =  167,232  ft.  long  to  avoid  the  rupture,  and 
257.28  X  2600  =  668,928  ft.  long  to  avoid  permanent  set;— 

which  are  rather  long  bars.  The  consequences  to  the  car  body  also  we  will  not 
consider,  but  the  example  will  serve  to  illustrate  the  laws  of  the  mutual  converti- 
bility of  energy  or  work,  and  velocity. 

397.  From  this  ready  interconvertibility  of  velocity  and  work 
results  the  undoubted  fact — too  little  considered  by  engineers — 
that  train  resistance,  in  practical  operation  (i.e.,  as  measured  by 
the  tension  on  the  draw-bar  of  the  locomotive,  or  graphically 
recorded  by  a  dynamometer)  bears  no  very  close  and  apparent 
relationship  to  what  may  be  called  the  dead  resistance,  as  deter- 
mined by  adding  the  nominal  grade  resistance  to  a  certain 
rolling  friction,  without  paying  any  regard  to  the  effect  of 
differences  of  velocity.  This  is  well  understood  by  all  those 
who  have  had  occasion  to  deal  with  dynamometer  experiments, 
and  is  the  greatest  difficulty  in  deducing  valuable  results  from 
such  experiments.  It  is  also  well  understood  in  a  practical  way 
by  locomotive  engineers,  who  appreciate  the  great  advantage  of 
a  "  run  at  a  hill  "  and  the  disadvantage  of  a  stop  on  it. 

398.  Now  the  object  before  the  engineer  in  laying  out  a  rail- 
way is,  obviously,  to  lay  out  his  line  so  that  the  demand  on 
THE  LOCOMOTIVE,  and  not  the  absolute  grade  resistance  (which 
latter  is  in  itself  a  thing  of  no  moment),  shall  be  as  nearly  uni- 
form as  possible,  under  the  conditions  which  actually  exist  in 
the  daily  routine  of  operation.  If,  at  a  certain  point,  the  veloc- 
ity of  the  trains  has  certainly  to  be  increased,  in  addition  to 
overcoming  the  normal  grade  and  rolling  resistances,  the  gradi- 
ent is  in  effect  increased  at  that  point.  If  at  a  certain  other 
point  velocity  can  safely  be  acquired  before  reaching  it  and  then 


CHAP,  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY.     347 

surrendered,  the  grades  are  in  effect  reduced.  The  virtuaT^ 
equivalent  profile,  including  these  effects  of  velocity,  is  what  the 
engineer  should  study,  and  should  consider  as  the  true  profile 
of  the  line  for  operating  purposes,  as  distinguished  from  the 
nominal  grades  shown  by  the  levels  and  the  plotted  profiles 

399.  The  two  are  widely  different  even  in  freight  service, 
and  much  more  so  in  passenger  service.     Thus,  when  a  train 
starts  out  from  a  station  it  has  to  acquire  a  certain  velocity  as 
speedily  as  possible-say  15,  20,  or  40  miles  per  hour;  giving 
which  velocity  is    mechanically  equivalent   to  lifting  the  train 
vertkally  (see  Table  118)   7.99,  14.20,  or  56.80  feet.     This   rise, 
divided  by  the  distance  in  which  the  velocity  is  or  must  be  at- 
tained, gives  a  grade  which  is  in  effect  an  addition  to  the  actual 
grade.     Thus,  if  there  be  a  station  at  A,  Fig.  6%^  on  a  nominally 
level  grade,  and  it  be   necessary  to  acquire  a  velocity  of  21  3 
miles    per    hour    (being    nearly    the    "velocity-head,"    as    per 
lable   118,  for  16.08  feet),  and  it  be  necessary  to  acquire  that 
velocity    in   at    most   2000   feet,   the    "virtual"    grade   is   that 

shown  by  the  solid  line  in  Fig.  (>^,  or  ^?  =  .804  per  cent. 
_  .  20  *^ 

If  the   train    then  strikes  a  down  grade,  no  change  in    the 
strain  upon  the  draw-bar  necessarily  takes  place,  nor  probably 
will  take  place,  if  the  grade  be  short 
or  the  speed  high.     More  probably, 
the   same   steam-power  and    ten- 
sion on  the  draw-bar  will  be  contin-  A 
uously  exerted,  and   the  excess  of 
power  over  that  consumed   by  the 

resistances  will  be  stored  up  in  the  train  as  velocity,  to  be 
surrendered  in  part  on  the  next  up  grade;  and  so  on  indefi- 
nitely. 

In  fast  passenger  service,  with  a  sufficiently  good  track  and 
alignment  to  admit  of  high  speed,  the  amount  of  energy  required 
to  cause  even  slight  modifications  of  speed  between  stations  is 
so  great  that  the  effect  of  undulations  of  gradients,  even  of  con- 
siderable size,  is  almost  wholly  eliminated. 


Fig.  68. 


348 


I  I  /I  I  I  I 

2  S/g  $   §  8 


\i 


CHAP.  IX.— RISE  AND  FALL. 

400.  Thus,  Fig.  69  is  an  ex- 
ample  from  actual  practice  of  a 
very  bad  undulatory  profile  (for 
freight  service),  which  not  only 
may  be,  but  actually  is,  operated 
by  express  passenger  trains  almost 
as  a  level  grade. 

To  determine  in  practice  how 
velocity  affects  the  operation   of 
this  or  any  other  similar  profile  is 
a  problem  of  the  simplest  possible 
character.     We    require    nothing 
to  aid  us  but  Table  118.    Thus, 
let  us  suppose   that   an   express 
passenger    train   approaches   the 
point  A,    Fig.    69,  as   it  actually 
does,  at  a  velocity  of  about   50 
miles  per  hour,  the  point  being 
situated  at  the  foot  of  a  long  gen- 
tle incline.      This  velocity  being 
given,  in  order  to  run  without  a 
stop  to  the  point  B,  a  distance  of 
about   eleven    miles,    no    further 
burden  is  laid  upon  the  locomo- 
tive  than   to   furnish   the  power 
which    is   necessary  to  keep  the 
train  moving  on  the  "  equivalent" 
maximum   grade,  which    in   this 
case  is  a  dead  level,  despite  the 
fact  that  the  profile  maximum  is 
I  per  cent  or  52.8  ft.  per  mile. 

The  process  of  determming  in 
advance  whether  it  will  be  possi- 
ble to  operate  this  undulating 
grade  as  a  level  gradient  in  this 
manner,  and  what  the  fluctuations 
of  velocity  must  be  to  do  it,  is  as 
follows: 

401.  The  train  at  the  point 
A,  moving  (by  assumption)  at  50 
miles  per  hour,  has  sufficient  vis 


CHAP.  IX— RISE  AND  FALL— EFFECT  OF  VELOCITY.     349 

viva  or  "velocity-head"  (Table  118)  to  lift  it  through  88.75  ^^et  verti- 
cally before  coming  to  a  state  of  rest.  In  running  to  b,  it  makes  a 
rise  of  130—80  =  50  feet,  and  if  the  engine  is  to  do  only  the  work  due  to 
a  level  grade  all  the  work  of  lifting  the  train  through  this  50  feet  must 
be  done  from  the  energy  stored  as  velocity,  and  there  will  consequently 
be  left  in  the  train,  on  reaching  b,  only  88.75  —  50  =  38.75  vertical  feet  of 
"  head,"  which  corresponds  (Table  1 18)  to  33  +  miles  per  hour.  The  par- 
ticular grade,  and  hence  the  horizontal  distance,  between  A  and  b  makes 
no  difference,  because  the  engine,  if  it  is  to  operate  the  grade  as  a  level, 
furnishes  the  power  to  overcome  the  frictional  resistances  on  a  level,  and 
no  more;  and  these  alone  are  affected  by  the  horizontal  distances. 

From  b  X.O  c  the  train  descends  30  feet.  Therefore,  the  engine  being 
supposed  to  continuously  exert  the  same  amount  of  force  to  overcome 
the  frictional  resistances,  all  the  additional  accelerating  force  due  to  the 
descending  grade  will  be  communicated  to  the  train  in  the  form  of  ve- 
locity, and  at  the  foot  of  the  grade,  at  c,  the  train  will  be  moving  with 
the  velocity  due  to  38.75  +  30=  68.75  vertical  feet,  which  (Table  118)  is 
44  miles  per  hour. 

From  c  \.o  d  there  is  a  vertical  rise  of  20  feet,  and  consequently  the 
train  will  be  moving  at  d  at  the  speed  due  to  68.75  —  20  =  48.75  feet,  or 
(Table  118)  37  +  miles  per  hour. 

402.  So  the  undulations  of  speed  continue,  as  shown  by  figures  and 
the  dotted  diagram,  until  on  reaching  the  points, which  is  neither  higher 
nor  lower  than  the  initial  point  A,  the  train  is  found  to  be  moving  with 
the  same  velocity  as  at  a,  or  50  miles  per  hour.  Whether  this  will  be  the 
case  at  any  point  we  can  determine  at  once,  without  tracing  up  the  inter- 
mediate velocities,  simply  from  its  relative  level  compared  with  A. 

Thus,  the  highest  point  on  the  stretch  is  at  elevation  140,  or  60  feet 
above  A.  The  train  here,  consequently,  will  have  only  the  velocity  due 
to  88. 75  — 60  =  28.75  vertical  feet,  or  nearly  28^  miles  per  hour.  The 
lowest  point  is  the  point  n,  which  is  70  feet  below  A,  and  the  velocity 
at  that  point  will  consequently  be  that  due  to  88.75  +  7°  =  158.75  vertical 
feet,  or  66.9  miles  per  hour. 

403.  Now  if  we  had  a  dynamometer  record  of  the  tension  on  the 
draw-bar  during  such  a  run  as  this  (which  the  writer  has  made  many 
times  over  that  identical  piece  of  track  at  approximately  the  assumed  ve- 
locities) we  should  find  it  absolutely  uniform  and  unvarying,  without  any 
appreciable  trace  or  evidence  in  the  recorded  strains  that  there  were  any 
undulations  in  grade  or  deviations  from  a  perfect  level  on  the  stretch 
passed  over.     If  we  were  to  stand  and  watch  any  coupling  of  the  train 


I 


350    CHAP.  IX.^RISE  AND  FALL-EFFECT  OF  VELOCITY. 

we  should  be  led  to  the  same  conclusion.  Assuming  the  vertical  curves 
connecting  the  grades  to  have  been  properly  put  in.  there  would  be  no 
'•slack"  at  any  time,  nor  crowding  of  one  car  upon  another;  but.  on  the 
contrary,  there  would  be  a  continuous  and  substantially  uniform  tension 
on  ever'y'draw-bar,  whether  going  up  hill  or  down,  and  the  motion  of  the 
train  would  be  as  steady  as  if  the  grade  were  in  fact  level,  as  to  all  intents 
and  purposes  it  is— AT  THAT  VELOCITY.  At  slower  velocities,  or  with 
intervening  stops,  or  with  very  high  summits,  the  conditions  are  widely 

different. 

404.  To  determine  the  effect  of  all  these  and  similar  facts  in  advance 
for  any  piece  of  track  and  any  assumed  speeds,  we  have  only  to  construct, 
with  the  assistance  of  Table  ii8.  what  may  be  termed  the  equivalent  or 
VIRTUAL  PROFILE,  which  is  the  actual  profile  so  modified  as  to  include 
these  effects  of  probable  or  admissible  variations  of  velocity.  Thus  at  A, 
Pi<r.  69  or  70,  moving  at  50  miles  per  hour,  the  train  is  in  the  same  con 


A'Coi-MilesperH.)],'^ ^ o^ 


Fig.  70. 

dition  mechanically,  as  respects  demands  upon  the  motive-power,  as  if  it 
were  at  A',  Fig.  70,  88.75  feet  higher,  moving  at  0+  miles  per  hour.  In 
either  case  it  would  arrive  at  the  point  b',  on  a  level  with  A\  at  a  velocity 
of  0+  miles  per  hour.  As.  however,  it  has  only  to  rise  50  feet  to  b,  it 
will,  on  arriving  at  b,  still  retain  a  velocity  which  will  lift  it  through 
38.75  vertical  feet,  and  consequently  the  point  for  the  equivalent  profile 
is  at  b'  38.75  feet  above  b.  To  have  the  equivalent  pr^'"Tle  continue  a  level 
line,  its  altitude  above  c  at  c'  must  be  68.75.  and  the  train,  consequently, 
must  be  moving  at  c  at  44  miles  per  hour.  As  this  is  an  admissible  pas- 
senger velocity,  to  operate  the  line  ac  as  a  virtual  level  at  passenger 

speed  is  not  impossible. 

405.  If.  at  the  point  c,  it  were  necessary  to  slow  up  to  a  velocity,  say, 
of  20  miles  per  hour,  to  pass  through  a  town  or  for  sharp  curvature,  or 
any  other  reason,  this  level  virtual  profile  could  not  be  maintained. 
What  the  equivalent  profile  would  actually  be  equivalent  to.  must  be 
determined  by  laying  ofl  above  c  the  vertical  altitude  due  to  a  velocity 


A" 

1 
1 

ie^^-- 

y  \ 

^  it 

• 

y    \  _, 

<to'^ 

<v 

,' 

•'^i„.^M 

«b 

-J^^zsC^ 

1 

6C 

0 

^ 

1    1 

^■!^_L. 

1  1  t  1 

Fig.  7x. 


CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY.     35 1 

of  20  miles  per  hour,  or  14.20  feet.  We  then  find  that  the  equivalent 
profile  becomes  a  sliarp  descent  to  c, — requiring  the  excessive  use  of 
brakes,— and  an  equally  sharp  ascent  to  d' :  thus  showing  that  it  is 
practically  impossible  to  resume  the  original  velocity  at  d. 

406.  To  determine  what  velocity  we  might  obtain  at  d:  Determine 
by  computation,  or  from  experience  elsewhere,  what  is  the  maximum 
grade,  p.  Fig,  71,  up  which  the 
full  power  of  the  engine  could  keep 
the  train  moving  at  20  miles  per 
hour,  which  will  be  a  pretty  stiff 
grade.  The  difference,  dd".  Fig.  71, 
between  the  elevation  which  the 
train  might  attain  on  such  grade 
and  that  which  it  actually  has  to  attain  at  d  will,  if  the  engine  does  so 
exeit  its  full  power  between  c  and  d,  be  communicated  to  the  train  in 
the  form  of  velocity,  and  it  will  be  moving  at  ^  with  the  velocity  due  to 
14.20  +  dd"  feet.  If  the  equivalent  grade  were  2  per  cent,  or  105.6  feet 
per  mile,  instead  of  the  actual  grade  of  0.5  per  cent  mile,  the  value  of  dd" 
would  be  30  feet,  and  the  train  would  be  moving  at  d  with  the  velocity 
due  to  14.20  +  30  =  44.20  feet  =  35.3  miles  per  hour.  The  point  at  which 
it  will  be  mechanically  possible  for  the  train  to  entirely  recover  from  the 
effect  of  a  check  or  stop  at  c  may  be  determined  with  equal  simplicity 
(assuming  that  the  train  resistance  did  not,  as  it  would,  increase  with 
speed)  by  prolonging  the  2  per  cent  equivalent  grade  cd"  until  it  inter- 
sects 2Xp  the  level  equivalent  grade  for  the  run  without  a  stop.  At  that 
point  the  traction  of  the  engine  may  be  reduced  to  that  due  to  a  level 
grade  and  the  run  continued  as  before,  as  shown  in  Fig.  69. 

407.  In  this  simple  manner,  it  will  be  evident,  an  equivalent 
profile — which  for  all  operating  purposes  is  the  profile,  and 
which  is  consequently  the  only  one  which  the  engineer  should 
consider  in  laying  out  the  line — may  be  constructed  almost  by 
inspection,  assisted  by  Table  118,  for  any  grade  or  section  of  line 
whatever,  and  for  any  speed  or  variations  of  speed  whatever. 
Such  an  equivalent  profile,  if  constructed  for  high-speed  trains, 
will  bear  little  or  no  resemblance  to  the  actual  profile;  and  even 
at  low  freight  speeds  it  will  be  very  seriously  modified,  and  widely 
differe,nt  in  appearance  from  the  actual  profile.  At  points  where 
a  stop  or  a  slackening  of  speed  occurs  the  equivalent  grade  may 
be  very  much  higher  than  the  actual.     At  other  points  where 


352     CHAP.  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY. 


considerable  velocity  at  the  foot  of  grades  is  probable  and  ad- 
missible it  will  be  very  much  lower. 

In  only  one  respect  is  such  a  profile 
liable  to  be  deceptive.  The  profile  it- 
self demands  no  allowances,  but  the 
hauling  power  of  an  engine  is  materially 
greater  in  making  a  start  from  what  it 
is  at  speeds  above  lo  or  15  miles  per 
hour,  at  which  latter  speeds  or  higher 
it  is  not  possible  ordinarily  to  utilize 
the  full  adhesion  of  the  locomotive,  for 
reasons  given  in  Chapter  XI.  and  XIII. 
Therefore  a  higher  virtual  grade  at 
stopping  points  only  is  not  necessarily 
a  limiting  gradient. 

408.  Fig.  72  is  a  representation  of  a  vir- 
tual and  actual  profile,  constructed  in  the 
above  manner,  for  an  assumed  maximum 
freight  speed  of  25  miles  per  hour.  We 
have  only  to  take  each  governing  point  in 
succession  ;  determine  for  each  what  is  the 
actual,  probable,  necessary,  or  safe  velocity 
at  that  point ;  lay  off  vertically  above  it  the 
vertical  feet  to  which  this  velocity  is  equiva- 
lent, as  given  in  Table  118;  and  connect  the 
points  thus  fixed  by  right  lines.  This  gives 
the  equivalent  and  for  all  operating  purposes 
the  actual  profile,  except  that  the  varying 
train  resistance  at  various  speeds  must  be 
remembered,  and  likewise  the  greater  adhe- 
sive power  of  the  locomotive  when  starting 
and  using  sand. 

409.  Thus  at  c,  where  a  stop  is  neces- 
sary, the  velocity  will  be  zero,  and  the  virtual 
and  actual  profiles  will  coincide.  The  grades 
approaching  this  position  on  each  side  are 
necessarily  much  heavier  in  the  virtual  than 

in  the  actual  profile.     At  other  points,  as  at  the  depression  d,  the  veloc- 
ity will  be  considerable,  and  the  approaching  grades  on  each  side  are 


CHAP.  IX.— RISE  AND  FALI^EFFECT  OF  VELOCITY.    353 

on  the  virtual  profile  very  much  reduced  by  that  fact.  At  still  other 
pomts,  as  at  the  foot  of  the  long  grade  e,  the  velocity  of  approach  may  be 
considerable,  and  yet  the  grade  so  long  that  this  velocity  has  but  a  slight 
effect  in  reducing  the  virtual  grade.  If  there  were  a  station  or  a  pretty 
heavy  minor  grade  near  the  foot  of  the  long  grade,  as  is  apt  to  be  the 
case,  no  surplus  velocity  at  all  could  be  assumed,  and  the  virtual  and 
actual  profile  would  again  coincide. 

For  a  further  example  from  practice  of  the  effect  of  varying  velocity  to  mod- 
ify gradienis.  and  of  the  deceptive  indications  of  the  power  of  engines  obtained 
by  neglectmg  it,  see  the  close  of  Chapter  XX. 

410.  It  will  be  evident  that,  in  practical  work,  a  virtual  profile  need 
not  be  constructed  for  the  entire  length  of  the  line,  but  only  at  points 
where  it  is  likely  to  make  an  important  difference.     On  long  stretches 
of  level  or  minor  gradients  we  need  feel  no  anxiety,  unless  at  stopping 
points.    On   long  stretches  of  maximum  grade  we  know  that  we  must 
accept  the  actual  as  the  virtual  grade.     In  such  a  sag  as  that  at  d.  Fig 
72,  It  IS  plain  that  virtual  profile  will  differ  importantly,  but  it  is  unneces- 
sary  to  draw  it  as  in  the  cut.     Granting  our  assumed  safe  velocity  in  the 
hollow  d,  of  25  miles  per  hour  (vel.-head.  by  Table  118.  22.2  ft.),  and  the 
assumed  velocity  of  10  miles  per  hour  (vel.-head.  3.55  ft.)  on  the  summits 
on  each  side,  the  assumed  difference  of  velocity  in  effect  makes  a  fill  2X 
dot  22.2-3.5  =  16.7  feet.     We  have  therefore  merely  to  lav  off  vertically 
16.7  feet  above  d  and  connect  the  point  thus  fixed  and  the  actual  sum- 
mits by  a  dotted  grade  line,  and  we  obtain  the  same  virtual  profile  as 
that  shown  in   Fig.  72,  but  3.55  feet  lower,  so  as  to  touch  the  actual 
grade  line  at  the  summit ;  and  so  at  any  other  point. 

411.  The  danger  in  using  such  a  process  as  this  as  a  basis  for 
laying  out  grades  is  solely  one  common  to  most  engineering 
and  other  work— bad  judgment  as  to  the  practical  possibilities 
and  necessities.  Thus,  a  stop  may  be  required  where  one  is  not 
anticipated,  or  a  velocity  may  be  assumed  which,  owing  to  cur- 
vature or  other  cause,  may  not  be  practicable  or  expedient.  The 
possible  use  of  sand  in  starting  or  at  particular  points,  or  the 
varying  power  of  the  locomotive,  may  be  forgotten,  or  a  speed 
may  be  assumed  at  summits  so  low  as  to  leave  an  insufficient 
margin  for  head  winds  and  similar  contingencies.  The  lowest 
speed  that  can  properly  be  assumed  at  a  summit,  as  a  general 
rule,  in  view  of  these  contingencies,  is  about  10  miles  per  hour 


I 


■' 


i  i 


1  ; 


;r( 


'  i\ 


354    CHAP.  IX,-RISE  AND  FALL-EFFECT  OF  VELOCITY, 

for  freight  trains  and  20  miles  per  hour  for  passenger  trains. 
Even  that  is  leaving  very  little  margin,  for  when  a  train  has 
fallen  below  a  speed   of  10  miles  per  hour  it  requires  very  little 

to  stall  it. 

Nevertheless  with  reasonable  care  and  skill  it  is  a  simple  mat- 
ter to  construct  such  a  profile  and  save  the  consequences  of  the 
vague  and  rash  guesses  as  to  the  effect  of  "  taking  a  run"  at 
grades,  which  are  sometimes  made,  when  the  effect  of  momentum 

is  considered  at  all. 

This  most  important  caution  should  be  remembered,  however: 
With  the  virtual  profile  once  properly  constructed,  no 
FURTHER  liberties  CAN  BE  TAKEN  WITH  IT.  The  maximum  vir- 
tual  grade  represents  precisely  the  power  of  the  engine;  and 
whether  the  virtual  gradient  be  100  feet  or  100  miles  long,  it  is 
equally  decisive  of  the  power  of  the  engine,  except  as  the  latter 

may  itself  vary. 

412.  It  will  be  evident  from  the  preceding  discussion  that 
rise  and  fall  has  the  most  serious  effect  on  slow  freight  service, 
and  will  in  all  cases  become  inadmissible  for  such  service  con- 
siderably before  it  becomes  of  serious  moment  for  passenger 
trains  Such  an  undulation  of  profile  as  is  shown  at  d.  Fig. 
72  for  example,  produces  hardly  any  measurable  effect  upon 
the  speed  of  a  fast  passenger  train,  simply  causing  an  undula- 
tion  of  a  few  miles  per  hour  in  ordinary  passenger  speed  (say 
from  50  to  55  miles  per  hour),  which  is  hardly  perceptible  to  the 
senses  In  this  rise  and  fall  is  unlike  curvature,  for  the  latter  (if 
the  grades  have  been  properly  compensated)  is  most  objection- 
able  for  high-speed  service. 

413.  The  extremelv  important  effect  which  even  very  mod- 
erate fluctuations  of  velocity  may  have  to  modify  nommal 
grades,  even  for  slow  freight  trains,  is  illustrated  in  F.g.  73- 
According  to  the  profile  this  is  a  0.8  per  cent  (42  feet  per  mile) 
maximum  grade,  and  even  allowing  somewhat  for  the  effect  of 
-  momentum"  it  would  be  very  apt  to  be  classed  as  a  0.6  grade. 
In  realitv,  the  0.8  grade  at  the  top  of  the  hill  may  be  one  n^ile 
long  and  it  can  still  be  operated  as  a  virtual  0.4  grade  (21  feet 


CHAP,  IX.— RISE  AND  FALL— EFFECT  OF  VELOCITY.    355 

per  mile)  if  we  may  count  with  certainty  on  approaching  the  foot 
•of  the  hill  at  a  speed  of  23}  ,  ^  miles  per   hour.     We   shall    still 
be  able  to  turn  the  hill  with  \ 
a  velocity  of  nearly  10  miles 
per  hour,  our  highest  inter- 
mediate  velocity   being    28 
miles  per  hour. 

If  we  cannot  count  on  a    V, 
higher  velocity  than  15  miles 
per  hour  at  the  foot  of  the 
hill,  whether   because  curva- 
ture, a  station,  or  bad  grades, 
we  cannot  quite  do  this.     We 
shall  have   only  18  instead  of 
24  vertical  feet  of   **  head  "  in 
the  train  at  elevation  120,  3  of 
which    we    must    have    at    the 
summit  to  avoid  danger  of  stall- 
ing.     As   we   use  up  0.4  feet  of 
head  for  each  station  of  0.8  grade 
the    0.8    grade,    at     the     top     of 
the    hill    cannot    be    longer    than 

18  —  3        15  .  .,    , 

=  -^  =  37.5   stations,   if  the 

0.4         0.4 

entire  grade  is  to  be  operated  as  a 
virtual  0.4. 

Such  undulations  are  often  ex- 
tremely desirable  for  economy's  sake, 
or  to  make  an  otherwise  impossible  lo- 
cation feasible.  Let  us  therefore  deter- 
mine their  exact  effect  on  slow  train 
service  and  the  consequent  limits  of  safe 
practice  ;  since  if  these  limits  are  passed 
unnecessary  injury  may  be  done  to  the 
line.  In  Fig.  73,  for  example,  the  virtual  gradient  shown  is  a 
reasonable  one  because  at  no  point  does  it  reduce  the  speed  verv 
low,  but  if  the  points  at  elevations  60  and  no  were  ten  or  fifteen 
feet  higher  it  would  no  longer  be  so. 


356  CHAP,  IX.-RISE  AND  FALL-SAFE  LIMITS  OF^ 


SAFE   LIMITS    OF   UNDULATIONS  OF   GRADE. 

414.  We  will  suppose  a  train  of  40  cars,  say  1300  feet  long  and  weigh- 
in-  1600  tons,  to  be  moving  with  a  uniform  velocity  of  15  miles  per  hour 
(22  feet  per  second)  toward  station  100,  Fig.  74-  The  pull  of  the  loco- 
motive is  perhaps  16.000  lbs.,  being  in  any  case  precisely  that  required 
to  move  the  train  at  1 5  miles  per  hour  on  a  long  0.2  grade. 

It  has  been  already  stated  (pars.  399.  403)  that  so  long  as  the  steam- 
power  of  the  locomotive  is  unvaried  the  relative  motion  of  the  tram  and 


r 


'IS. 


■(y.99) 


I 

I 

100 
M/Ves  BtrHour— 

IS.  .  ««•» 
Vel.  Heads. 


ieio' 


(7.  as) 


Fig.  74* 


Oa.99) 


the  tension  on  each  draw-bar  will  be  practically  un>forra  and  unvarymg, 
wharever  the  variation  of  grade,  the  change  in  resistance  taking  the  form 
Ifincreased  or  decreased  velocity.  The  only  time  when  the  tension  on 
1  driw  bar  is  not  absolutely  fixed  and  unvarying  is  in  pass.ng  from 
one  grade  to  another,  and  this  occurs  as  follows  :  ,„„,:nnouslY 

415  As  the  enc'ine  passes  over  station  loo,  Fig.  74-  contmuously 
exen'g  the  same  steam'power.  the  change  in  the  rate  of  grade  (rom 
+  0  2  to  -  0.2)  makes  a  difference  of  8  lbs.  per  net  ton  of  >ts  weight,  or 
iv  8x62  5  =  oo  lbs.  in  all,  in  its  pull  on  the  draw-bar,  thus  increasing 
^  pull  on  the  rain  for  the  moment  from  i6.<»o  to  .6  500  lbs.,  or  about 
fir  cent.  This  increased  traction  will  immediately  begm  to  make  he 
tr^n  r^ove  faster,  and  as  some  of  it  must  be  absorbed  •"  "'^'king  the 
eng?ne"tself  move  faster,  not  all  of  it  will  be  transmitted  backward  to 

^'''me"  seconds  afterwards,  two  other  cars  will  have  Pas^^^o-r  sta- 
tion .00  and  will  increase  the  traction  on  the  drawbars  behind  them  by 
sLme  ~o  lbs.  more.  This  increase  of  tractive  force,  likewise,  having  no 
ZTa  resistance  to  use  it  up.  will  take  the  form  of  an  increase  in  velocity. 
So  ^tch  car  in  succe^ion  passes  over  the  break  of  grade  the  acul^ 


CHAP.  IX.— RISE  AND  FALL— SAFE  LIMITS  OF,  357 

^erattng  force  gradually  increases  from  zero  (as  the  engine  approaches 
station  100)  to  8  lbs.  per  ton  of  weight  of  the  whole  train,  when  the 
entire  train  has  finally  passed  over  the  apex. 

416.  The  instant  that  this  occurs  the  tension  on  the  draw-bars  will  be 
precisely  the  same  as  before  throughout,  viz.,  that  due  to  the  work  of  the 
engine  only,  and  will  be  employed  in  the  same  manner — in  overcoming 
the  normal  train  resistance  on  a  grade  of  +  0.2  at  the  original  velocity ; 
while  the  extra  accelerating  force  from  the  change  of  grade  will  be  act- 
ing upon  the  train  independently  to  communicate  velocity,  precisely  as 
if  it  were  descending  the  same  plane  without  resistance  and  with  no 
Other  force  acting. 

The  final  velocity  at  stations  125  and  140  will  be  precisely  the  same  as 
if  it  had  fallen  freely  through  a  height  equal  to — not  the  actual  differ- 
ence of  level  between  100  and  140 — but  through  a  vertical  height  equal 
to  the  drop  in  the  actual— 0.2  grade  from  the  dotted  +0.2  grade,  on 
which,  by  assumption,  the  locomotive  was  exerting  just  enough  power  to 
keep  the  train  moving  at  15  miles  per  hour. 

What  will  be  the  velocity  of  motion,  then,  at  125  ?  Computing  it  as 
before,  we  have — 

The  original  velocity  of  15  miles  per  hour  is  equivalent  to  a 

fall  through  space  of  (see  Table  118) 7.99  feet. 

The  dip  in  the  grade  is 10.00    " 

Hence  the  train  at  125  will  have  the  velocity  "  due"  to  a  free 

fall  of 17.99    " 

which  by  Table  118  will  be  22.5  miles  per  hour. 

This  is  an  entirely  safe  and  unobjectionable  velocity.  At  station  140 
the  "dip"  is  16  feet  instead  of  lo.o  feet,  and  the  velocity  acquired  is 
16.0  +  7.99  =  23.99  vert,  feet  =  a  velocity  of  26.0  miles  per  hour,  which 
may  be  claimed  to  approach  the  utmost  limit  of  expediency  for  freight 
service. 

Had  the  dip  been  20  feet,  the  velocity  acquired  would  have  been 
about  28.1  miles  per  hour.  A  dip  of  20  feet  may  therefore  be  considered 
about  the  maximum  which  it  is  permissible  to  ride  over  in  freio-ht  ser- 
vice without  shutting  off  steam,  on  good  track  and  with  favorable 
alignment. 

417.  These  velocities  would  actually  be  somewhat  less  than  the  fig- 
ures given,  owing  to  the  fact  (i)  that  the  centre  of  gravity  of  the 
train  does  not  rise  quite  as  high  or  fall  quite  as  low  as  the  highest  or 
lowest  point  of  the  track,  and  (2)  that  the  resistance  of  the  train  in- 


III 


358 


CHAP,  IX.-RISE  AND  FALL^SAFE  LIMITS  OF, 


creases  with  the  velocity  (see  Table  120  and  Chap.  XIII.),  whereas  we 
have  assumed  it  to  be  constant;  but  as  the  difference  is  of  no  great 
moment  in  the  details  we  are  now  considering,  and  as  the  neglect  of  it 
tends  to  safety,  it  is  not  here  considered. 


Table  120. 

Approximate  Grades  of  Repose  for  Various  Trains  (as  Determined  in 

Table  166).    See  also  Table  180. 

Approximate  General 
Average. 


Velocity. 

Miles 

Per 

Hour. 


ID. 
20. 

40 
50. 
60. 
70. 


Freight  Trains 

Of- 


Twenty 
Cars. 


0.30 
0.36 
0.46 
0.5S 

0.73 
1. 10 


Fifty 
Cars. 


0.28 

0.33 
0.40 

0.48 

0.59 
0.90 


Passenger  Trains 

OF — 


Four 
Cars. 


0.34 
0.40 

0.52 
0.69 
0.88 

1.38 
2.02 
2.81 
3.74 


Twelve 
Cars. 


27 

34 
42 

53 
65 
98 

39 
1.89 

2.49 


o 
o 
o 
o 
o 
o 
I 


Grade 
Per  Cent. 


0.30 
0.35 
0.40 
0.50 
0.65 
1. 00 
1.50 
2.25 
3.00 


Feet 
Per  Mile. 


16.84 
19.48 
21.12 
26.40 
36.32 
52.80 
79.20 
118.80 
168.40 


The  resistance  in  pounds  per  ton  is  given  by  multiplying  the  above  by  20. 

418.  Now,  what  takes  place  in  the  hollow  at  140,  when  the  engine  be- 
gins to  ascend  ?  Here,  if  anywhere,  is  the  point  of  danger,  and  here  is  in 
fact  a  very  great  danger,  the  precise  nature  and  limits  of  which  should  be 
determined.  The  danger  arises  from  the  fact  that  in  the  hollow  of  a 
grade  where  the  head  of  the  train  is  on  an  up  grade  and  the  rear  of  the 
train  on  a  down  grade,  there  is  liable  to  be  a  momentary  crowdmg  to- 
gether of  the  train. 

This  liability  occurs  only  when  the  head  and  rear  of  the  tram  are  on 
different  grades.  We  have  just  seen  (pars.  41 5.  4i6)  that  when  the  whole 
train  is  on  the  same  grade,  however  great  its  rate  of  ascent  or  descent,  the 
tension  on  the  draw-bars  will  remain  the  same,  being  that  arising  from  the 
traction  of  the  locomotive,  and  the  additional  energy  communicated  to  or 
taken  from  the  train  by  the  grade  will  take  the  form  of  an  increase  or 
decrease  of  velocity,  which  is  uniform  throughout  the  tram  because  the 

grade  is  uniform.  . 

419.  In  the  hollow  of  a  grade  this  is  not  so.  and  hence  arises  the 
tendency  for  the  rear  of  the  train  to  run  up  against  the  front  when  pass- 
ing such  points  under  certain  conditions,  taking  all  the  "  slack"  out  of 


CHAP.  IX.— RISE  AND  FALL—SAFE   LIMITS  OF. 


359 


the  train  and  bringing  the  draw-bars  into  more  or  less  compression.  The 
next  instant,  when  the  hollow  is  passed  and  the  uniform  grade  (whatever 
it  may  be)  is  struck,  the  normal  condition  of  tension  throughout  the  train 
returns,  but  returns  with  a  jerk;  for  with  the  present  awkward  style  of 
couplings  the  difference  in  length  of  a  train  in  tension  or  compression  is 
very  considerable.  The  "  slack"  varies  from  4  to  6  inches  or  more  per  car, 
according  to  the  degree  of  force  with  which  the  springs  are  compressed 
and  extended,  so  that  a  train  of  60  or  80  empty  cars  may  shorten  as  much 
as  30  to  40  ft.  The  jerk,  when  this  slack  is  "taken  out,"  is  exceedingly 
apt  to  break  the  train  in  two,  and  it  is  at  such  hollows  in  grades  that  most 
of  such  breakages  occur. 

420.  The  reality  of  the  danger  may  be  illustrated  by  a  literally  truthful 
anecdote :  In  the  old  days  of  iron  rails,  some  thirty-five  years  ago,  when 
derailments  were  much  more  frequent  and  more  easily  caused  than  now,  a 
certain  especially  poor  road  was  having  very  frequent  derailments,  so  that 
each  conductor  was  having  derailments  every  few  days.  One  of  the  older 
conductors  was  singularly  exempt  from  such  accidents,  for  which  no 
reason  appeared.  In  answer  to  repeated  questions,  he  at  last  confessed 
that  he  "always  kept  his  caboose  brake  set  up  a  little."  This  was  con- 
trary to  orders,  but  it  had  the  practical  effect  of  keeping  the  draw-bars 
always  in  tension,  and  at  the  cost  of  a  slight  waste  of  power  prevented 
the  more  serious  danger. 

Such  crowding  together  is  dangerous,  not  only  for  the  quick  jerk 
which  must  almost  inevitably  follow  it.  but  because  it  tends  to  crowd  the 
cars  out  sidewise  against  one  or  the  other  rail,  and  so  produce  irregularity 
of  motion,  causing  the  wheels  to  hunt,  as  it  were,  even  more  zealously 
than  they  ordinarily  do.  for  the  first  defect  by  which  they  may  escape 
from  the  track.     Especially  on  curves  this  is  very  dangerous. 

421.  The  philosophy  of  trains  breaking  in  two  is  simply  this :  At  the  top  of 
the  grade  the  steam  is  partially  shut  off  and  the  brakes  put  on  slightly  ;  but 
before  reaching  the  foot  of  the  grade  the  brakes  are  almost  always  let  off,  and 
the  train  strikes  the  foot  of  the  ascent  "  full  of  slack."  A  careful  engineman 
will  then  let  on  steam  gently,  and  all  will  be  well.  The  more  careless  will  "  pull 
out"  with  a  jerk,  and.  if  he  be  careless  enough,  he  will  be  almost  certain  to 
break  a  link  or  pull  out  a  draw-head,  for  such  parts  can  hardly  be  made  strong 
enough  (at  least  in  the  present  fashion)  to  resist  a  too  sudden  exertion  of  the 
power  of  the  engine.  To  a  great  extent  the  number  of  such  accidents  is  en- 
tirely in  the  hands  of  the  engineer.  It  has  not  unfrequently  happened  that, 
when  the  employes  were  annoyed  by  an  increase  of  train  or  other  cause,  the 
feeling  of  annoyance  has  taken  the  form  of  a  jerky  fashion  of  pulling  out  the 
throttle,  which  has  resulted  in  an  alarming  increase  in  such  accidents  and  ter- 


360  CHAP,  IX.— RISE  AND  FALL— SAFE  LIMITS  OF. 


rifled  a  doubling  or  inexperienced  superintendent.  So,  too,  the  introduction  of 
heavier  engines  has  had  and  will  almost  certainly  have  dangerous  consequences, 
— for  a  time, — partly  because  the  enginemen  are  really  inexperienced  in  hand- 
ling such  powerful  machines  and  partly  from  a  secret  willingness  to  throw  dis- 
credit upon  them. 

422.  We  will  consider  the  mechanical  reasons  why  a  very  slight  set- 
ting up  of  brakes  on  a  rear  car  should  reduce  these  dangers,  and  how — 
as  that  remedy  is  objectionable  as  a  regular  reliance — it  also  can  be  safely 
dispensed  with  in  passing  sags. 

A  train  of  cars  coupled  together  may  be  considered  as,  mechanically, 
a  single  solid  body.  All  solid  bodies  have  m  ore  or  less  elasticity,  and 
alter  their  dimensions  under  exterior  force  applied  to  certain  parts  only. 
A  train  has  more  than  usual  longitudinal  elasticity:  that  is  all. 

The  motion  of  such  a  body,  as  respects  the  action  of  gravity,  is  the 
same  as  if  its  mass  were  concentrated  at  its  centre  of  gravity. 

423.  The  centre  of  gravity  of  such  a  train  does  not  descend  into  the 
apex  of  the  hollow  in  Fig.  74  or  75  (assuming  such  sharp  intersections  of 


L«vet. 


Fig.  75. 


grade  to  exist  in  practice),  although  each  individual  car  does.  Its  path 
lies— for  simple  geometrical  reasons  which  the  student  may  be  assumed 
either  to  understand  or  to  take  for  granted— at  a  uniform  distance  above 
a  circular  arc  or  parabola  (according  to  the  assumptions  made)  tangent  to 
the  two  grades  at  the  points  e.g.,  one  half  train-length  from  the  apex.  In 
Fig.  75  we  assume,  as  the  simplest  case,  that  a  level  grade  intersects  an 
0.6  per  cent  ascent,  instead  of  a  —  0.2  and  +  0.4  grade  in  Fig.  74-  The 
results  we  shall  reach  are  not  essentially  varied,  whatever  the  rates  of  the 
separate  grades,  if  their  angle  of  intersection  is  the  same. 

Let  us  assume  for  the  moment  the  train  in  Fig.  75  ^o  be  exerting 
within  itself  just  energy  enough  to  balance  its  own  resistances,  so  that  it 
is  in  the  theoretical  condition  of  a  body  moving  in  vacuo  without  either 


CHAP.  IX.— RISE  AND  FALL— SAFE  LIMITS  OF.  361 


gaining  or  losing  velocity,  and  moving  at,  say,  26  miles  per  hour,  equal 
to  a  "  velocity-head  "  (Table  118)  of  23.99  leet.  For  simplicity  we  will 
assume  the  train  to  be  1200  feet  long  and  to  weigh  uniformly  one  ton 
per  foot,  and  we  will  assume  it  to  consist  of  only  8,  12,  or  more  very  long 
cars  instead  of  some  40,  as  it  probably  would. 

424.  Under  these  conditions,  when  the  train  has  reached  the  position 

mdicated  by  the  black  line  OC  in  Fig.  76,  with  the  rear  car  just  past  the 

apex  O,  its  centre  of  gravity  B  will  be  precisely  6.00  x  0.6  =  3.6  feet  higher 

than  at  A,  and  the  train  as  a  whole  will  have  surrendered  an  amount  of 

^energy  and  of  velocity  corresponding  to  that  height.    The  centre  of 


H2e.o 


J L 


Leve/. 


Fig.  76. 


•^avity  will  have  moved  in  the  arc  AOB,  and  the  velocity  with  which 
the  tram  as  a  whole  is  moving  at  any  point  Oor  ^  is  given  with  absolute 
precision  by  substracting  the  ordinates  to  the  curve  from  the  base-line 
AA  from  the  mitial  "  velocity  head,"  as  is  done  in  Fig.  76.  At  B  the 
velocity  will  be  only  24.0  miles  per  hour. 

With  the  train  in  this  position,  each  car  considered  separately  would 
have  surrendered  the  energy  and  velocity  represented  by  the  successively 
dimmishmg  ordmates  aa\  and  if  the  train  were,  as  assumed,  a  body 
movmg  through  space  from  original  impulse  without  resistance  or  com- 
municated force,  the  inevitable  effect  of  such  conditions  would  be  to  pro- 
duce a  uniform  compression  throughout  the  body  at  all  the  points  aa' 
(each  rear  particle  pressing  against  that  in  front  of  it)  whenever  the  path 
of  the  body  were  deflected  upward,  however  slightly. 

425.  But  the  train,  although  as  a  whole  it  is  in  the  condition  stated, 
yet  internally  to  itself  is  in  very  different  condition.  A 'strong  acceler- 
atmg  force  fthe  engine)  is  acting  in  front  at  C;  a  strong  retarding  force 
(say  10  lbs.  per  ton)  throughout  the  rear  of  the  body.  The  two  counter- 
act and  destroy  each  other,  their  net  resultant  being  zero ;  but  in  so  doing 
they  produce,  or  tend  to  produce,  a  state  ot  tension  throughout  the  train. 


362  CHAP,  IX.-^RISE  AND  FALL—SAFE  LIMITS  OF. 


What  is  required  is,  not  that  this  tension  shall  not  be  reduced  m 
passing  changes  of  grade,  but  that  it  shall  not  be  exchanged  in  any  part 
of  the  train  (or  only  in  a  very  small  part)  for  a  state  of  compression.  A 
train  may  be,  as  respects  its  couplings,  in  three  conditions : 

1.  In  tension,  its  normal  condition,  which,  whether  greater  or  less,  will 
only  extend  the  springs  a  little  more  or  less,  but  make  no  material  differ- 
ence in  the  whole  length  of  the  train. 

2.  In  neither  tension  nor  compression,  the  two  adjacent  cars  tending 
for  the  moment  to  move  with  the  same  velocity,  so  that  no  force  of  any 
kind  is  communicated  from  one  to  the  other.  This  condition  can  only 
be  momentary. 

3.  In  compression,  the  cars  behind  crowding  upon  those  in  front. 

In  the  transition  from  the  first  to  this  last  condition  lies  the  whole 
danger.  So  long  as  we  do  not  pass  the  second  (which  is  more  properly 
merely  a  line  of  demarcation  between  the  first  and  third)  we  are  safe. 

426.  This  we  shall  avoid  if  the  rear  car  (or  cars),  where  the  tension  is 
least,  nowhere  itself  tends  to  move  faster  than  the  train  as  a  whole  is 
moving  at  the  same  moment,  during  the  period  of  transition  from  one 
grade  to  another.  Figs.  75,  76,  or  78. 

The  rear  car,  when  travelling  on  a  grade  of  any  rate,  as  a,  b,  or  c,  Fig. 

yy,  has  a  certain  frictional  resistance 
which  will  make  it  of  itself,  without 
exterior  assistance,  surrender  veloc- 
ity as  if  it  were  moving  on  the  dot- 
ted grade  without  friction,  instead  of 
Fig.  77.  on   the  actual    grade  with    friction. 

The  difference  between  the  dotted  and  actual  grade  is  the  so-called 
"  grade  of  repose,"  marked^  in  Fig.  78.  By  even  a  slight  application  of 
brakes  this  grade  of  repose  may  be  very  greatly  increased. 

Since  the  train  as  a  whole,  then,  is  moving,  mechanically,  without 
friction,  and  surrendering  velocity  at  the  same  rate  as  if  its  mass  were 
concentrated  at  its  centre  of  gravity  and  moving  in  the  path  thereof  {A 

B,    Figs.  76  and  78),  at 

=  Gr&cfe  of  Repose  of/ctst  Can^f  ^ 


T 


c^.    '■ 


Fig.  78. 


each  point  in  the  passage 
from  A  to  B  the  tram 
as  a  whole  is  surrender- 
ing velocity  at  the  rate 
due    to    the    grade    on 


which  the  centre  of  gravity  is  for  the  moment  moving  m  its   path  AB. 
The  steepest  point  on  this  curve  is  at  the  tangent  point  B,  at  which  same 


CHAP.  IX.— RISE  AND  FALL— SAFE  LIMITS  OF. 


363 


instant  the  rear  car  of  the  train  itself  strikes  the  up  grade  at  6^,  and  en- 
counters the  same  retarding  resistance  as  the  rest  of  the  train,  so  that 
the  danger  of  its  crowding  up  on  it  is  then  past. 

427.  By  comparison  of  the  conditions  just  stated  for  the  last  car  and 
the  whole  train  we  deduce  this  simple  rule : 

To  OBVIATE  ALL  DANGER  OF  THE  REAR  PORTION  OF  THE  TRAIN 
CROWDING  UPON  THE  CARS  IN  FRONT,  WITHOUT  THE  USE  OF  BRAKES, 
AT  ANY   SAG   IN   A   GRADE   LINE: 

The  rate  of  the  grade  on  which  the  head  of  the  train  stands  must  in  no 
case  exceed  that  on  which  the  rear  of  the  train  stands  by  more  than  the 
"grade  of  repose"  of  the  last  car.  Otherwise  the  latter  will  crowd  up 
upon  the  train. 

428.  The  grade  of  repose  may  be  increased  for  the  time  being  above 
the  normal  (i)  by  applying  brakes,  and  (2)  by  the  engineman  "  pulling 
out  "or  beginning  to  exert  more  force  upon  the  train  at  or  quite  near  to 
the  apex  O.  In  the  latter  case,  until  the  train  has  acquired  a  velocity 
corresponding  to  the  new  tractive  force,  the  "grade  of  repose"  of  the  rear 
car,  or  its  resistance  to  moving  with  the  train,  will  be  considerably  greater. 
The  first  of  these  remedies  is  objectionable  as  a  regular  reliance,  and  the 
second  is  too  uncertain.  Therefore  the  rule  above  may  be  considered 
one  which  it  is  desirable  to  adhere  to  strictly  whenever  possible. 

429.  Since  the  conclusions  reached  above  depend  on  the  differ- 
ences in  the  rate  of  grade  (see  Figs. 

yy  and  78),  it  is  obvious  that  they  ap- 
ply alike  to  all  hollows  in  grade  lines, 

whether  both  be  ascending,  both  de-  Fig.  79. 

scending,  or  one  descending  and  one 
ascending.  To  see  this  more  clearly 
(which  should  be  almost  self-evident), 
tip  Fig.  78  in  various  directions  so  as 
to  correspond  to  all  the  conditions  of  practice.  It  will  be  obvious  that 
although  the  changes  in  the  absolute  velocity  of  the  train  and  every  part 
of  it  will  be  greatly  modified,  yet  that  the  relation  of  the  motion  of  the 
rear  car  to  the  whole  train  will  not  be  modified. 

430.  We  see  in  what  has  preceded  the  urgent  reasons  why  the 
use  of  long  and  easy  vertical  curves  in  the  hollows  of  grade  lines 
should  never  be  neglected.  The  conditions  are  entirely  different 
in  a  salient  or  rising  angle  in  a  grade-line  like  Fig.  79  and  in  a 
hollow  like  Fig.  80.     In  passing  over  the  former  there  is  only  a 


Fig.  80, 


3^4 


CHAP.  IX.^RISE  AND  FALL— SAFE  LIMITS  OF, 


CHAP.  IX.— RISE  AND  FALL^SAFE  LIMITS  OF. 


36s 


momentary  increase  in  the  normal  tension.  If  too  sudden,  this 
is  objectionable,  so  that  vertical  curves  should  be  used  in  all 
cases;  but  it  is  the  reversal  of  strain  in  a  hollow  which  is  par- 
ticularly objectionable,  and  for  them  the  rule — The  cnange  in 
rate  of  grade  in  a  train-length  should  never  exceed  the  grade  of 
repose  of  the  last  car — should  be  strictly  adhered  to  when  the 
cost  of  doing  so  is  not  too  great. 

431.  From  this  it  follows  that  the  longer  the  train  and  the  lower  the 
grade  of  repose  the  easier  should  be  the  vertical  curve,  and  vice  versa. 
As  the  grade  of  repose  increases  with  the  velocity,  it  is  evident  that 
short  trains  at  high  speed,  like  passenger  trains,  are  in  little  danger  of 
any  such  effect,  and  that  to  obviate  it  altogether  the  longest  possible 
train  and  the  lowest  possible  resistance  for  the  last  car  or  cars  should 
be  assumed. 

The  lowest  probable  resistance  for  the  rear  of  the  train  at  any  such 
point  is  about  6  lbs.  per  ton.  Dynamometer  tests  of  freight  trains  show, 
indeed,  average  resistances  of  3^  to  4  lbs.  in  frequent  instances,  but  the 
speed  is  likely  to  be  high  at  the  particular  localities  in  question,  and 
there  is,  moreover,  a  certain  atmospheric  resistance  from  suction  at  the 
rear  of  the  train  (which  may  be  estimated,  by  analogy,  from  experiments 
on  a  small  scale,  at  about  half  as  much  per  square  foot  as  that  at  the 
head  of  the  train)  which  will  increase  the  resistance  of  the  rear  cars 
somewhat  above  the  rest  of  the  train.  Curve  resistance,  if  uncompen- 
sated (and  still  more  when  compensated,  in  descending  a  grade),  may 
affect  the  question  either  way,  according  to  its  location.  Grade  resist- 
ance, as  we  have  seen,  does  not  in  itself  affect  the  question  in  the  slight- 
est. The  difference  between  the  grades  at  the  rear  and  head  of  the  train 
alone  concerns  us. 

432.  The  utmost  length  of  train  will  depend  on  the  ruling  grade 
of  the  road.  An  empty-car  train  will  have  about  twice  the  length  of  a 
loaded  train  ;  but  empty-car  trains  are  unusual,  their  rolling  friction  is 
higher,  and  the  phenomenon  is  not  so  objectionable  that  it  may  not  in 
occasional  instances  be  permitted,  especially  as  it  can  be  avoided  by 
brakes,  or  "  pulling  out,"  if  desired.  A  35-  or  40-car  train  will  be,  say, 
1200  ft.  long,  and  this  may  not  unreasonably  be  taken  as  an  average  maxi- 
mum. On  heavy-grade  lines  a  shorter  assumed  length  of  train  may  suf- 
fice, and  on  low-grade  lines  the  trains  may  be  much  longer. 

433.  Assuming  1200  ft.  (12  stations)  length  of  train,  and  6  lbs.  per 
ton  (0.3  grade)  for  the  resistance  of  the  rear  car  or  cars,  we  have  the  rule — 


Vertical  curves  in  sags  should  be  400  ft.  long,  or  200  ft.  on  each  side 
I \ 200 \ 
of  the  vertex  \ J ,  for  each  tenth  in  change  of  rate  of  grade,  making 

the  change  in  rate  of  grade  per  station  not  over  0.025  per  station,  if  ALL 
POSSIBILITY  of  bringing  the  draw-bars  of  any  part  of  the  train  into  cotn- 
pression  while  passing  over  it  is  to  be  avoided.  With  half  this  length  of 
curve,  which  is  considerably  more  than  is  usual  in  laying  out  vertical 
curves,  all  danger  of  "  taking  out  the  slack  "  in  the  front  half  of  the  train, 
where  there  is  most  danger  of  breaking  in  two,  will  be  avoided. 

434.  A  short  and  simple  method  of  putting  in  vertical  curves  is  given  at 
the  close  of  this  chapter.  The  omission  of  such  curves,  and  the  neglect  to  make 
them  long  enough  when  used  at  all,  is  one  of  the  most  prevalent  and  unfortu- 
nate of  the  minor  errors  of  location,  for  it  often  converts  a  sag  which  would 
otherwise  be  almost  innocuous  into  a  serious  disadvantage.  The  bad  results  in 
such  a  case  will  very  naturally  be  ascribed  to  the  sag  itself  instead  of  to  the 
bad  manner  of  putting  in  the  sag  ;  and  in  this  way  a  prejudice  even  greater 
than  the  facts  justify  exists  against  such  breaks  of  grade.  With  proper  care 
they  may  be  used  harmlessly  with  some  freedom,  especially  as  it  is  nearly 
always  possible  to  take  them  out  in  part  or  whole  at  any  time  when  circumstan- 
ces seem  to  require  and  permit,  by  increasing  the  height  of  the  fills  or  grading 
a  new  line.  In  this  manner,  in  fact,  it  is  often  possible  to  provide  for  eventually 
securing  better  line  and  grades  than  it  would  otherwise  be  possible  to  obtain. 

So  soon  as  an  automatic  close  coupler  shall  be  adopted,  eliminating  all  loose 
slack  from  the  train  (and  it  is  now  clear,  for  reasons  given  in  Chapter  XII., 
that  such  a  coupler  is  the  only  proper  form  to  adopt),  much  of  the  impor- 
tance of  connecting  breaks  of  grade  by  extremely  easy  vertical  curves  will 
disappear.  It  is  hardly  safe,  however,  to  count  upon  any  speedy  and  gen- 
eral action  in  that  direction. 

435.  Let  it  therefore  be  repeated,  that  so  long  as  (i)  it  is  not  neces- 
sary to  alter  in  any  way  the  steam-power  of  the  engine  to  avoid  too  high 
speed,  and  (2)  so  long  as  the  transition  from  one  grade  to  another  is  ex- 
tremely gentle  and  gradual,  such  breaks  are  a  matter  of  the  most  trifling 
moment.  But  to  this  rule  there  are  some  exceptions.  Thus,  a  sag  of  10 
or  15  feet  might  be  entirely  innocuous  on  a  long  tangent  between  sta- 
tions, yet  at  some  other  point  on  the  line,  where  the  profile  is  precisely 
the  same,  it  might  be  a  serious  and  even  dangerous  evil.  A  sharp  curve 
at  the  bottom  of  the  sag  might  necessitate  a  very  low  speed  there,  or  a 
heavy  grade  near  at  hand  make  high  speed  desirable.  A  station,  or  a 
siding,  or  crossing,  or  water-tank  may  in  the  future,  if  not  at  present,, 
necessitate  a  stop  there.  In  any  such  case  the  sag  would  at  once  change 
its  character  from  a  harmless  economy  to  a  serious  and  costly  error,  if  it 
be  for  any  reason  a  permanency.     If,  on  the  other  hand,  it  can  be  taken 


f 
fl 


it 


366      CHAP.  IX.— RISE  AND  FALL— LIMITS  OF  CLASSES. 


\v-\ 


Fig.  8z. 


leve/_. --5J 

Fig.  83. 


out  at  any  time  by  simply  filling  up  the  hollow,  of  course  far  greater 
boldness  may  be  used. 

436.  It  will  be  obvious,  furthermore,  that  the  effect  and  disadvan- 
tages of  such  sags  are,  other  things  being  equal,  the  same,  whatever  the 

rate  of  the  grade  on  which  the 
^  sag  occurs.  Thus  in  Fig.  81 
there  is,  literally  speaking,  no  rise 
and  fall  at  all,  because  it  is  i  con- 
tinuous up  grade ;  yet  if  the  loco- 
motive be  ascending  this  grade, 
and  exerting  just  power  enough 
to  maintain  a  uniform  velocity, 
the  effect  of  the  mere  break  of 
grade  is  precisely  the  same  as  the 
actual  sag  and  rise  and  fall  in  Fig. 
82.  In  each  case,  if  the  train  be 
moving  at  a  uniform  velocity  of  12  or  15  or  20  miles  per  hour  (=  velo- 
city-head, by  Table  118,  of  5.1 1,  7-99.  and  14.20  ft.),  the  sag  will  increase 
the  velocity- head  by  4.0  ft.,  to  9.1 1,  11.99,  and  18.20  ft.,  and  the  velocity 
in  the  bottom  of  the  hollow  (neglecting  the  fact,  as  heretofore,  that  the 
centre  of  gravity  of  the  train  does  not  rise  quite  so  high  nor  fall  quite  so 
low  as  the  angles  of  the  grade)  will  be  increased  to  16.0,  18.4,  and  22.6 
miles  per  hour.  After  passing  the  bottom  of  the  hollow  the  train  begins 
to  lose  velocity,  and  on  again  reaching  the  main  grade  is  moving  at  the 
same  velocity  as  when  it  left  it. 

437.  The  above  makes  clear  that  it  is  a  fallacy  to  count  up  the  num- 
ber of  feet  of  rise  and  fall  merely  from  the  ups  and  downs  as  shown  by 
the  differences  of  elevation  of  the  profile,  as  one  of  the  criterions  of  the 
excellence  of  a  line.  Ordinarily  this  may  not  prove  very  deceptive  but 
the  true  comparative  importance  to  be  ascribed  to  rise  and  fall,  and 
hence  the  limits  of  the  three  classes  of  rise  and  fall.  A,  B.  and  C,  as  sum- 
marized in  par.  367,  and  again  in  par.  451,  must  be  determined  in  a  dif- 
ferent way. 

LIMITS  OF  THE  CLASSES  OF   RISE  AND   FALL. 

438.  Limits  of  Class  A.  (The  least  objectionable  class.)— The  nor- 
mal freight  speed  may  be  assumed  to  be  15  miles  per  hour,  but  in  certain 
locations  it  is  not  likely  to  be  more  than  10  miles  per  hour,  and  in  other 
locations  it  may  usually  and  naturally  be  as  high  as  20  miles  per  hour. 
Assuming  a  train  to  be  approaching  a  sag  in  any  grade  line  at  these  rates 


CHAP.  IX.-RISE  AND  FALL-LIMITS  OF  CLASSES. 


367 


•of  speed,  we  have  in  Table  121  the  maximum  velocity  which  sags  of  vari- 
ous depths  will  give  to  the  train. 

Table  121. 
Effect  of  Sags  of  Various   Depths  below  a  Continuous   Grade-Line 

AND    having    the    ForM    OF  EITHER    FiG.    8l   OR   FiG.    82   TO  MODIFY  THE 

Speed  of  Trai.ns. 

(Computed  by  the  aid  of  Table  118,  as  explained  in  par.  400  ./  seg.) 


Greatest 

Dkpth  of 

Sag  in 

Feet. 


None. . . . 

5 

10 

15 

20 

25 

30 


Vel.-Head  in  Train  at  Lowest 

Point  of  Sag  for  Speeds  of  Approach 

IN  Miles  Per  Hour  of— 


10 


3-55 
8.55 
13-55 
18.55 
23-55 
28.55 
33-55 


15 


7-99 
12.99 

17.99 
22.99 
27.99 
32.99 
37-99 


20 


14.20 
19.20 
24.20 
29.20 
34.20 
39- 20 
44.20 


Maximum  Speed  in  Botiom  of  Sag 

for  Speed  of  Approach  in  Miles 

Per  Hour  of— 


10 


10. 

15-5 

19-5 
22.9 

25.8 
28.3 
30.8 


15 


15- 
19. 1 
22.5 

25.4 

28.  T 

30.5 
32.7 


20 


20. 

23.2 
26.1 
28.7 
31  o 

33-2 
35-3 


This  table  assumes  that  the  train  is  approaching  at  a  uniform  speed,  and  that  the 
locomotive  continues  to  exert  the  same  uniform  power  in  passing  the  sag.  The  oridnaJ 
velocity  will  then  be  resumed  after  passing  it.  v         }.         ^>^.     i  ne  original 

If  there  is  an  excess  of  accelerating  or  retarding  force  in  approaching  the  sag  both  the 
speed  in  the  bottom  of  the  sag  and  the  speed  after  passing  it  will  L  correspondin^v 
higher  or  lower  than  the  speed  of  approach,  but  the  table  will  not  be  essentiluy ZdifiS! 

The  manner  of  computing  Table  I271h^  be  care^T^uidied^It 
will  be  seen  how  little  the  speed  of  approach  affects  the  resulting  speed 
at  the  bottom  of  a  sag  in  grade-Iine  of  any  considerable  depth  Twice 
the  speed  of  approach.  20  miles  per  hour  instead  of  10,  increases  the 
speed  in  the  hollow  only  some  15  per  cent,  or  4i  miles  per  hour.  It  will 
also  be  seen  how  comparatively  slight  is  the  effect  of  increased  depth  of 
sag.  A  lo-ft.  sag  increases  10  miles  per  hour  to  20,  but  it  takes  20  ft. 
more,  or  a  30  ft.  sag  in  all,  to  increase  the  20  miles  per  hour  to  30  At  a 
speed  of  approach  of  20  miles  per  hour  a  lo-ft.  sag  increases  the  speed 
6.1  miles  per  hour ;  the  next  10  ft.  (20  ft.  in  all)  only  4.9  miles  per  hour, 
and  the  next  10  ft.  only  4.3  miles  per  hour. 

^h^xJm^'^^^'  likewise  shows  in  part  (for  fuller  explanation  see 
Chap.  XVIII.)  why  a  very  slight  break  upwards  from  a  long  continuous 
grade-hne  .s  so  very  much  more  injurious  than  even  a  considerable  droo 
below  It.  Sags  even  of  30  ft.  will  not  produce  an  absolutely  dangerous 
speed,  but  a  rise  of  even  3i  ft.  above  a  grade- line  will  bring  a  train  mov- 


~1 


68       CHAP,  IX.— RISE  AND  FALL— LIMITS  OF  CLASSES. 


ing  at  lo  miles  per  hour  to  a  stop,  or  a  train  moving  at  15  miles  per  hour 
to  a  speed  of  1 1.2  miles  per  hour. 

440.  The  highest  freight-train  speed  which  can  be  regarded  as 
reasonably  safe  and  practical  at  favorable  points  is  about  30  miles,  per 
hour.  Such  speeds  are  ordinarily  far  less  objectionable  on  long  straight 
grades  than  on  undulating  grades,  for  the  reason  that  the  true  objection 
to  high  freight  speeds  (within  reason)  is  not  the  speed  itself,  but  abrupt 
alterations  of  speed.  With  long  and  easy  vertical  curves  (usually  want- 
ing), and  with  breaks  of  grade  so  designed  that  their  depth  will  not  give 
a  dangerous  maximum  speed  if  they  are  operated  as  virtual  continuous 
grades,  by  making  no  change  in  the  work  done  by  the  locomotive  but 
permitting  its  excess  of  work  to  take  the  form  of  velocity,  speeds  of  30. 
miles  per  hour  for  the  moment  only  on  good  alignment  cannot  be  con- 
sidered as  in  the  least  objectionable,  and  are  very  common  in  present 
practice,  and  likely  to  become  more  so.     (See  par.  444.) 

If  we  assume  30  miles  per  hour  as  a  maximum  speed  at  certain  favor- 
ably situated  points  where  considerable  speed  is  desirable,  it  results  (see 
Table  121)  that  sags  of  20  or  even  30  ft.  from  a  grade-line,  according  to- 
the  speed  of  approach,  may  be  operated  as  a  virtual  continuous  grade. 

441.  We  therefore  conclude  that,  as  a  general  rule,  but 
with  a  number  of  modifying  special  conditions,  a  sag  of  not 
exceeding  20  ft.  in  vertical  depth  from  the  main  grade-line,  if 
eased  off  by  a  long  and  easy  vertical  curve  in  the  hollow,  will 
not  require  any  slacking  up  or  variation  in  steam-power,  and 
that,  if  it  does  not,  it  is  entirely  innocuous,  except  for  the  greater 
wear  and  tear  which  may  result  from  the  higher  speed.  That  ex- 
pense we  will  estimate  in  par.  452  et  seq. 

442.  If  the  sag  be  deeper  than  20  ft,,  and  sometimes  if  it  be  consider- 
ably less  than  20  ft.,  we  have  a  more  objectionable  class  of  rise  and  fall 
(Class  B,  pars.  367  and  451).  It  will  then  be  necessary  either  to  put  on 
brakes  (which  is  really  the  best  practice)  or  to  merely  shut  off  steam  and 
"  pull  out"  again  at  the  foot  of  the  grade,  which  is  the  too  common  prac- 
tice. 

It  is  in  this  latter  kind  of  sags,  especially  if  they  have  no  adequate 
apology  for  a  vertical  curve,  that  most  of  the  draw-heads  are  pulled  out 
and  trains  broken  in  two,  in  the  way  explained  in  par.  418-421.  In  part 
this  is  avoidable  by  care  in  running.  Nevertheless,  with  the  greatest 
practicable  care,  it  is  not  possible  to  prevent  frequent  serious  jerks  to 
trains  in  sags  of  considerable  depth,  which  will  sometimes  break  tben> 


CHAP.  IX. -RISE  AND  FALL-LIMITS  OF  CLASSES. 


36^ 

in  two.     Such  sags,  therefore,  become  more  and  more  objectionable  as 

V:r^:Z^Tt'  7w  ^^^'^"  ''  ''  "^^  "^^^-^^^  -  use^ny  brats 
443.   ^^^  Po^nt  at  wh^ch  zt  certamfy  becomes  necessary  to  ajp/y  braJ^es 

accel^Sforcl'r'  '"^^.^"---^P-^^'  -.,  the  grades  on  which  the 
acceleratmg  force  of  gravity  just  suffices  of  itself  to  keep  the  train  in 

either  gam  01  loss  of  velocity,  are  about  as  given  in  Table  120.  page  358 

par  o  'tt7    T  ''''^^  "°'  ''''  ''  '''  ^^"^'^^'^^^  ^-^^  -f  speed^l'fny 
part  of  the  line  be  given,  any  grade,  however  long,  on  a  rate  not  exceel 

^n^l^egracie  of  repose  for  that  speed,  may  be  of  indefinite  leng"  wilho^ 

ever  requiring  the  use  of  brakes,  because  all  that  is  necessary  is  to  shut 

ing  the  grade,  will  of  itself  either  acquire  or  lose  velocity  until  it  attains 


Fig.  83. 

The  dotted  line  shows 
the  virtual  gjade-line  of  a  c^      , 

iSiTv"  whl"h^  ^'■'"5  ''^f  ^"^P  °^  ^^^  ^'"  ^ith  a  small  ve- 
i^i^Jth  ^f^"^"y  increases  until  it  becomes  as 
On  tl  .  ^u ''^il''^L'''"  "^  ^'■^^'ty  's  able  to  maintain, 

^nd  .hi  oT*"  .^i  "-^^  ^^^  ^"^  resistance  are  small  T-- 

next^sttclThtrelisreTst^t^'t!^^^^  ^^^  Ifl"  -  -^ocity.     On  the 

cess  of  acceleration.     So  wkh  the  nex?  stretcS    but  J  t h'/P^^"^;  ^"'  "^^'^  '^  ^'"^  ^°  ^^- 
higherwitheachincreaseofvelo^itvthei  npi'c  o  -I  'esistance  grows  higher  and 

and  acceleration  bala^S  eaL'Kf  Is 'g?ven^^^^^  ^  ^^'"^  "'^^^  ^^^  --^^--e 

reslsIalTJ'"  ^V^'^V''  -f  erating  force  precisely  balances  the  rolling 
tra  n  sneH    ^^'^^^^^^  ^'"  ^^  «^^"  ^«  ^^  ^^ry  high  for  fast  passenger 
train  speeds,  so  that  there  can  rarely  or  never  be  necessity  for  the  use  of 
brakes  on  descending  grades  of  less  than  i  per  cent  (52.8  a.  per  mile)  in 
ordinary  passenger  service,  merely  to  avoid  excessive  speed  due  to  the 

orntd"h  \^'^""^^"^^-  U^-'^y-  h— -.  heavy  gradi^its  are  accom! 
panied  by  heavy  curvature,  which  latter  will  often  necessitate  on  long 
grades  a  rate  of  speed  but  little  higher  than  the  freight  maximum.  ^ 

444.  The  customary  speed  in  freight  service  shows  a  steady  tendency 
to  increase  at  points  where  velocity  is  of  assistance  in  hauling  heavy 
trams.  It  is  of  course  greatly  affected  by  the  character  of  the  line  as  to 
24 


370      CHAP,  IX.— RISE  AND  FALL— LIMITS  OF  CLASSES. 


CHAP.  IX.— RISE  AND  FALL— LIMITS  OF  CLASSES.      371 


.5 

■    *! 

r. 

i  I 


curvature,  but  the  idea  formerly  prevalent  that  the  most  economical 
speed  for  freight  trains  is  a  very  slow  one  has  been  pretty  thoroughly  ex- 
ploded, both  by  theory,  practice,  and  experiment.  Experiments  by  Mr. 
P.  H.  Dudley  on  the  Lake  Shore  &  Michigan  Southern  Railway  have 
shown  directly  that  "  with  long  and  heavy  freight  trains  it  required  less 
fuel  with  the  same  engine  to  run  trains  at  18  to  20  miles  per  hour  than  at 
10  to  12  miles  per  hour."  *  This  result— as  to  the  substantial  correctness 
of  which  there  is  little  room  for  doubt— is  not  due  to  the  actual  resist- 
ances to  motion  being  any  lower,  or  as  low,  at  the  higher  speed,  but  to 
the  joint  action  of  the  following  causes  : 

1.  To  the  saving  of  power  at  undulations  of  grades,  in  the  manner 
heretofore  discussed  in  this  chapter,  the  extra  velocity  serving  as  a  reser- 
voir of  power  and  so  preventing  waste  thereof. 

2.  To  the  less  time  of  exposure  of  the  locomotive  to  radiation— a  sav- 
ing, in  all  probability,  of  very  great  importance.     (See  pars.  344  e/  al.) 

3.  To  the  less  time  for  radiation  from  the  interior  surface  of  a  cylin- 
der into  the  exhaust  steam  ;  also  a  very  important  source  of  loss. 

On  the  other  hand,  evidence  presented  in  Chapter  XIII.  makes  it  at 
least  doubtful  if  the  resistance  is  more  than  a  pound  or  two  per  ton 

greater. 

445.  Whatever  may  be  the  cause,  the  expediency  and  economy  of  m- 

creasing  freight-train  speeds,  on  fair  alignment,  up  to  20  and  even  (at 
points)  30  miles  per  hour  is  very  generally  recognized  and  acted  on  by 
the  more  prominent  managing  officers.  This  tendency  will  probably  be 
greatly  strengthened  in  the  near  future  by  (i)  the  general  adoption  of 
some  form  of  freight-train  brake  and  of  a  more  durable  and  stronger 
coupler,  and  by  (2)  the  increase  in  average  car-load  and  consequent  de- 
crease in  number  of  freight  cars  per  train,  with  the  natural  attendant  in- 
crease of  care  in  the  construction  of  freight  cars.  On  lines  using  the 
"speed  gauge"  the  usual  maximum  speed  specified  is  22  miles  per  hour, 
a  rate  in  all  probability  which  at  some  points  on  some  lines  has  been  ex- 
pensively low,  and  would  have  been  still  more  so  except  that  the  grades 
at  stations  are  usually  the  de-facto  limiting  grades,  and  not  those  between 

stations. 

446.  It  will  therefore  be  safe  in  all  cases  to  assume  a  maximum 


♦Trans  Am  Soc.  C.  E.,  Oct.  1876.  The  explanation  there  given  by  Mr. 
Dudley  that  at  the  higher  speeds  "  the  locomotive  seems  to  produce  its  power 
more  economically  by  using  the  steam  expansively  to  a  greater  extent  ihan  at 
slow  speeds"  would  seem  to  be  certainly  incorrect,  except  as  the  less  time  lor 
internal  radiation  may  be  supposed  to  be  referred  to. 


freight-train  speed  of  about  22  to  25  miles  per  hour  on  long  grades,  cor- 
responding  to  a  grade  of  repose  of  something  under  0.5  per  cent,  or  26.4 
feet  per  mile;  and  this,  under  favorable  circumstances,  for  important 
ends,  may  be  assumed  to  be  increased  to  nearly  30  miles  per  hour,  corre- 
sponding to  a  degree  of  repose  of  something  over  0.6  per  cent,  or'32  feet 
per  mile.  On  grades  not  exceeding  these  limits  rise  and  fall  on  grades 
of  any  length  will  not  be  likely  to  require  the  use  of  brakes,  or  to  en- 
danger objectionable  "  slack"  in  the  train,  with  the  most  moderate  care 
in  running, 

447.  The  point  at  which  a  grade  on  rates  exceeding  these  limits  be- 
comes so  long  that  the  use  of  brakes  will  become  necessary  is  readily 
<ietermined  as  follows : 

Let  AB,  Fig.  84,  be  such  a  grade  and  AB'  be  the  average  grade  of  repose 
while  attaining  the  assumed  admissible  velocity,  say  0.4  per  cent,  for  a 


1^ 


Fig.  84. 

tnaximum  velocity  of  25  miles  per  hour,  or  0.5  per  cent  for  30  miles  per 
hour.  Let  the  lowest  velocity  at  which  it  is  necessary,  expedient,  orprob- 
able  that  trams  will  approach  A  be  also  determined.  It  will  depend  on  the 
character  of  the  line  back  of  A.  If  A  be  at  the  foot  of  a  long  grade,  no 
lower  velocity  than  the  maximum  admissible  could  safely  be  assumed 
and  the  application  of  brakes  would  be  immediately  necessary  on  reach- 
ing A.  If  A  were  a  station  the  initial  velocity  would  be  O.  It  is  desira- 
ble that  the  velocity  should  be  as  low  as  possible,  but  as  enginemen  do 
not  always  pay  close  attention  to  little  matters  of  economy  such  as  sav- 
ing the  use  of  brakes— especially  if  behind  time— it  should  not  be  taken 
too  low.     Let  us  suppose  it  to  be  10 or  15  miles  per  hour;  then  we  have; 

^"ritlr^''''!^-^  ^^  ^i     •      u     .       ^o  miles  per  hour.  IS  miles  per  hour. 
Corresponding  velocity-head 3.55  ft.  7.  'i  f^ 

Corresponding  velocity-head  at  maxi- 

mum  velocity  of  25  miles  per  hour.  22.20  "  22.20  " 


Difference , 18.65 


<( 


14.21 


372       CHAP.  IX.— RISE  AND  FALL— LIMITS  OF  CLASSES. 


CHAP.  IX.— RISE  AND  FALI^LIMITS  OF  CLASSES.       373 


which  latter  is  the  vertical  distance  A  Fig.  84,  which  the  grade  will  have 
to  fall  below  the  grade  of  repose  before  the  train  will  acquire  the  maximum 
admissible  velocity. 

This  being  given,  it  is  a  simple  matter  to  compute  the  horizontal  dis- 
tance AD'  and  the  corresponding  vertical  fall  D  +  D'.     In  the  above 

example,  the  excess  of  the  actual  grade  over  the  assumed  0.4  grade  of 

18.65  .        , 

repose  being  0.6  per  cent,  we  find  Z>  +  /?'  to  be  -^  =  311  stations  for 

,  14.21  . 

an  initial  speed  of  10  miles  per  hour  and  —^  =  23.7  stations  lor  an  in- 
itial speed  of  15  miles  per  hour.  In  this  manner  we  may  construct  Table 
122. 

448.  Any  grade,  at  any  given  rate  whatever,  which  does  not  exceed 
in  length  and  vertical  rise  the  limits  of  Table  122  can  be  operated  in  the 
routine  of  freight  service  without  the  use  of  brakes  (the  cost  of  such  rise 
and  fall  being,  consequently,  very  much  less)  provided  that  there  be  no 
excessive  curvature  or  other  special  cause  near  the  foot  of  the  grade  to 
require  especially  low  speed  at  that  point.     Ordinary  curvature,  with  a 

Table  122. 

Distance  within  which  the  Velocity  of  Trains  descending  Various 
Grades  without  Steam  or  Use  of  Brakes  will  exceed  the  Limits 
OF  25  and  30  Miles  Per  Hour,  starting  with  Various  Initial  Ve- 
locities. 


Ratb  of 

Graob. 

Admissible  Maximum  Velocity 
OF  25  MiLBS  Per  Hour. 

Admissible  Maximum  Velocity 
OF  30  Miles  Per  Hour. 

■>cr  Cent. 

Less  Grade 
of  Repose. 

Initial  Velocity  at  Top  of 
Grade,  in  Miles  Per  Hour. 

Initial  Veloc' 
Grade,  in  Mil 

ty  at  Top  of 
es  Per  Hour. 

0  + 

10 

15 

20 

0  + 

10 

15 

20 

0.4 
0.5 

0.0 

Infinite 

Infinite 

Infinite 

Infinite 

Infinite 

Infinite 

Infinite 

Infinite 

o.z 

aaa.o 

166.5 

142.  X 

80.0 

it 

It 

t« 

tt 

0.6 

o.a 

ZII.O 

83.2 

71. 0 

40.0 

3'9-5 

284.0 

239.6 

177-5 

0.7 

0.3 

74.0 

55-5 

47-4 

26.7 

»59-7 

142.0 

119. 8 

88.8 

0.8 

0.4 

5S-5 

41.6^ 

35-5 

20.0 

X06.5 

94-7 

79-9 

59-3 

0.9 

0.5 

44-4 

33-3 

28.4 

16.0 

79-9 

71.0 

59-9 

44-4 

t.o 

0.6 

37-0 

27.7 

23-7 

»3-3 

63.9 

56.8 

47-9 

35-5 

s-5 

I.X 

20.3 

I5-I 

12.9 

7-3 

32.0 

28.4 

24.0 

17.7 

s.o 

1.6 

»3-9i 

10.4 

8.9 

SO 

21.3 

18.9 

x6.o 

II. 8 

3-0 

a.6 

8.5 

6.4 

5-5 

3-> 

12.8 

II. 4 

9.6 

7.« 

Table  122. — Continued. 

Total  Vertical  Fall  in  Feet  from  Top  of  Grade  to  Point  where  the 
admissible  Maximum  Velocity  is  attained,  as  above. 


0.4 

0-5 
0.6 

t».7 
0.8 
«.9 
s.o 
1-5 
S.o 
30 


Infinite 

III.O 

66.6 

51-8 

44-4 
40.0 

37-0 
30-3 
27.8 
17.0 


Infinite 
83.2 

49-9 
38.8 

33-3 
30.0 
27.7 
22.6 
20.8 
12.8 


Infinite 
71.0 
42.6 
33-2 
28.4 
25-5 
23.7 
19.4 
17.8 

II. o 


Infinite 
40.0 
24.0 

•  18.7 

16.0 

14.4 

13-3 
10.9 

10. o 

6.2 


Infinite 

tt 

191. 7 

111. 8 
85.2 
72.0 
63.9 
48.0 
42.6 
38.4 


Infinite 

tt 

170.4 

99-4 
75-8 

63-9 
56.8 
42.6 
37-8 
34-2 


Infinite 

tt 

143-8 

839 
64.0 

54 -0 

47-9 
36.0 

32.0 
28.8 


Infinite 
tt 

106.5 
62.2 

47-4 
40.0 

35-5 
26.6 

23.6 

21.3 


Computed  as  follows : 


At  speed  of 

0 
0.00 
22. 20 

10 

3-55 
22.20 

15 
7-99 
22.20 

20 
14.20 
22.20 

0.00 
31-95 

3-55 
31-95 

7-99 
31  95 

Vel.-head 

Do.  at  25  (and  30)  m.  p.h. 

14.30 

31.95 

Difference 

22.20 

16.65 

14.21 

8.00 
.40 

31-95 

28.40 

23.96 

Assumed  average  grade 
of  repose 

17.7s 
.50 

Then  the  actual  rate  of  grade,  less  the  grade  of  repose,  gfives  the  fall  per  station  which 
goes  to  increase  the  velocity,  and  the  "differences"  above,  divided  by  the  surplus  fall  per 
station,  gives  the  number  of  stations  within  which  the  permitted  maximum  velocity  will 
be  attained,  as  in  the  first  part  of  the  table  above.  The  number  of  stations  x  rate  of 
^ade  per  cent  gives  the  second  part  of  the  table. 


Toad-bed  in  good  condition,  can  be  operated  by  all  trains  with  almost  as 
great  safety  at  25  to  30  miles  per  hour  as  at  any  lower  speed,  if  the  speed 
does  not  require  to  be  suddenly  checked.  In  ascending  such  a  grade 
the  same  conditions  obtain  as  in  descending,  except  (i)  that  the  locomo- 
tive ascends  the  grade  using  steam,  whereas  it  descends  without  steam  ; 
and  (2)  that  it  starts  or  may  start  with  the  high  velocity  which  gradually 
decreases  instead  of  with  the  low  velocity  which  gradually  increases. 
We  are  not  now  considering  the  effect  of  limiting  gradients,  which  is  an 
entirely  different  matter,  but  assuming  that  the  locomotive  has  sufficient 
power  to  ascend  all  grades  at  necessary  speeds,  as  of  course  in  all  cases 
it  must.  The  cost  of  decreasing  the  length  and  increasing  the  number 
of  trains  to  effect  this  end,  which  constitutes  the  chief  objection  to  gradi- 
ents, is  not  now  under  consideration  at  all. 


374       ^HAP.  IX.-RISE  AND  FALL— LIMITS  OF  CLASSES. 

449.  Summarizing  the  preceding  discussion  of  the  nature 
of  rise  and  fall,  we  have  found  that  it  may  be  divided  into  the 
following  classes,  having  a    very  different  effect  on   operating 

expenses : 

Class  A.  Rise  and  fall  on  minor  gradients  and  for  small  un- 
dulations, not  sufficient  to  make  it  necessary  to  vary  the  power 
of  the  engine,  but  merely  causing  a  momentary,  gradual,  and 
unobjectionable  fluctuation  of  speed. 

Class  B.  Rise  and  fall  similar  to  class  A,  in  its  effect  in  speed, 
provided  steam  be  shut  off  in  descending,  but  not  requiring  the 
use  of  brakes  in  descending,  nor  seriously  taking  the  power  of  the 
engine  on  the  ascent.    Tables  121-2  give  the  limits  of  this  class. 

Class  C.  Rise  and  fall  requiring  the  use  of  brakes  in  descend- 
ing, in  addition  to  shutting  off  steam,  in  order  to  avoid  exces- 
sive velocities,  and  consequently,  in  almost  all  cases,  more  or 
less  use  of  sand  in  ascending. 

450.  Rise  and  fall  is  most  conveniently  estimated  by  the 
number  of  vertical  feet  of  it,  since  the  cost  of  it  (which  in- 
eludes  no  limiting  effect  on  trains)  depends  primarily  on  the 
length  of  grades  and  not  at  all  on  their  rate,  except  as  the  rate 
may  change  the  rise  and  fall  from  one  to  the  other  of  the  above 
classes.  A  foot  of  "rise  and  fall"  is  ordinarily  considered  as 
one  foot  of  ascent  with  its  corresponding  foot  of  descent,  so  that 
in  passing  over  a  hill  100  feet  high  there  are  100  feet  of  rise  and 
fall,  and  not  100  feet  ascending  +  100  feet  descending  =  200  feet. 

451.  The  amount  of  rise  and  fall  of  each  kind  on  the  profile 
should  be  determined  thus  : 

A.  All  rise  and  fall  arising  from  hollows  in  grade-lines  not 
exceeding  the  limits  specified  in  connection  with  Table  121  (par. 
435  ft  seq.\  if  the  grades  are  connected  by  easy  vertical  curves  and 
are  not  too  near  stations,  05  very  bad  curvature,  will  belong  to 
the  least  objectionable  class,  A.  If  the  hollows  are  sharp  and 
abrupt,  however,  even  if  quite  small,  the  rise  and  fall  will  be 
more  objectionable  than  the  worst  class  here  considered. 

B.  All  rise  and  fall  on  grades  too  long  to  come  under  Class  A, 
but  on  rates  of  grade  so  easy  that  the  train  can   never  obtain 


CHAP.  IX.— PISE  AND  FALL— COST  OF. 


375 


a  dangerously  high  velocity  when  running  without  brakes  with 
steam  shut  off,  will  belong  to  Class  B.  So  also  will  rise  and  fall 
on  any  grade,  however  steep,  which  is  not  long  enough  for  the 
train  to  obtain  a  dangerously  high  velocity,  as  fixed  in  Table  122 
and  par.  447  et  seq.  So  also,  strictly  speaking,  will  the  upper 
part  of  any  grade,  however  steep  and  however  long,  on  which 
no  dangerously  high  velocity  can  result  according  to  Table  122  ; 
but  it  would  be  an  objectionable  refinement,  tending  to  an  under- 
estimate of  the  cost  of  bad  details  of  location,  to  so  consider. 

C.  Class  C,  therefore,  should  be  considered  to  include  the 
entire  length  of  all  grades  so  long  and  steep  as  to  require  the 
use  of  brakes  in  descending. 

The  ruling  grade  of  the  line  may  belong  to  either  Class  B  or 
Class  C.  In  either  case  it  will  involve  the  occasional  use  of 
sand  and  more  or  less  slipping  of  wheels,  and  perhaps  breaking 
in  two  of  trains  in  ascending,  and  thus  make  an  addition  to  the 
cost  of  either  class  which  would  not  apply  to  the  same  grades  if 
they  were  not  ruling  grades,  and  hence  did  not  so  severely  tax 
the  power  of  the  engine. 

The  limit  of  these  classes  will  vary  in  every  case,  but  there  is 
a  tolerably  sharp  line  of  demarcation  between  the  cost  of  each, 
which  may  be  estimated  as  follows : 


the  cost  of  rise  and  fall. 

452.  Fuel. — Except  as  wasted  by  brakes,  there  is  no  loss  of  power 
(energy),  and  except  as  wasted  by  brakes  and  radiation  combined,  there 
is  no  loss  of  either  fuel  or  power,  from  any  amount  of  rise  and  fall  of 
Class  A,  if  we  neglect  the  slight  difference  in  frictional  resistances  result- 
ing from  a  (so  to  speak)  regularly  irregular  speed  instead  of  from  a  uni- 
form speed  averaging  the  same  in  miles  per  hour.  This  necessarily  fol- 
lows from  elementary  dynamic  laws.  Even  if  there  be  a  difference  in 
the  level  of  the  two  termini,  what  power  iS  lost  in  going  in  one  direction 
is  regained  in  returning. 

When,  in  the  case  of  rise  and  fall  on  easy  gradients  requiring  no 
brakes  (Class  B),  we  run  a  part  of  a  distance  of  one  or  two  miles  (the 
ascent)  under  steam  and  another  part  of  it  (the  descent)  with  steam  shut 
off,  assisted  by  gravity  only, — or  in  other  words,  assisted  by  the  energy 


■ 


37t) 


CHAP.  IX.— RISE  AND  FALL— COST  OF. 


CHAP.  IX.— RISE  AND  FALL— COST  OF. 


377 


stored  in  the  train  during  the  run  over  the  up  grade  by  the  act  of  lifting 
it  against  gravity, — the  total  time  that  the  locomotive  is  exposed  to  ex- 
terior radiation  is  the  same,  and  probably  also  the  loss  of  heat.  The  loss 
from  interior  radiation  in  the  cylinders,  a  very  important  loss,  explained 
in  Chapter  XL,  is  affected  as  follows: 

It  is  increased  by  the  (probable)  lower  piston  speed  in  ascending  the 
up  grade. 

It  is  decreased  by  the  (probable)  later  point  of  cut-off,  and  hence  less 
oscillation  of  temperature  in  the  cylinder;  the  disadvantage  of  this  latter 
very  nearly  balancing,  as  experiment  shows,  the  theoretical  gain  from  an 
earlier  point  of  cut-off.  This  is  to  say,  from  both  of  these  causes  com- 
bined, tlie  steam  used  for  equal  work  in  the  locomotive  engine  is  about 
the  same  at  all  points  of  cut-off  less  than  half  stroke ;  which  leads  to  the 
conclusion  that  the  steam  (not  fuel)  used  to  run  an  engine  two  miles 
will  be  about  the  same  whether  the  work  is  uniform  for  the  whole  run  or 
is  all  done  during  the  first  mile  in  taking  the  engine  up  an  easy  grade, 
down  which  it  runs  by  gravity  for  the  second  mile.  Tiie  loss  by  ex- 
ternal radiation  during  the  last  mile  will  be  a  net  loss.  The  fuel  used 
will  probably  be  much  more  increased,  not  only  by  possible  blowing  off 
of  steam  from  the  safety-valve,  but  by  blowing  out  more  unconsumed  coal 
from  and  wasting  more  heat  through  the  smoke-stack,  owing  to  the 
stronger  draft.  In  Chapter  XI.  it  is  shown  that  in  proportion  as  the  work 
of  the  engine  is  increased,  economy  of  fuel  consumption  is  decreased. 

From  all  these  causes  combined  a  locomotive  running  without  brakes 
or  steam  down  grades  too  steep  to  continue  the  steam-power  unchanged, 
but  not  steep  enough  or  long  enough  to  require  the  use  of  brakes,  will 
burn  probably  one  fourth  to  one  fifth  more,  and  certainly  not  over  one 
third  more  fuel  in  ascending  one  mile  on  the  grade  equal  to  the  grade  of 
repose  (assumed  at  26  feet  per  mile,  or  0.5  per  cent),  and  then  descend- 
ing one  mile  without  steam,  than  in  running  two  miles  on  a  level.  Al- 
lowing one  third  more,  80  vertical  feet  of  rise  and  fall  on  such  grades 
will  waste  fuel  equal  to  the  average  consumption  per  mile. 

453t  When  brakes  are  required,  owing  to  the  grade  being  either  too 
steep  or  too  long  to  permit  of  operating  it  without  them,  the  power  used 
in  ascending  is  entirely  lost,  except  that  portion  of  it  which  is  just  suffi- 
cient to  keep  the  train  in  motion  on  the  grade  of  repose.  That  is  to  say : 
The  rise  and  fall  at  BC,  Fig.  85,  consists  of  two  parts,  the  upper  part,  B, 
belonging  to  Class  B,  and  the  lower  part  only,  C,  belonging  to  Class  C, 
which  is  very  much  more  costly,  objectionable,  and  dangerous.  In  laying 
out  a  line  this  fact  must  be  borne  in  mind  ;  the  lower  portion,  C,  estimated 


at  its  true  value  and  avoided  if  possible ;  the  upper  portion,  B,  less  care- 
fully avoided.  The  limit  between  classes  B  and  C  may  be  taken  in  round 
figures  as  the  height  of  the  point  b.  Fig.  85,  above  or  below  the  grade  of 
repose  descending  from  A, 
although,  strictly  speaking, 
the  grade  of  repose  should 
be  drawn  in  starting  from 
the  point  on  the  grade 
where  the  limits  of  Table 
122  and  par.  447  are  passed,  '*^'    ^' 

so  that  dangerously  high  speed  before  reaching  the  foot  of  the  grade  is 
•certain.  But  when  this  point  is  once  passed  great  care  in  handling  the 
train  on  a  grade  where  brakes  are  known  to  be  essential  cannot  fairly 
be  assumed,  so  that  it  is  fairer  and  more  reasonable  to  assume  that  all 
the  fall,  C,  Fig.  85,  will  be  of  the  objectionable  class. 

When  an  engine  is  descending  a  grade  without  steam,  the  wastage  of 
fuel  by  radiation  and  slow  combustion  is  at  first  (say  for  10  or  15  minutes) 
very  considerable — about  one  fourth  of  the  usual  consumption  per  mile. 
The  loss  of  fuel  on  this  most  objectionable  class  of  rise  and  fall  may  be 
taken  as  equal  to  the  average  consumption  in  running  a  mile  for  every 
26  feet  of  rise  and  fall. 

454.  Repairs  of  Cars  and  Locomotives. — The  use  of  brakes  is 
excessively  destructive  to  wheels.  Table  114,  page  318,  will  make  it 
clear  that  something  like  one  third  of  the  total  cost  of  wheels  arises  from 
this  cause,  and  other  data  that  as  much  as  forty  or  fifty  per  cent  arises 
from  them.  Brakes,  however,  are  used  even  more  for  stopping  and 
starting  than  on  grades — sometimes  very  much  more;  and  the  whole 
cost  of  wheels  is  only  some  30  per  cent  of  freight-car  repairs  and  very 
much  less  of  passenger  cars.  The  records  of  wheels  drawn  on  the 
Pennsylvania  Railroad  indicate  {a)  that  about  30  per  cent  of  passenger- 
car  wheels  are  drawn  for  being  "  worn  flat  from  sliding,"  and  that  their 
life  is  from  this  cause  abbreviated  from  one  third  to  one  half.  About 
one  sixth  of  the  wheels  are  drawn  for  being  "worn  flat  or  hollow  on 
tread."  which  class  of  wear  is  distinctly  ascribed  in  the  Pennsylvania 
classification  to  "  wear  from  rail," 

If  we  should  consider  only  such  facts  as  these,  we  might  reach  the 
conclusion  that  the  wear  due  to  grades  must  be  a  very  important  element 
in  the  cost  of  freight-car  repairs;  but  by  referring  to  Table  86,  page  203, 
and  remembering  that  grades  are  only  one  of  many  causes  for  wear  and 
tear  of  cars,  we  shall  see  reasons  for  concluding  that,  while  it  is  exceed- 


i 


--t;  \ 


I 

w 


378 


CHAP,  IX.— RISE  AND  FALL— COST  OF: 


ingly  difficult,  in  fact  impossible,  to  reach  an  exact  estimate  in  such  a. 
mattter  as  this,  yet  that  it  is  not  probable,  if  all  grades  were  levelled  down 
fiat  so  as  not  to  require  in  any  case  the  use  of  brakes,  except  for  stops^ 
wheel  renewals  would  not  be  reduced  more  than  one  sixth  nor  car 
repairs  as  a  whole  more  than  one  tenth.  The  only  item  of  car  repairs 
other  than  the  wheels  affected  to  an  important  extent  is  the  cost  of 
draw-gear  and  links  and  pins,  and  the  loss  in  this  respect,  as  we  have 
seen  (par.  419),  arises  more  from  lack  of  proper  vertical  curves  at  breaks 
of  grade  than  from  the  grades  themselves. 

Table  123. 
Variations  in  the  Quality  of  Water  Supply,  Chicago,  Burlington  & 


QuiNCY  Railroad. 


Locality. 


Chicago  Division  : 

Best 

Worst 

Average 

St.  Louis  Division  : 

Best 

Worst 

Average 

Lake  Michigan 

Hudson  River 

Croton  River,  N.  Y  . . . . 
Loch  Katrine,  Scotland.. 


Grains  Per  Gallon. 


Incrusting 
Solids. 


10  666 

28.8*51 


16.405 

4.898 
20.178 


11.490 


7-305 
7177 
5.362 
O.9II 


Alkalies  and 
Non-crusting. 


1.365 
10. 788 


2.853 

1.458 
2.449 


1.678 


0.626 
1. 136 
1. 5" 
1-333 


Lbs. 

Incrusting 

Matter  in  Tank 

of  2750 

Gallons. 


4.19 
11-33 


6-44 

1.92 
7-93 


4-51 


2.87 
2.82 
2. II 
0.36 


Comparative 

Incrusting 

Matter. 

Lake  Michigaa 


=  1. 00. 


1.5 
3.9 


2.2 

0.7 

2.8 


1.6 


i.o 

I.O 

0.7 

o.z 


Incrusting  solids  include  silica,  oxide  of  iron  and  alumina,  carbonates  of  lime  and 
magnesia,  and  sulphates  of  lime  and  magnesia. 

The  standard  tank  of  the  road  carries  2750  gallons. 

The  non-incrusting  matter  may  be  partly  deposited  as  mud  and  partly  mechanically 
combined  with  the  scale.  According  to  this  table,  an  engine  consuming  three  full  tanks 
of  water  per  day  would  in  a  week's  work  with  the  average  water  in  the  Chicago  Division 
accumulate  at  least  116  lbs.  of  incrustation.  With  the  best  water  on  the  St.  Louis 
Division  (taken  from  the  Mississippi  at  Rock  Island)  the  result  of  a  similar  week's  work 
would  be  only  34^^  lbs,  of  incrustation.  The  difference  shows  the  importance  of  good 
water. 

The  water  of  Loch  Katrine,  Scotland,  from  which  Glasgow  derives  its  supply,  is  about 
the  purest  and  softest  known. 


CHAP.  IX.— RISE  AND  FALL— COST  OF. 


179 


455.  The  cost  of  locomotive  tires  will  be  affected  in  much  the  same 
way  and  to  the  same  extent  as  the  cost  of  car  wheels.  The  life  of  the 
boiler  is  likewise  unfavorably  affected  by  an  intermittent  instead  of 
regular  demand  for  power,  although  this  effect  is  slight  in  comparison 
with  the  injury  suffered  from  the  cooling  off  of  boilers  at  the  end  of  the 
trip,  from  the  effect  of  bad  water  and  many  other  causes  not  connected 
with  the  grades  between  stations.  Table  123  gives  an  idea  of  how  im- 
portant is  the  effect  of  bad  water  on  locomotive  repairs. 

456.  It  is,  moreover,  true  of  both  engine  and  car  repairs  that,  as 
noted  in  par.  164,  when  we  search  for  evidence  of  the  effect  of  much 
rise  and  fall,  or  curvature,  or  (as  usually  happens)  both  together,  by 
comparing  the  cost  of  engine  and  car  service  per  mile  run  on  roads  or 
divisions  having  much  and  having  little  curvature  and  rise  and  fall,  we 
fail  to  find  it.  As  respects  grade,  this  results  in  part,  no  doubt,  from 
lower  speed  and  more  careful  handling  on  them ;  but  as  this  costs  the 
company  nothing  except  a  slight  delay,  we  may  fairly  regard  it  as  an 
offset,  to  some  extent.  In  the  first  edition  of  this  treatise  the  writer 
estimated  the  effect  of  rise  and  fall  at  5  per  cent,  on  the  total  cost  of 
repairs  of  engines  and  cars  per  mile,  for  each  25  feet  per  mile  (0.5  per 
cent,  nearly)  which  would  amount  in  2  per  cent  grades  to  something 
over  20  per  cent  per  mile  of  ascent  and  descent.  Taking  an  average  of 
the  mountain  divisions  of  the  Pennsylvania  Railroad,  this  would  require 
that  a  difference  of  at  least  15  per  cent  should  be  visible,  and  on  the 
Baltimore  &  Ohio  at  least  20  per  cent,  whereas  in  fact  no  such  difference 
appears  in  either  case.  This  fact,  together  with  a  careful  estimate  by 
items,  which  cannot  be  given  more  fully  than  above,  leads  the  writer  to 
believe  that  his  original  estimate  was  too  high  and  it  is  reduced  in  the 
estimate  below  (Table  124)  to  4  per  cent,  which  is  the  utmost  that  the 
statistical  evidence  seems  to  justify. 

On  Class  A  of  rise  and  fall  there  cannot  be  considered  to  be  any 
measurable  increase  in  the  cost  of  rolling-stock  maintenance  if  proper 
vertical  curves  are  used.  On  Class  B  (requiring  shutting  off  steam  for 
descending,  but  not  the  use  of  sand  or  brakes)  there  is  very  little — cer- 
tainly not  over  one  fourth  of  what  exists  on  the  worst  class,  C. 

457.  Wear  of  Rails. — The  effect  of  grades  on  the  wear  of  rails  is 
exaggerated  in  popular  belief  for  want  of  a  proper  distinction  between 
the  effect  of  a  heavy  ruling  grade,  which  increases  the  number  of  trains 
and  the  proportion  of  engine  tonnage,  and  the  effect  of  rise  and  fall 
simply,  on  which  the  number  of  trains  and  proportion  of  engine  tonnage 
is  the  same  as  on  adjacent  sections  of  level  track.    Thus,  in  an  able  and 


38o 


CHAP,  IX.— RISE  AND  FALL— COST  OF. 


CHAP.   IX.— RISE  AND  FALL— COST  OF. 


elaborate  report  on  the  wear  of  rails  on  the  Pennsylvania  Railroad, 
already  quoted,  an  increase  of  some  75  per  cent  in  the  wear  of  rails  on 
grades  over  which  almost  three  times  as  many  engines  pass  as  on  ad- 
jacent sections  of  level  track  was  ascribed  to  the  effect  of  grades  as  such, 
whereas  it  is  in  reality  merely  an  expression  of  the  fact  that  an  engine 
wears  the  rails  several  times  as  much  as  the  same  weight  of  cars  (par. 
115).  In  so  far  as  this  is  the  cause  of  extra  wear  of  rails  it  is  an  effect 
arising  from  the  limiting  effect  of  gradients,  and  not  at  all  an  inherent 
property  of  gradients  as  such. 

When  we  eliminate  this  extraneous  question  we  are  driven  to  the 
conclusion  that  the  wear  of  rails  due  to  gradients  as  such  is  almost  nil, 
except  as  their  rate  may  be  such  to  require  the  use  of  brakes  and  sand. 
The  use  of  sand  is  exceedingly  destructive  to  rails.  The  writer  found 
that  at  specially  exposed  localities  (near  stations  for  the  most  part),  where 
the  use  of  both  brakes  and  sand  was  usual,  the  wear  as  measured  by  loss 
•of  weight  was  increased  some  75  per  cent ;  but  loss  of  weight  alone  is  an 
unfair  criterion,  since  the  wear  at  joints  is  a  very  important  factor  in  the 
life  of  rails,  and  often  requires  their  removal  before  they  are  fully  worn 
•out.  Such  extreme  use  of  either  brakes  or  sand,  moreover,  is  not 
<;ommon  on  any  grade  as  at  the  points  covered  by  the  writer's  tests. 

458.  In  tlie  first  edition  of  this  treatise,  a  considerable  body  of  sta- 
tistics being  presented  and  discussed  to  which  it  appears  unnecessary  to 
again  give  space,  the  writer  estimated  that  the  wear  of  iron  rails  was  in- 
creased not  over  5  per  cent  per  25  vertical  feet  of  rising  grade  and  the 
same  on  the  corresponding  descent,  or  10  per  cent  for  each  25  feet  of 
rise  and  fall,  making,  on  a  2  per  cent  grade  (106  feet  per  mile)  a  differ- 
ence of  20  per  cent  in  the  aggregate  of  this  item  on  both  the  ascent  and 
•corresponding  descent.  He  sees  no  reason  to  believe  that  this  estimate 
is  materially  in  error  in  either  direction  (unless  in  excess)  as  measuring 
the  effect  of  gradients  pure  and  simple,  without  modification  in  the  num- 
ber of  engines  used  for  a  given  number  of  cars,  and  this  latter  occurs  only 
on  the  worst  class  of  rise  and  fall,  C.  For  that  class,  a  proper  estimate 
for  iron  rails  might  be  expected  to  still  hold  good  for  steel,  since  the 
proportions  of  the  grade  near  to  the  level  wear  has  not  been  greatly  af- 
fected by  the  introduction  of  steel  on  such  steep  grades,  where  speed  is 
slow. 

On  Class  A  there  is  certainly  no  direct  evidence  that  the  wear  of  rails 
is  affected  at  all,  with  steel  rails.  With  iron  rails,  which  failed  mostly 
from  lamination  and  which  speedily  wore  to  an  irregular  surface  on  top, 
on  which  any  considerable  increase  of  speed  caused  greatly  increased 
wear  and  tear,  the  case  was  different. 


, 38r 

Class  B  of  rise  and  fall  likewise  has  little  effect  to  increase  rail  wear,, 
but  as  it  is  apt  to  cause  a  somewhat  high  velocity  in  the  hollows,  it  un- 
doubtedly has  some  ill  effect ;  possibly  about  one  half  as  much  as  Class  C. 

459,  Maintenance  of  Road-bed  and  Track.— In  the  former 
edition  of  this  treatise  the  cost  of  these  items  was  estimated  as  increased 
in  about  the  same  ratio  as  the  rail  wear,  viz.,  5  per  cent  for  each  25  feet 
per  mile  (0.5  per  cent  nearly)  of  rise  and  as  much  for  the  corresponding^ 
fall.  A  liberal  estimate  in  such  a  matter  is  proper,  and  we  may  continue 
the  former  estimate  for  Class  C,  although  it  is  probably  somewhat  too 
high  for  average  conditions. 

On  Class  A  and  Class  B  the  disadvantages  and  advantages  of  the 
grade  may  be  fairly  considered  to  balance  each  other  as  respects  main- 
tenance of  road-bed  and  track.  A  great  compensating  advantage  from 
the  grade,  besides  the  lower  speed,  is  the  more  perfect  drainage,  giving 
a  firmer  road-bed  and  prolonging  the  life  of  ties  and  ballast  as  well  as 
preserving  the  surface.  Level  cuts  are  always  very  objectionable,  as  has 
been  rediscovered  many  times  since  one  of  the  early  English  engineers 
laid  out  one  several  miles  long,  which  caused  immense  difficulty  (and 
still  causes  it),  several  costly  tunnel  culverts  having  to  be  driven  to  drain 
it.  Grades  of  any  moment  are  usually  situated  in  comparatively  rugged 
and  difficult  regions,  and  the  increased  expense  arising  from  that  cause 
is  very  apt  to  be  erroneously  ascribed  to  the  effect  of  the  gradients 
themselves.  Creeping  of  rails  is  an  annoying  effect  due  in  part  to  gra- 
dients, but  has  been  largely  done  away  with  in  recent  years  by  improved 
forms  of  joints. 

460.  Train  Wages.— It  is  quite  conceivable  that  one  or  more  addi- 
tional brakemen  may  be  required  on  a  line  of  much  rise  and  fall,  yet  it 
would  ordinarily  be  quite  improper  to  include  this  as  one  of  the  ex- 
penses arising  from  it,  for  this  reason  :  Whether  or  not  such  additional 
force  will  be  required  is  usually  determined  by  the  general  character  of 
the  line  beyond  hope  of  change  by  the  engineer.  In  comparing  two 
radically  different  lines,  it  might  be  an  element  worthy  of  consideration,, 
but  the  slight  modifications  which  are  ordinarily  alone  possible  can 
rarely  be  sufficient  to  in  themselves  make  any  difference  in  this  respect. 

461.  Station,  Terminal,  and  General  Expenses,  as  well  as  train 
wages  and  a  large  proportion  of  the  other  running  expenses,  cannot  be 
considered  as  affected  to  any  appreciable  extent  by  any  changes  in  rise 
and  fall  not  of  the  most  radical  and  extensive  nature. 

462.  From  all  that  has  preceded  we  may  deduce  that  no  lead- 
ing item  of  railway  expenditure  is  largely  affected  by  rise  and 


<;-« 


382  CHAP.   IX.— RISE  AND  FALL— COST  OF. 

fall  in  itself,  and  very  many  of  them  not  at  all  affected.  In 
Table  124  appears  a  detailed  summary  of  the  aggregate  effect 
to  increase  expenses  of  ieach  of  the  three  classes  of  rise  and  fall, 

A,  B,  and  C: 

A.  Not  requiring  shutting  off  steam  nor  change  in  the  natural 
velocity,  nor  use  of  brakes  or  sand.    (See  foot-note  to  Table  124.) 

B.  Requiring  shutting  off  steam  at  the  head  of  the  grade,  but 
not  use  of  brakes  or  sand. 

C.  Requiring  use  of  both  brakes  and  sand. 

463.  The  summary  of  the  cost  per  year  of  a  foot  of  rise  and 
fall  at  the  foot  of  Table  124  shows  its  cost  to  be— 

Class  C.  Class  B.  Class  A. 

Cost  on  minor  gradients $2  67  $0  84  $0  28 

Cost  on  ruling  gradients 3  50  167           

Addition  to  cost  of  same  amount  of  rise 

and  fall  if  on  ruling  gradient o  83  o  83           

These  sums,  divided  by  the  rate  of  interest  on  capital,  what- 
ever it  may  be,  will  give  the  justifiable  expenditure  per 
DAILY  TRAIN  to  avoid  oue  foot  of  rise  and  fall.  Thus,  if  capital 
cost  6  per  cent,  the  justifiable  expenditure  per  daily  train  to 
avoid  100  feet  of  rise  and  fall  (i.e.,  100  feet  up,  with  the  corre- 
sponding 100  feet  down)  will  be  for  each  class,— multiplying  the 
above  sums  by  100  and  dividing  by  0.06, — 

Class  C.  Class  B.        Class  A. 

If  on  minor  gradients $4,45°         $1,400         $467 

If  on  a  ruling  gradient 5>833  2,783 

To  reduce  the  ruling  to  a  minor  gradi- 
ent (leaving  the  ruling  gradient  else- 
where unchanged) IjS^S  1*383 

It  would  be  impossible,  however,  that  there  should  be  so 
much  as  100  feet  of  rise  and  fall  of  Class  A  at  any  one  point, 
since  if  there  were  so  much,  or  even  half  or  one  quarter  so  much, 
it  could  not  belong  to  Class  A.  The  value  given  for  reduction 
of  a  ruling  to  a  minor  gradient  refers,  of  course,  merely  to  the 
DIRECT  saving  of  wear  and  tear  by  having  tiie  grade  easier,  and 


CHAP.   IX.— RISE  AND  FALL— COST  OF. 


383 


Table  124. 
Estimated  Cost  Per  Train-Mile  and  Per  Daily  Train  of  26.4  Feet  of 
THE  Various  Classes  of  Rise  and  Fall. 
(Cost  of  train-mile  assumed  at  $i.oo.) 


Item. 


Fuel 

Water,  oil,  and  waste, . . . 

Repairs  of  engines 

Swiiching-engine  service.. 
Train  wages  and  supplies. 

Repairs  of  cars 

Car-mileage 

Renewals  of  rails . . 

Adjusting  track 

Renewing  ties 

Earthwork,  ballast,  etc. . . 

Yards  and  structures 

Station  and  general 


Total 

Cost  of 

Item. 


Total. 


7.6 
1.2 
5.6 
5.2 

154 
10.  o 
2.0 
2.0 
6.0 
3.0 
4.0 
8.0 
30.0 


Percentage  of  same 
increasing  with  26.4 
feet  of  ribe  and  fall 

belonging  to — 
Class  C       Class  B. 


100. 0 


P-  c.  p.  c. 

100  33i 

50  20 

4-0  i.o 

Unaffected. 

4.0  1.0 

Unaffected. 
10. O  5.0 

50  0.0 

5-0  0.0 

50  0.0 

Unaffected. 


Cost  per  train-mile 
of  26.4  feet  of  rise 
and  fall  belonging 

to- 
Class  C.       Class  B. 


9-7 


PC 

7.6 
0.6 
0.22 


0.4 

•    •    •    • 

0.2 

0.3 

0.15 

0.2 


p.  c. 

2.53 
0.24 

0.06 


O.IO 

■    «    •    • 

0.10 
0.00 
0.00 
0.00 


3.0         9.67  3.03 


Per  Foot  of  Rise  and  Fall 

Per  Foot  of  Rise  and  Fall  per  Daily*  Train'(roundVrip). 


.366 
$2.67 


*"5 

$0.84 


Cxll'P'l  ^''^  ^""^^  ^^  ''''  """^   Maximum  Grade,   whether  on   Class   B~or 

W  r^"  '"^"  °^  rolling-stock  and  track  will  be  so  increased  as  to  add  at 

^co'zzr^ '""""' '" ''' '"'  °'  ^'^ ''''  °'  "^^  ^^^  ^^"'  ^--^  -  '^^  f«»-- 

^°' aCe*?^"^  *I"^'°  ^'  ^"^^  ""^  "'^  ^^  ^^"  °°  ^^^°^  Gradients,  as' 

Additioritocost'ofthesan^egT^de  if  a  Ruling  Gradient  due  io  the 
extra  wear  and  tear  on  ruling  gradients,     .         .  "uc  lu  me 

^''''gra'^IENTS°''  ^'  "^^"^  '"^'^  ^'  ^'^'''^  "'^  ^"^  ^^"  °°   ^^^ING 


Class  C.    Class  B. 


$2.67 
0.83 


$0.84 
0.83 


(par  4^''  "^  ^"'  '''"'  ^^^^  °''^'  ^  ^''°'  ""^  ^''°'  ""''^  '"^  correspondf^g  des^nt 

fromtrnrt^"^-  ^T  ^"""^  ''\''^''  "^^  '"''"'^^  ^"  *'^^  *^^^^'  because,  as  will  be  seen 

n  in  anT?^"f    ^'T  °'  '''  '"'"''  °'  ^^^"^^^'  "°  '""^^'^  ^^  ^  ^--^ly  traced 

Hm  taLTr  HH^        T'  ,^^^«°^^^^""^  this  apparently  doubtful  conclusion  the  strict 

air?  tit        '^   "^  '"'"  '^  '"  ^^''  ^-^5  ''  ^eg.  are  to  be  remembered.     Moreovef 

andTv^L^l "tr"'  "'"^^"^^^^^  ^"^'"^  ^--  -^h  "se  and  fall  for  this  cause  alone, 
d  It  W.U  lead  to  no  senous  error  to  assume  its  cost  at  one  fourth  to  one  third  the  cost  0/ 


384 


CHAP.   IX.— RISE  AND  FALD—COST  OF. 


CHAP.   IX.-^RISE  AND  FALL— VERTICAL   CURVES.       38$ 


not  at  all  to  the  much  greater  value  which  results  from  reducing 
all  ruling  grades  throughout  the  line,  so  that  the  length  of 
trains  can  be  increased. 

464.  The  above  values  are  to  be  further  multiplied  by  the 
estimated  number  of  trains  per  day  (round  trip).  Thus,  if  there 
are  expected  to  be  10  trains  per  day  each  way,  the  value  of  sub- 
stituting a  level  for  a  hill  100  feet  high  becomes  $14,000  to 
$44,500  for  minor  gradients,  and  $27,830  to  $58,330  for  ruling 
gradients — which  are  very  considerable  sums  if  we  remember 
that  they  are  quite  apart  from  all  limiting  effect  of  the  gradi- 
ents. The  value  of  changing  the  rise  and  fall  from  Class  C  to 
Class  B  is  nearly  $30,000,  and  of  reducing  a  ruling  gradient  to  a 
minor  gradient  without  changing  the  class,  nearly  $14,000. 

465.  In  the  first  edition  of  this  treatise  the  cost  of  rise  and  fall  on  all  grades 
of  over  40  feet  per  mile  was  found  to  be — 

On    I2|        feet  per  mile  (about         0.25)  grades $1  04 

25  ......(..  0.5  )       "     I  56 

35  •'      ..      ««     ^    «.  o^  )       ..     I  8y 

40  to  50  **      "     "     (    "  0.8  to  i.o  )       '•     2  g8 

80  "      ....(..  15)       ..     2  29 

125  "      ••     ••     (    **  2.5  )       "     2  40 

The  writer  has  been  forced  to  the  conclusion  that  these  estimates  were  too 
small  to  be  on  the  safe  side,  and,  despite  the  fact  that  the  steel  rail  and  other 
mechanical  betterments  have  materially  reduced  the  disadvantages  of  rise  and 
fall,  has  increased  its  estimated  cost  as  above. 


466.  It  will  be  clear  from  all  that  has  preceded  in  this  chapter 
that  the  disadvantages  of  rise  and  fall  are  measured  more  truly 
by  the  number  of  breaks  of  grade  than  by  the  actual  amount 
of  it  in  vertical  feet,  except  on  the  worst  class  of  all,  C,  on  which 
both  brakes  and  sand  have  to  be  constantly  used.  Even  on  the 
heaviest  grades  this  is  in  a  measure  true.  Thus,  the  long  i  per 
cent  grade  in  Fig.  86,  belonging  to  Class  C,  will  be  considerably 
more  objectionable  to  operate  than  a  corresponding  easy  grade 
belonging  to  Class  A  or  B  of  rise  and  fall,  as  the  0.5  continuous 
grade  in  Fig.  86;  but  the  breaking  up  of  the  i  per  cent  grade 
at  frequent  intervals  by  stretches  of  lighter  grade,  so  that  the 


descent  is  made  half  on  one  grade  and  half  on  the  other,  so  far 
from  decreasing  the  aggregate  cost  of  the  grade  over  the  straight 


^^4V  V*  w«»W«»ww«» 


r~~r-i  — I — r~n 
'  Fig.  86. 

I  per  cent,  will  in  fact  make  it  considerably  more  expensive  to 
operate. 

467.  Again,  1000  feet  of  rise  and  fall  concentrated  on  a  single 
grade  is  not  nearly  so  expensive  in  wear  and  tear  as  when  the 
same  amount  of  it  is  scattered  around  in  a  dozen  or  more  shorter 
and  widely  scattered  grades  of  the  same  rate  and  class  (par. 
462).  If  its  class  is  changed  by  such  breaking  up  the  case  is 
different.  Thus,  the  least  objectionable  class.  A,  of  rise  and  fall 
can  only  exist  when  there  is  very  little  at  one  point. 

468.  We  have  seen  (par.  414  et  seq.)  that  long  and  easy  verti- 
cal curves,  properly  used,  very  largely  obviate  the  disadvantages 
of  every  class  of  rise  and  fall,  however  much  broken  up  into 
short  sections;  in  fact,  properly  used,  they  forbid  the  breaking 
it  up  into  over-short  sections. 

It  is  so  extremely  important  that  vertical  curves  should  be 
sufficiently  long  and  should  be  properly  put  in,  that  we  may 
anticipate  here,  from  the  field-book  which  follows  this  volume, 
some  notes  as  to  the  proper  manner  of  putting  in  such  curves: 

469.  We  have  seen  (par.  426^/  seg.)  that  the  length  of  vertical  curves 
should  be  determined,  not  arbitrarily,  regardless  of  the  angle  between 
gradients,  but  by  the  amount  of  change  of  grade  per  station  which  is 
admiFc.ble;  the  safest  rule  being  as  already  given-that  the  difference  in 
tb  J  rate  of  grade  under  the  head  and  rear  of  the  train  shall  not  exceed 
Ihe  grade  of  repose  of  the  last  car. 

A  rate  of  change  per  station  (100  feet)  of  .025  will  most  completely 
25 


386 


CHAP.   IX.-RISE  AND  FALI^VERTICAL   CURVES. 


CHAP.   IX.— RISE  AND  FALL—VERTICAL   CURVES.       387 


fulfil  this  condition  with  all  kinds  of  trains,  including  those  with  a  great 
deal  of  slack  in  the  couplings,  like  coal  trains  :  but  .05  per  =tat.on  w.ll 
obviate  all  the  more  serious  effects,  especially  if  the  speed  be  high  or  the 
°rain  short,  or  both.  After  the  introduction  of  improved  f  re.ght  couplers 
oc  oer  station  will  be  ample. 
■     Both  of  these  rates  give  a  longer  curve  than  is  usual ;  but  more  ch^^ge 


•"  Fig.  88. 

Fig.  87. 

cer  sution  than  that  last  specified  should  never  be  used  in  sags  (Fig. 
8^  .  unless  for  high  speed  and  very  short  trains.  On  sumnut  curves 
(F  g.  88)  shorter  curves  are  admissible ;  but  these  also  should  not  be 
shorter  than  o.i  per  station-if  for  no  other  reason, because  .t  is  needless 

'°  "yorCa^gle  between  grade-lines.  ..  Figs.  87.  88.  is  considered  to 
be  the  sum  or  difference  in  the  rate  per  cent  of  the  ^='d«^°^;''"^ 
deflection  from  each  other.  In  Fig.  87,  a  =  ..4 :  m  F.g.  88;  «  "  '^°-^^ 
If  we  let  r  =  the  change  of  rate  per  stat.on  *h.ch  is  con  .dered  adnus^ 
sible,  =  0.025  to  0.10  according  to  circumstances,  then  the  aggregate 
length  of  any  curve  is  at  once  given  by  the  equation 

If  the  angle  between  grade-lines  te  i.o  per  cent,  this  gives  a  vertic^ 
curve  10.  20.  or  40  stations  long,  according  as  the  assumed  value  of  r  .s 

"■'•^^IZmo.  that  the  change  in  rate  of  grade  shall  be  uniform  per 


Fig.  89. 
an  this  cut,  which  is  rather  poorly  executed, 
I  •   :i   4.  s  are  successive  stations  of  too  feet 
fiom  the  tangent  point  T.  but  the  "  curve"  as  drawn  is 
supposed  to  consist  merely  of  a  series  of  straight  hnes, 
ab    be,  cd,  etc.,   tangent  to  the  curve  at  these  stations, 
thise  ungents,  as  prolonged  by  the  dotted  lines,  bemg  supposed 
to  differ  from  each  other  in  rate  of  grade  by  a  constant  change 
of  rate,  r.)  ^.u^*  ««♦ 

sution  or  other  unit  results  in  the  generation  of  a  curve  such  as  that  out- 
lined  in  Fig.  89,  which  is.  mathematically,  a  parabola. 


471.  It  is  to  be  remembered  that  all  geometrical  diagrams  connected 
with  railway  location  are  greatly  exaggerated  or  distorted,  so  that  the 
succession  of  chords  outlined  in  Fig.  89  are  in  fact  practically  coincident 
with  the  curve.  Fig.  90  gives  to  correct  scale  the  intersection  of  a  4 
per  cent  (211  feet  per  mile)  grade  with  a  level,  which  is  periiaps  twice  as 
large  an  intersection  angle  as  actually  occurs  on  any  located  line  in  the 
United  States,  even  on  the  engineer's  profile,  and  four  or  five  times  as 
much  as  is  usual ;  topographical  reasons  generally  requiring  one  or  more 
intermediate  grades  in  cases  of  such  abrupt  change. 

Fig.  90  will  also  make  it  clear  that  in  the  two  sketches  of  vertical 

,lsmvf€ ,11  . 


Fig.  90. 

curves  shown  in  Figs.  91  and  92  the  tangents,  the  chord  M,  and  the 
curves  themselves  are  sensibly  of  the  same  absolute  length,  independent 
of  the  fact  that,  all  distances  being  measured  horizontally,  they  are  neces- 
sarily equal  as  measured  in  the  field. 

472.  From  the  law  of  the  parabola  it  results  that  in  any  vertical 
curve,  Fig.  91  or  92,  the 
curve  bisects  the  middle 
ordinate   IM  in    c,    and 


from  elementary  geomet- 
rical relations  we  have  for 
the  distance    Ic  =  c,    by  fig.  91. 

which  the  curve  departs  vertically  from  the  intersection  of  tangents  : 
I      a      la 

^=7  ^4  =-8-'         'h^^      r 


or,  as  /  =  -  (par.  470), 


a' 


^  = 


8r* 


473.  From  this  formula  we  can  compute  the  following  Table  125,  giv- 
ing the  first  detail  which  it  is  desirable  to  know  in  laying  out  a  vertical 
curve,  viz. :  How  much  vertical  change  it  will  produce  in  the  position  of 
the  grade-line,  which  is  greatest  at  the  middle  of  the  curve  and  thence 
rapidly  diminishes  in  each  direction,  being  only  one  fourth  as  much  at 
the  "quarter-points" of  the  curve  or  at  the  middle  of  each  tangent. 

474.  Having  determined  from  Table  125.  or  otherwise,  what  rate  of 
per  station  will  be  necessary  or  feasible :  To  lay  out  a  vertical  curve, 

HAVING  GIVEN  THE  RATE  OF  THE  TWO   GRADIENTS   AND  THEIR  ANGLE 


388 


CHAP.   JX.-RISE  AND  FALL- VERTICAL   CURVES. 


Table  125. 

VERTICAL  CHANGE  IN  THE  POSITION    OF  THE    ^^ADE-LlNE  AT  InTE^s™ 

OF  Gradients  resulting  from  Vertical  Curves  of  Various  Rates  T 
AND  WITH  Various  Grade-Angles  a. 

(Computed  by  formula  of  par.  472.) 


Grade-Angle 

a. 

Figs.  91,  9«' 


Vertical  Distance  of  Curve  from  Intersection  of 
Gradients  =  Ic,  Figs.  91  and  93,  for  Change  of  Rate 
OF  Grade  per  Station,  =  r  of—  


L 


0.1 
0.2 
0.3 
0.4 
0.5 
0.6 

0.7 
0.8 

0.9 
i.o 
I.I 
1.2 

1.3 
1.4 
1.5 
1.6 

1.7 

1.8 

1.9 
2.0 


0.2 


Feet. 
.006 
.025 
.061 
.100 
.156 
.225 
.306 
.400 

.501 
.625 

.756 
.goo 
1.056 
1.225 
1.406 
1.600 
1.806 
2.025 
2.256 
2.500 


0.1 


0.05 


Feet. 

Feet. 

.01 

.025 

.05 

.1 

.11 

.225 

.2 

.4 

•  31 

.625 

.45 

.9 

.61 

1.225 

.8 

1.6 

1. 01 

2.025 

1.25 

2.5 

1. 51 

3  025 

1.8 

3-6 

2. II 

4.225 

2.45 

4.9 

2.81 

5.625 

3.2 

6.4 

3-6i 

7-225 

4.05 

8.1 

4.51 

9.025 

5-0 

10. 0 

0.025 


Feet. 
.05 
.2 

.45 
.8 

I.2S 

1.8 

2.45 
3.2 

4.05 
5.0 
6.05 
7.2 

8.45 
9.8 
11.25 
12.8 

14.45 
16.2 
18.05 
20.0 


The  vertical  change  in  the  position 
curve,  or  at  the  middle  of  the  tangents, 

The  whole  length  of  the  curve  (both 


of  the  grade-line  at  the  "quarter-points"  of  the 
is  in  each  case  one  fourth  of  the  above. 

grade-angle 


tangents)  =  '  = 


change  of  grade  per  station 


OF  INTERSECTION  ..THE  RATE  PER  STATION  r,  AND  THE   STATION   OF 
THE  INTERSECTION  OF  GRADIENTS  :  ^ 

I  The  total  length  of  the  curve  in  stations  is  -  (which  let  =  n 
.tations^  one  half  of  which  is  the  length  of  each  tangent,  whence  the 
sutron  of  the  tangent-point  can  be  determined  and  the  elevation  of  the 
grade  at  that  point. 


CHAP,  IX.— RISE  AND  FALL— VERTICAL   CURVES.       389 


2.  Having  given  the  station  and  elevation  on  either  grade,  and  the 
rate  (which  let  =  R)  of  the  grade  in  which  it  lies,  write  successively 
R  —  \r,  R—  i\r,  R  —  2^r,  etc.,  adding  or  substracting  r  from  each 
(as  the  case  may  require)  until  n  quantities  have  been  written  down, 
paying  strict  attention  to  the  algebraic  signs,  as  below  specified. 

The  «th  quantity  thus  determined  will  differ  from  the  rate  R'  of  the 
other  tangent  by  \r,  and  the  addition  of  the  several  quantities  thus  de- 
termined to  the  elevation  of  the  first  tangent-point  w^ill  give  the  elevation 
of  each  station  of  the  curve,  to  and  including  the  other  tangent- point, 
where  the  elevation  will  check  upon  that  independently  fixed  by  the 
tangent  grade-line  for  the  second  tangent,  if  the  work  has  been  correctly 
done. 

When  the  angle  between  the  grade-lines  is  upward,  or  on  a  summit, 
the  successive  additions  of  r  are  -,  or  subtractions;  when  the  angle  of 
the  grades  is  downward,  the  additions  are  positive. 

Examples.— Curves  to  connect  the  gradients  shown  in  Figs.  93,  94,  95,  each 
"With  the  intersections  of  gradients  at  station  100  and  elevation  loo. 


(9«.9;  o    ^  ..    (^.9> 

Fig.  93. 

Fig.  93. 

Angle  between  grade-lines 1.6 

Rate  of  change  of  grade  per  station.         0.2 
Total  length  of  curve 8  sta. 

Station  of  tangent-points -J    ^ 

Elevations  of  grade  at  do.  (computed).  \  ^^'2 


Rafe,o.f 

6  Stafhns 


Fig.  94. 


Additions. 

P.C. 

R-\r. 0.7 

R  —  l\r. 0.5 

R  —  2\r, 0.3 

R  —  3\r. 0.1 

Etc —0.1 

-  0.3 

P.T -0.7 


Eleva-     Stations. 

TIONS. 


969 
97.6 
98.1 
98.4 
98.5 
98.4 
98.1 
97.6 
96.9 


96 

97 
98 

99 
100 

lOI 

102 
103 
104 


Fig.  94. 
0.6 
O.I 

6  stations. 

97 
103 

100.9 
97.3 


Addi- 
tions. 


—  0-35 
-0.45 
-0.55 

—  0.65 

-0.75 

—  0.85 


Elevations. 

TOO  90 
100.55 
100.10 

99-55 
98.90 
98.15 
97.30 


Sta- 
tions. 

97 

9« 

99 
100 

lOI 

102 
103 


OoB^o) 

'20  stafions  *• 

Fig.  95* 

I.O 

Angle  between  grade-lines •  •  *  * q  05 

Rate  of  change  of  grade  per  station ^o  station*. 

Total  length  of  curve  (    go 

Station  of  tangent-poinU I  I08.0 

Elevation  of  grade  at  tangent-points j  102 .0 

Elevations.  Stations. 

Additions.  ^^g^  ^o 

*^''-*  Il2^  »o4.^  a 

-  375  "-'»5  S 
I  *?«                    102.5  '°^ 

I  I25  102.0  102 

""  'ill         101.7  '^ 

-  02!  101.6  106 

i^.r.   t:i75 

This  .ethod  is  practically  n.uch  the  -fj;--^^^^^^^^^ 

begins  and'ends  at  a  ^ "1\  ^t^^^^"' ^[^^^^^^^^  ^ZZL  cases  the  following 
ing  grades  for  half  stations  or  otherwise. 

•"%7rB?t.e  property  of  the  p^^-j^ '':^,r-'^:::oTthVranc: 

^ngents  parallel  to  the  "  ^^^e  h^-no  ™  O  AKD  A^.  Fig.  96, 
!.'o°'"J™rors:xs  rrJrcUKVK,  .  ..  ."  at  distances  .  «'.  «' 
from  the  P-  C, 


CHAP.   IX.— RISE  AND  FALD-VERTICAL   CURVES.       39 1 


Letting  iV  =  the  length  of  one  tangent  we  have,  for  any  offset  o  what- 
ever at  a  distance  n  from  the  P.  C, 

nr^  =  Zi>  whence  o  =  0-tjI 


N 


n 


Thus,  if  we  divide  the  tangent  N  into  five  parts  the  first  offset,  0,  will  be 

I*        O 
O  x—i,  or — ,  and  the  succeeding  ones  will  be  4,  9,  16  times  the  first. 

By  this  formula  we  may  compute  the  elevation  of  any  two  points  100 


Pro.  9(5. 

feet  apart  on  any  vertical  curve  (presumably  at  full  stations)  and  deter- 
mine the  rate  of  grade  between  them  ;  whence,  knowing  the  change  per 
station  in  rate  of  grade,  all  remaining  stations  are  determined  by  succes- 
sive additions  as  above.  To  avoid  cumulative  error,  the  computation 
should  be  carried  out  to  more  decimals  than  it  is  expected  to  use. 

The  entire  curve  may  likewise  be  computed  by  determining  the  off- 
sets 0,  </,  0",  which  ordinarily  involves  little  labor. 


PART  III. 


LIMITING  GRADIENTS  AND  CURVATURE. 


**  The  crime  which  bankrupts  men  and  states  is,  job-work;— declining 
from  your  main  design  to  serve  a  turn  here  and  there." 

— R.  W.  Emerson,  Essay  on  ''Wealth,^ 


PART   III. 

LIMITING  GRADIENTS  AND  CURVATURE. 


CHAPTER   X. 


THE   RELATIVE   IMPORTANCE   OF    GRADIENTS. 


476,  To  summarize  the  conclusions  we  have  reachea  in  the 
preceding  four  chapters  as  to  why  the  minor  details  of  align- 
ment are  properly  so  called,  both  separately  and  collectively; 
Let  us  assume  that  we  have  a  line  over  which  an  estimated 
traffic  of  lo  trains  per  day  each  way  wmU  pass, — a  very  fair  traffic, 
— and  that  we  have  two  alternate  lines  for  it,  one  of  which  (A) 
is  200  miles  long,  while  the  other  (B)  is  210.  Let  line  A  have 
the  favorable  alignment  of  the  Illinois  Central,  which  (Table  102) 
has  only  8°  of  curvature  per  mile,  and  line  B  the  very  crooked 
alignment  of  the  Lehigh  Valley,  which  has  100°  per  mile,  giving 
1600°  in  all  on  line  A  against  21,000°  in  all  on  line  B.  Let  the 
rise  and  fall  on  A  average  only  10  feet  per  mile,  or  2000  feet  in 
all,  instead  of  20  feet  per  mile  on  B,  or  4200  feet  in  all ;  always 
assuming,  however,  that  the  ruling  gradients  and  length  of  trains 
are  the  same  on  each.  Then  the  entire  value  of  these  very 
marked  and  very  improbably  great  differences  in  minor  details 
will  be  as  follows: 


396      CHAP.   X.^RELATIVE  IMPORTANCE   OF  GRADIENTS. 


CHAP.  X.— RELATIVE  IMPORTANCE   OF  GRADIENTS.      397 


DiFFERBNCBS  AGAINST   LiNE  B. 


Estimated  Cost  Per  Year. 
Per  Daily        For  10  Daily 
Train.  Trains. 


$2,665  00  $26,650  00 

8,400  00  84,000  00 

2,670  00  26,700  00 

4,200  00  42,000  00 


10  miles  excess  of  distance,  which  we  will  assume 

will  not  affect  train-wages,  as  that  is  the  more 

probable,  and  which  may  have  a  credit  side  as 

large  as  the  debit,  but  which  we  will  assume  has 

no  credit  side  (see  par.  196  and  Table  89),  .  . 
19,400°  excess  of  curvature  (Table  115),  at  43.3  cts. 

per° 

2200  ft.  excess  of  rise  and  fall,  assumed  to  be  all  of 

\  1000  ft.  on  minor  grades,  .     . 
Class  C,  and,  say,  j  ^^^  ^^  ^^  ^^^^^  ^^^^^^^  ^    ^ 

.(See  par.  463,  and  Table  124.)  

Total  difference  in  yearly  expenses  against  line  B,$i  7.935  ^  $i79.35o  00 

Capitalizing  this  sum  at  7  per  cent,  which  is  lower  interest 
than  most  new  lines  ought  to  require  before  increasing  expendi- 
tures, this  represents  a  capital  valuation  of  $2,562,000  or  812,810 
per  mile,  as  the  difference  due  to  the  most  extreme  differences  in 
all  minor  details  at  once. 

477.  On  the  other  hand,  the  total  operating  expenses  of  line 
A,  at  $1.00  per  train-mile  (on  which  cost  the  above  valuations  are 
based),  would  be  $1,460,000  per  year,  and  we  are  about  to  see 
that  something  like  half  of  that  great  sum— sometimes  more, 
sometimes  less — will  vary  directly  with  the  number  of  trains  re- 
quired to  transact  its  business.  If  therefore  we  adopt  grades 
which  will  cut  down  trains  to  something  less  than  half  what 
they  might  have  been,— which  is  an  easy  thing  indeed  to  do  by 
probable  errors  of  location, — we  shall  increase  its  operating  ex- 
penses by  something  like  $365,000  per  year  against  only  $i79.3So 
from  excessive  and  entirely  improbable  differences  in  each  and 
all  of  the  minor  details  of  alignment,  against  the  same  line  : 
differences  which  might  lead  to  most  unfavorable  conclusions  of 
what  was  really  the  best  line,  by  one  carelessly  inspecting  it; 
whereas  difference  in  ruling  grade  of  no  greater  comparative 
importance  might  well  attract  little  attention,  since  it  would  in- 
volve only  a  moderate  difference  in  ruling  grade. 

478.  Again,  the  gross  revenue  of  such  a  line  would  probably 


be  something  like  one  and  a  half  times  its  operating  expenses,, 
or  $2,190,000  per  year.     Probable  differences  of  location  will,  in 
almost  every  case,  cause  the  loss  or  gain   of  as  much  as  10  per 
cent  of  this,  and  in  very  many  instances  may  be  readily  shown- 
to  have  had  (probably)  two  or  three  or  five  times  that  effect. 
Ten  per  cent  extra  revenue,  as  we  have  seen  (par.  40),  may  in  » 
rude  way  be  taken  as  almost   so  much   pure  gain,  although  of 
course  there  always  is  a  debit  side  to  even  so  small  a  difference 
of  revenue,  possibly  as  much  as  25  per  cent.     Even  then   a  net 
difference  to  revenue  of  as  much  as  $164,000  per  year  not  only 
may,  but  probably  will,  hang  on  decisions  reached   in  location, 
which  may  be  capitalized  at  7  per  cent,  as  equal  to  a  valuation 
of  $2,343,000,  or  nearly  $12,000  per  mile  added  to  or  taken   from 
the  value  of  the  property.     This  moderate  difference  in  revenue 
thus  suffices  to  overbalance  all  the  disadvantages  of  the  assumed 
differences  in  minor  details,  which  go  far  beyond  any  that  ever 
existed,  probably,  in  any  two  alternate  lines  between  the  same 
termini. 

Granting  that  questions  of  revenue  cannot  be  reduced  to  pre- 
cise figures,  and  may  be  beyond  the  engineer's  control  (although 
correct  action  in  respect  to  them  will  largely  depend  upon  him 
and  affect  his  other  work),  the  question  of  what  ruling  gradients 
to  adopt  can  be  reduced  to  tolerably  precise  figures,  and  will 
rest  exclusively  in  his  hands;  and  of  the  questions  which  so  rest, 
we  have  now  seen  the  reasons  why  it  may  almost  be  called  the. 
question  before  him,  to  the  exclusion  of  all  others.  It  must 
therefore  be  studied  with  some  care. 

479.  We  have  seen  in  the  opening  to  Chap.  IX.  that  the  ex- 
pense of  gradients  arises  from  two  causes,  which  are  totally  dis- 
tinct and  must  be  kept  so  to  form  any  correct  idea  of  their  cost 
or  proper  adjustment ;  the  one  being  the  direct  or  inherent 
effect  of  all  rise  and  fall  or  curvature  to  increase  wear  and  tear 
and  expenses  per  train-mile  (considered  in  the  preceding  chap- 
ters), and  the  other  the  effect  of  the  heaviest  grade  or  sharpest 
curve  to  limit  the  weight  and  length  of  train,  and  thus  cause  an 
additional  expense  which  does  not  appear  at  all  in  the  expenses- 


398      CHAP,  X.— RELATIVE  IMPORTANCE  OF  GRADIENTS. 


CHAP.   XI.— THE  LOCOMOTIVE  ENGINE. 


399 


per  train-mile,  but  simply  in  the  number  of  trains  required  to 
handle  the  traffic.  The  distinction  between  these  diverse  sources 
of  expense  was  so  fully  drawn  in  Chap.  IX.  that  it  need  not  be  re- 
peated,  but  it  should  be  always  borne  in  mind.  For  the  present 
we  assume  the  gradients  to  be  the  limiting  cause,  as  is  nearly 
always  the  case,  although  it  may  be  curvature  or— conceivably— 
any  other  cause,  like  the  strength  of  couplings. 

480.  To  be  prepared  to  deal  intelligently  with  questions  of 
gradients  we  must  begin  from  the  foundation  and  consider,  in 
some  detail,  what  we  may  call  the  physiology  as  distinguished 
from  the  anatomy  of  the  locomotive  engine,  especially  as  re- 
spects the  running  gear.  The  general  question  of  limiting  gra- 
dients  will  then  divide  itself  naturally  into  the  following  different 

heads  : 

First  Ruling  gradients  proper,  and  their  effects  on  tram- 
loads  and  operating  expenses  (Chaps.  XIV.,  XV.). 

Secondly.  The  use  of  concentrated  or  "  bunched  "  grades  on 
high  rates,  operated  by  assistant  engines  or  "pushers,"  with 
lower  grades  elsewhere,   as  against  uniform  gradients  (Chap. 

XVI.).  ^       ^ 

Thirdly.  The  proper  balance  of  grades  from  excess  of  traffic 

in  one  direction  (Chap.  XVII.). 

Fourthly.  Limiting  curvature,  which  may  intervene  in  ad- 
vance of  gradients  to  limit  the  length  of  trains  (Chaps.  XVIII., 

XIX.).  ^  ^     . 

Fifthly,  The  choice  of  gradients  and  devices  for   reducing 

them  (Chap.  XX.). 

All  of  these  problems  come  up,  potentially  at  least,  in  the 
location  of  every  line.  Before  attempting  to  solve  them  we  will 
lay  the  necessary  basis  therefor  in  the  three  following  chapters  on 
the  Locomotive  Engine,  RoUing-Stock,  and  Train  Resistance. 


CHAPTER  XI. 

THE   LOCOMOTIVE   ENGINE.* 

481.  The  locomotive  engine  is,  so  far  as  the  skill  and  foresight  of  the 
designers  can  make  it,  and  practical  considerations  permit,  a  delicately- 
balanced  machine,  having  these  three  forces  in  equilibrium  for  the  par- 
ticular service  required  of  it : 

1.  The  STEAM-PRODUCING  OR  BOILER  POWER:  the  boiler,  fire-box, 
and  attached  parts. 

2.  The  MECHANICAL  OR  TRANSMITTING  POWER :  developed  through 
the  cylinder  and  attached  parts,  and  transmitted  to  the  driving-wheels. 

3.  The  TRACTIVE  POWER  OR  ADHESION  for  exerting  or  transmitting 
the  energy  produced;  developed  through  the  frictional  resistance  to 
sliding  of  the  drivers  on  the  rail. 

482.  The  amount  available  of  each  of  these  forces  is: 
Boiler  power. — Limited  by  the  quantity  of  steam  which  can  be  pro- 
duced in  a  boiler  of  admissible  weight  and  size. 

Cylinder  power. — Indefinitely  great.  The  cylinder  is  a  mere  trans- 
mitting machine  for  the  transformation  of  one  form  of  energy  into  an- 
other, and  can  be  adapted  (within  wide  limits)  to  the  transmission  of  any 
amount  of  power  (ft. -lbs.)  in  any  desired  ratio  of  speed  (ft.)  to  force 
(lbs.)  by  mere  variation  of  proportions. 

Tractive  power. — Limited  by  the  total  weight  of  the  machine  and 
the  proportion  thereof  which  can  be  placed  on  the  coupled  driving-wheels. 

483.  Thus  it  is  seen  that  the  limit  to  the  work  which  can  be  done  by 
any  well-designed  engine  lies  either  in  the  boiler  power  or  in  the  adhe- 
sion, and  never  in  the  cylinder,  which  latter  always  has,  or  should  have 

♦  The  writer  had  gone  more  fully  into  the  theory  of  the  locomotive  than  was 
absolutely  essential  and  he  finally  concluded,  more  fully  than  was  wise,  in  the 
belief  that  a  broader  general  knowledge  of  the  locomotive  by  civil  engineers 
would  in  many  ways  conduce  to  good  practice;  but  in  order  to  keep  the  volume 
within  reasonable  size  he  finally  concluded  to  abbreviate  this  chapter  very  ma- 
terially from  his  original  draft.  Much  of  the  data  thus  prepared  was  thought 
to  be  entirely  new.  and  still  more  of  it  has  not  been  systematically  presented  in 
treatises  on  the  locomotive,  but  it  must  be  given  in  another  form,  if  at  all. 


400 


CHAP,  XI.— THE  LOCOMOTIVE  ENGINE, 


CHAP.   XI.— THE  LOCOMOTIVE  ENGINE. 


401 


(in  any  engine  of  ordinary  type),  power  in  excess  of  either  what  can  be- 
transmitted  by  the  adhesion  or  developed  through  the  boiler,  or  both. 
That  the  cylinder  power  should  be  in  excess  of  one  or  the  other  of  the 
other  two,  under  all  ordinary  circumstances,  as  it  is,  is  plain.  The  ulti- 
mate power  of  the  engine  is  fixed  by  the  weakest  one  of  these  three 
forces.  Two  of  them  can  only  be  increased  by  radical  modifications  of 
the  machine,  while  the  other  can  be  made  as  great  as  desired  (within 
wide  limits)  by  trifling  modifications  of  detail,  affecting  cost  and  weight 
but  very  slightly.  Therefore,  it  is  plain,  it  would  be  inexcusable  neglect 
not  to  make  the  link  in  the  chain  whose  strength  we  can  control  strong 
enough  to  certainly  utilize  the  full  strength  of  the  other  two,  which  we 
cannot  control,  without  a  radical  change  in  the  machine ;  so  that  the 
ultimate  power  of  the  machine  as  a  whole  should  never,  at  anytime  or 
under  any  circumstances,  fall  by  mere  negligence  in  design  below  the 
limits  fixed  by  natural  causes. 

484.  That  the  comparative  conditions  stated  in  regard  to  the  possi- 
bility of  increasing  these  three  forces  do  in  fact  prevail,  is  evident  from- 
the  data  as  to  comparative  weights  of  the  various  parts  of  a  locomotive 
engine  given  in  Table  126:  To  increase  the  boiler  power  of  these 
ENGINES  10  PER  CENT  (assuming  it  to  be  possible  at  all  without  exceed- 
ing the  admissible  load  per  wheel  or  the  limits  of  physical  possibility) 
means  an  increase  of  nearly  10  per  cent  in  the  weight  of  the  boiler  and 
at  least  5  per  cent  in  the  weight  of  the  rest  of  the  engine.  As  this  would 
increase  the  available  adhesion  it  would  naturally  lead  to  increasing  the 

Table  126. 

Comparative  Weight  in  Lbs.  of  the  Various  Parts  of  a  Locomotive. 

Engine. 


Light  American. 


Consolidation,  Penn. 
Class  I 

Per  cent 


Total 

Weight  in 

Service. 

Lbs. 


60,807 
xoo.o 

91,640 
100. o 


Boiler  and  At- 
uched  Pans 
varying  there- 
with. 


Water. 


6,000 
9.9 

9.S43 
10.4 


Metal. 

15,989 
96.3 

24,262 
36.5 


Cylinders, 
Valve-geai-, 

and 

Connecting 

Rods. 


10,032 
.6.5 

15,397 
16.8 


Running 
Gear. 


16,663 
97.4 

26,119 
28.5 


Frame. 


5tI2I 

8.4 

7,500 
8.3 


Cab, 

Smoke-box, 

Lagging, 

and  Misccl. 

Trimmings. 


7,002 
XI. 5 

8,819 
9.6 


The  light  American  engine  is  that  given  in  detail  in  Table  133;  the  Consolidation  is 
given  in  detail  in  Tables  129  and  132.  The  singular  constancy  of  ratio  in  the  weights  oi. 
these  widely  different  locomotives  is  notable. 


cylinders  correspondingly,  but  even  without  doing  so  we  have  an  increase 
of  about  7  per  cent  in  the  weight  of  the  machine. 

485.  To  INCREASE  THE  CYLINDER   POWER  lO  PER  CENT  WC  have  Only 

to  decrease  the  size  of  the  drivers,  effecting  an  actual  decrease  in  the 
weight  of  the  machine.  For,  since  the  cylinder  pressure  (which  let  =  C), 
whatever  it  be,  acts  with  a  leverage  of  half  the  stroke  (=  s)  against  a  lev- 
erage of  half  the  diameter  of  the  driver  (=  K),  we  have,  for  the  tractive 

force  exerted  by  the  cylinders, 

^     sC      ^  ^      TR 

T  =  —n  and  C  =  — . 
R  s 

To  increase  T'by  any  amount  without  changing  either  the  stroke  (j) 
or  the  diameter  of  the  cylinder  {€)  we  have  only  to  decrease  7?.  This, 
however,  is  at  the  expense  of  increasing  the  piston  speed,  because,  as  the 
driver  is  made  smaller,  it  must  turn  so  much  oftener  per  mile. 

486.  To  increase  the  cylinder  power  10  per  cent  without  increasing 
the  piston  speed,  however,  nothing  more  is  required  than  the  addition  of 
from  2  to  8  per  cent  to  the  weight  of  the  cylinders  and  attached  parts 
alone,  the  remainder  of  the  machine  remaining  unaffected  except  in  a 
few  trifling  details.  Whether  the  increase  be  2  or  8  per  cent  depends^ 
chiefly  on  how  it  is  effected — whether  it  be  by  merely  lengthening  the 
cylinder  or  by  increasing  its  diameter;  but  in  either  case  the  total  addi- 
tion to  the  weight  and  cost  of  the  machine  is  trifling.  Assuming  8  per 
cent  added  to  the  weight  of  the  cylinders,  it  amounts  (see  Table  126)  to 
but  a  little  over  one  per  cent  of  the  whole  weight  of  the  engine. 

487.  Cylinder  power  may  also  be  increased  after  the  machine  is  com- 
pleted by  the  simple,  but  ordinarily  not  permissible  or  wise,  expedient 
of  increasing  the  boiler  pressure.  It  has  also  been  not  unfrequently  de- 
creased in  the  same  way,  so  as  to  be  smaller  than  either  the  boiler  power 
or  traction,  with  unfortunate  results  upon  the  efficiency  of  the  engine. 

488.  To  INCREASE  THE  TRACTIVE  POWER  lo  PER  CENT,  or  by  any 
other  amount,  we  must  either  increase  the  load  per  drivers  or  the  num- 
ber of  drivers,  or  both.  The  possibility  of  increasing  the  load  per  wheel 
is  strictly  limited  by  that  which  the  permanent  way  and  structure  will 
sustain.     The  load  per  wheel  is  in  practice,  and  for  certain   reasons  may 

properly  be  in  theory,  greatest  with  those  engines  (fast  passenger  engines) 
which  have  and  require  the  least  amount  of  total  tractive  power.  To  in- 
crease the  number  of  drivers  we  must  take  a  new  type  of  engine,  and 
here,  too,  the  range  is  strictly  limited.  A  few  special  engines  excepted, 
the  largest  number  of  drivers  now  in  practical  use  on  a  large  scale  is 
eight  (Consolidation  and  Mastodon  types),  and  the  least,  four  (American 
type),  with  a  few  extra  fast  but  very  heavy  engines  hiivir.g  only  a  single 
26 


CHAP.   XL— THE  LOCOMOTIVE  ENGINE. 


CHAP,   XL— THE  LOCOMOTLVE  ENGINE. 


403 


402  

driving-axle.  In  any  case,  to  increase  tractive  power  10  per  cent  we 
must  increase  the  load  on  drivers  by  some  40  P^^^^^^'^^^^^V^^^'.;;: 
creasing  the  total  weight  of  the  machine  by  from  50  to  60  per  cent,  ^e 
have,  therefore,  as  the  addition  to  weight  of  engine : 

To  increase  boiler  power  10  per  cent.    .  .    7  to    8  per  cent. 
To  increase  cylinder  power  10  per  cent.    .     i  to    li 
To  increase  tractive  power  10  per  cent.  ..  50  to  60 

Proving  the  statement  made,  that  cylinder  power  is  a  mere  matter  of  ad- 
3ustment,  readily  capable  of  indefinite  increase,  and  hence  should  always 
be.  as  it  generally  is,  in  excess  of  the  other  two. 

489  For  the  very  reason  that  the  amount  of  cylinder  power  is  a  mere  detail 
of  Ichanicll  design,  having  no  natural  limit  in  either  direction,  tt  furn.shes  a 
:  nv^n  n  mLs-e  of  relative  capacity  and  power  for  -n^paring  one  eng.ne^vnh 
another  In  other  words,  cylinders  of  the  same  size  can  be  sa.d  w.lh  far  more 
^xl  tness  to  give  ngines  of'always  eqttal  power  than  a  similar  identuy  m  any 
o"  on  detail  of  the  locomotive.  A  "  17  X  24'  engine,  which  .s  now  looked 
on  as  the  standard  or  unit  type,  maybe  either  a  fast  passenger  or  a  slow 
freight  en^ne  but  it  will  always  be.  roughly  speaking,  of  about  the  same 
weighl  and  cost,  and  will  ordinarily  exert  and  be  capable  of  exertmg  about  the 

-  o«,,.,int  of  oower  (foot-pounds)  in  the  same  time. 
'400  This  is  there  ore  a  very  common  and  often  aU-sufficien.  descript.on  of 
an  en«°;e  then  U  is  desired  to  give  a  general  idea  in  a  few  words  of  us  charac- 
ter  bu^this  should  not  lead  to  the  mistaken  conclusion  (as  it  someumes  does, 
hat  the  ylinder  is  an  important  element  of  design  .n  a  locomo uve  >n  the  sense 
of  beine  a  governing  element  by  which  its  power  in  serv.ce  >s  l.m.ted.  On  he 
^ntrlry.  the  logicaf  order  of  design  (but  not  necessarily  for  that  reason  the 
order  that  a  practised  designer  will  follow)  is—  ,,•  -     ■ 

FM  to  L  the  total  admissible  or  desired  weight  of  the  machine 
r.Ldl  (U.  a  freight  engine)  the  proportion  of  this  weight  which  can  be 
util'edfof 'adhesion   or  (in  a'passenger  engine)  the  largest  boiler  power  which 
can  be  eotten  without  exceeding  that  weight.    .  ,      .  j 

IhMly.  to  adapt  the  boiler  power  and  adhesion  to  each  other;  and 
FZrthiy.  to  fix  the  size  of  the  cylinders  to  correspond,  making  sure  to  ha^e 

'"^Thr^'u'rrefous  disadvantage  in  having  cylinders  unnecessarily  largej^or 
u  I L  L  done  due  to  external  and  internal  radiation,  which  lim.K  some- 

llt.  le  dtcr^tit:  s'pecified.  but  not  so  greatly  as  to  affect  the  substance 
of  what  has  been  said. 

491    The  boiler  power  of  a  locomotive,  like  that  of  any  other  source 
of  enel^Jor  dynatnll:  force,  is  ultimately  measurable  in  foot-pounds  per 


Jiour,  or  other  unit  of  time.  So  far  as  boiler  power  is  concerned,  there- 
fore, a  locomotive  is  capable  of  hauling  any  load  whatever  if  the  speed 
be  made  low  enough,  or  of  attaining  any  speed  whatever  at  the  expense 
of  the  load  hauled. 

HOKSE-POWERS  or  other  equivalent  units  are  merely  certain  multiples 
of  foot-pounds.  Whatever  the  name  of  the  unit  for  the  measurement  of 
energy,  it  is  always  made  up  of  the  three  elements  of  lifting  a  certain 
weight  through  a  certain  distance  in  a  certain  time  against  the  natural 
force  of  gravity,  gravity  being  the  only  constant  and  ever-present  force 
with  which  we  are  familiar,  and  hence  a  natural  unit  for  comparison. 

492.  The  tractive  power  is  measurable  only  in  pounds,  being  a  mere 
static  or  dead  force,  serving  for  the  transmission  of  energy,  like  a  belt  or  a 
.shaft,  but  not  affecting  its  amount.  The  tractive  power  is— with  impor- 
tant limitations  to  be  considered— an  approximately  constant  quantity  at 
all  speeds  and  under  all  circumstances. 

493.  Therefore,  remembering  (i)  that  the  cylinder  power  is  not  an 
element  in  fixing  the  working  power  of  an  engine,  and  (2)  that  speed 
includes  the  two  elements  of  time  and  space,  which,  with  the  third  ele- 


Fig.  97.— Indicating  the  Manner  ok  adapting  the  same  Boiler  Power  to  Passenger  or 

Freight  Service. 

ment,  weight  or  force,  make  up  the  three  which  are  necessary  for  the 
£xact  description  of  the  amount  of  any  kind  of  power,  we  may  express 


404 


CHAP.   XI.— THE  LOCOMOTIVE  ENGINE. 


graphically  the  variations  which  can  be  made  in  the  manner  of  utilizing 
or  distributing  the  power  of  an  engine  as  follows  (Fig.  97)  '• 

494.  On  a  pair  of  co-ordinate  axes  intersecting  at  O,  Fig.  97,  let  dis- 
tances on  the  vertical  axis  OA  represent  pounds  of  tractive  power,  and 
distances  on  the  horizontal  axis  OC  represent  the  compound  unit  speed, 
including  the  two  primary  units,  distance  and  time. 

Then  the  capacity  of  any  given  boiler,  which  is  measurable  only  by  a 
productof  the  three  units. /<^J.  x //.  x  //;;/^,  may  be  represented  on  such 
a  diagram  by  a  rectangle  of  a  given  fixed  area  (OABC,  OA'B'C, 
OA"B"C")  which  may  be  proportioned  in  any  ratio  of  height  to 
length  desired,  provided  the  total  area  included  within  it  be  not  exceeded. 
The  number  of  such  possible  rectangles,  as  will  be  apparent  from  the 
figure,  is  infinite. 

As  a  matter  of  mere  mathematical  curiosity,  of  no  immediate  practical 
moment,  it  may  be  noted  that  if  an  hyperbola  be  drawn  passing  through  the 
point  B,  with  the  axes  OA,  OC,  as  asymptotes,  any  point  B'  on  it  will  be  the 
apex  of  a  rectangle  of  always  equal  area. 

495.  Each  one  of  these  rectangles  will  represent  a  possible  locomotive;, 
each  different  from  the  other,  which  may  be  designed  to  fit  the  same 
boiler,— with  this  sole  limitation  :  The  tractive  power  in  pounds  of  ordi- 
nary forms  of  locomotives  is  a  limited  quantity,  which  cannot  be  indefi- 
nitely increased  ;  and  consequently  at  a  certain  point  on  the  diagram  A'' 
we  reach  a  vertical  limit,  beyond  which  it  is  not  possible,  by  any  ordinary 
device,  to  increase  the  tractive  power.     It  follows  directly  from  this  fact 
that  we  have  a  certain  minimum  of  speed  OC,  below  which  it  is  not  pos- 
sible to  decrease  the  speed  and  still  utilize  the  full  power  of  the  boiler  by 
increasing  the  load  hauled.     As  might  naturally  be  expected,  this  limita- 
tion is  at'times  very  inconvenient,  when  it  is  desired  to  obtain  the  maxi- 
mum hauling  capacity  regardless  of  speed,  as  in  engines  for  yard  service 
or  for  working  on  heavy  grades.     It  is.  in  fact,  practically,  the  most 
serious  theoretical  defect  of  the  locomotive.     Various  exceptional  de- 
vices are  employed  to  evade  it  in  part,  the  simplest  and  most  common  of 
which  is  to  carry  the  water  supply,  and  sometimes  the  fuel  also,  upon  the- 
drivin--'  wheel-base.     A  still  more  radical  remedy  is  mentioned  in  par. 
511.  and  yet  another  device  is  the  so-called  traction-increaser,  throw- 
inga  part  of  the  weight  of  the  tender  on  the  drivers- for  the  time  being  by- 
cylinders  attached  to  the  piston,  or  by  various  combinations  of  levers. 
Finally,  the  device  of  a  rack  between  the  rails,  or  of  a  central  rail  which 
the  driving  wheels  grip  by  spring  power  or  other  pressure,  enables  the- 
gravity  of  the  engine  to  be  wholly  dispensed  with  for  furnishing  the  trac- 


CHAP.   XL— THE  LOCOMOTIVE  ENGINE. 


405 


live  force,  by  substituting  for  it  frictional  adhesion,  and  thus  removes  all 
limit  whatever  to  the  load  that  a  given  boiler  can  move,  provided  the 
speed  be  made  slow  enough. 

496.  When  this  is  done,  all  limits  to  the  diagram  in  Fig.  97  are  like- 
wise removed  :  so  that  it  then  becomes  literally  true  that,  so  far  as  boiler- 
power  is  concerned,  there  is  no  limit  whatever  to  either  the  speed  of  a 
locomotive  or  to  the  load  it  can  haul,  provided  one  decreases  as  the 
other  increases;  but  since  the  load  to  be  hauled  can  in  no  case  be  de- 
creased below  the  weight  of  the  engine  itself,  a  limit  of  possible  speed  is 
soon  reached  as  well  as  of  tractive  force,  and  the  limit  of  expediency  in 
€ach  direction  is  much  narrower  than  that  of  possibility. 

A  very  interesting  and  instructive  study  of  the  differences  of  designs  in 
locomotives  and  of  the  causes  therefor,  which  the  writer  feels  compelled  to 
omit,  may  be  made  by  constructing  diagrams  similar  to  Fig.  89  for  various 
actual  locomotives;  laying  off  the  load  on  drivers  on  the  vertical  axis  ;  taking 
the  boiler  power  as  proportional  to  the  heating  surface,  and  adding  various  de- 
tails of  grate-area,  etc. 

497.  It  will  be  sufficiently  clear  from  what  has  preceded,  that  in  the 
practical  working  of  engines  a  deficiency  in  any  one  of  the  three  co-ordi- 
fiate  forces  which  when  combined  make  the  complete  machine  will  be 
shown  in  the  following  ways: 

1.  1/  adhesion  or  tractive  power  be  the  smallest  of  the  three,  the  en- 
gine will  slip  her  drivers. 

2.  If  boiler  power  be  the  smallest,  the  boiler  pressure  as  indicated  by 
the  steam-gauge  will  fall,  and  the  engine  will  from  this  fall  of  pressure 
be  unable  to  turn  the  wheels. 

3.  If  cylinder  or  engine  power  be  the  smallest,  the  engine  will  be  stalled 
while  utilizing  to  the  utmost  a  full  pressure  of  steam  and  while  yet  un- 
able to  slip  its  drivers. 

498.  The  last  is  either  an  evidence  that  the  engine  is  out  of  the  ser- 
vice for  which  it  was  designed, — as  for  instance  a  fast  passenger  engine 
hauling  freight  trains. — or  it  is  an  evidence  of  bad  design.  It  is  one  of 
the  most  discreditable  faults  an  engine  can  have,  for  the  reason  that  it 
is  an  entirely  unnecessary  sacrifice  of  a  portion  of  its  capacity  for  work, 
and  it  is,  naturally,  a  fault  of  rare  occurrence.  It  has  occurred  in  in- 
stances on  a  considerable  scale,  however,  as  an  eflect  of  cutting  down 
the  permitted  boiler  pressure  to  120  lbs.  after  copying  the  general  pro- 
portions of  engines  designed  to  carry  130  or  140  lbs.  The  effect  of  such 
action  on  the  pounds  of  tension  which  can  be  exerted  is  the  same,  and 


4o6 


CHAP.    XL— THE  LOCOMOTIVE  ENGINE, 


as  injurious,  as  if  the  boiler  power  itself  had  been  reduced,  which  latter, 
however,  does  not  at  all  follow  from  the  reduction  of  pressure  (par.  552). 

499.  The  indication  of  deficient  hauling  power  first  above  specified, 
slipping  of  drivers,  is  that  which  should  first  occur  in  all  well-designed 
freight  engines;  for,  since  hauling-power  and  not  speed  is  the  desidera- 
tum in  such  engines,  the  boiler-power,  however  small  (within  limits),  can 
be  made  to  exert  an  indefinitely  great  force  in  pounds  at  the  expense  of 
speed,  by  proper  design  of  the  engine;  which  can  hence  be  so  designed 
that  the  boiler  shall  be  able  to  exert  continuously  a  force  always  in  ex- 
cess of  the  tractive  power  when  at  its  maximum  (as  when  using  sand) 
by  a  little  at  least,  in  order  that  the  full  measure  of  the  latter  may  in  all 
cases  be  utilized. 

500.  This  theoretical  principle  is  limited  in  part  by  this  fact:  Convenient 
operation,  requires  that  it  should  not  be  100  easy  to  slip  the  drivers  under  ordi- 
nary conditions  but  should  require  nearly  a  full  head  of  steam  to  do  so,  or  the 
difficulty  of  throttling  the  pressure  just  right  (par.  527)  will  lead  to  too  frequent 
slipping.  Hence  it  is  desirable  that  the  cylinder  power  should  be  only  a  little 
in  excess  of  the  adhesion,  and  from  this  it  may  result  that  the  ultimate  maxi- 
mum of  adhesion,  when  using  sand  on  a  dry  rail  with  boiler  pressure  perhaps  a 
little  low.  cannot  be  advantageously  realized.  There  are  also  certain  disad- 
vantages in  an  over-large  cylinder,  from  greater  loss  by  radiation,  condensa- 
tion, etc.,  as  well  as  some  advantages.     See  also  foot  of  page  408. 

601.  But  it  is  probable  that  all  these  disadvantages  have  been  over-esti- 
mated,  or  the  whole  question  inadequately  considered,  in  designing  many  of 
the  engines  now  running,  a  considerable  minority  of  which  cannot  utilize  the 
full  ultimate  adhesion,  and  are  in  consequence  compelled  to  haul  smaller  loads 
than  they  otherwise  might ;  although  most  freight  engines  can  slip  their  drivers 
in  ordinary  working,  when  starting  or  running  very  slowly,  and  do  so  liberally. 
No  well-designed  engine  will  slip  its  drivers  when  running  at  speed,  unless  the 
rails  are  in  bad  order,  as  the  average  cylinder  pressure  is  then  much  lower  than 
in  starting  (i>ar.  594).  Over-frequent  slipping  of  drivers  is  an  evidence  of 
want  of  skill  or  care  in  the  engineman.  He  can  with  ease  slip  the  drivers  with 
the  lightest  train  or  with  no  train  at  all.  and  in  fact  must  use  care  not  to.  unless 
the  cylinders  are  too  small  for  the  engine,  because  only  an  infinite  force  can 
set  in  motion  the  lightest  body  instantly. 

502.  The  second  indication  of  deficient  hauling  capacity  above  speci- 
fied, deficiency  of  boiler  power,  is  the  only  one,  in  theory,  by  which  a 
passenger  engine  should  ever  fail ;  since  a  fraction  only  of  its  weight,  if 
on  the  drivers,  will  give  a  hauling  power  in  pounds  far  in  excess  of  the 
available /^^/-/^w«iy  of  boiler  power  at  a  high  speed  in  feet  per  minute. 
Neither  do  passenger  engines  often  fail,  in  fact,  for  any  other  cause,  be- 
tween stations,  on  moderate  grades.  The  necessity  of  starting  heavy  trains 


Vf 


CHAP.  XL— THE  LOCOMOTIVE  ENGINE. 


407 


quickly,  however,  and  of  maintaining  a  high  rate  of  speed  even  on  long, 
heavy  grades,  makes  the  demand  for  adhesion  on  passenger  engines  very 
unequal,  and  at  times  very  great,  so  that  it  is  often  in  practice  the  actual 
limiting  cause  which  it  is  desirable  to  increase.  It  is  not  essential  to  do 
this  permanently.  Any  device  which  increases  the  load  on  the  drivers 
temporarily,  especially  for  stopping  or  starting,  answers  every  purpose, 
and  a  better  purpose  in  fact  than  a  permanent  increase.  Such  attach- 
ments are  now  in  use  on  extra-fast  engines  and  to  a  limited  extent  on 
others,  and  it  is  probable  that  their  use,  or  that  of  some  equivalent,  might 
be  greatly  extended,  for  both  passenger  and  freight  engines,  without  any 
disadvantage  at  all  comparable  to  the  gain. 

503.  But  however  well  an  engine  may  have  been  designed  for  the 
average  contingencies  of  ordinary  service,  when  the  engine  is  once  in 
service  there  are  limitations  to  or  variations  in  the  efficiency  of  each  of 
its  three  primary  forces  which  have  an  important  effect  upon  the  load  it 
can  haul,  and  which  we  need  to  consider. 

In  the  following  Tables  127  to  137  are  given  a  variety  of  data  as  to 
the  dimensions,  weight,  cost,  and  life  of  locomotives  which  we  shall  have 
occasion  to  use  or  refer  to,  which  are  here  grouped  together  for  conven- 
ience of  reference. 

Table  127. 

Comparative  Dimensions  of  Engines  of  the  American  Type. 


Weight  on  drivers.. 

Weight  on  truck 

Weight,  total  (lbs.). 


Grate  surface 

i  Fire-box 
Tubes... 
Total... 
Barrel  of  boiler 

Diameter  of  drivers 


Tender : 


I  Total 
capacity -j  (3jj^,  (ibs.).... 

Wheel-base: 

DrivinsT 

Total  engine 

Tender 

Engine  and  tender 


17x24  Cylinders. 


Mason. 

1873. 


40.000 
22.000 
62,000 

sq.  ft. 
16.38 
105 
906 

lOII 

46" 
66" 


2,250 


8'o" 
22'  o" 


No. 
Pac. 

1884. 


54,350 
iq.450 
83,800 

sq.  ft. 
16. 
117 

I  I2l8 

»335 
51" 

62" 


27,900 

29^438 

57.338 

3,8oo 

6,105 

8'  6" 
23'  3H" 


45'  iH" 


Brooks. 

1884. 


48.000 
26,000 
74,000* 

sq.  ft. 
16.45 

£.990. 

1093. 

48" 

67" 


2,640 


S'o" 
22'  7" 


42'  6' 


C,  B. 

&0. 

1884. 


53,600 
27,600 

8l,200 

sq.  ft 
17.6 
q8. 
1 968. 
1066. 
49«" 
69" 


24,183 

37.467 

61,650 

2,750 

14.550 


8'  6" 
22'  6»4" 
14'  11" 
44'  9" 


18  X  24  Cylinders. 


C,  B. 

&Q. 

1884. 


54  500 
28,^00 
82,800 

sq.  ft. 
17.7 
102. 

1 958. 
1060. 

49^" 

69" 

65" 


J  69"  p. 

1 65"  n. 


24,183 

37.467 

61,650 

2.750 

M.550 


.8'  6" 
22'  tM" 


14 
44'  9 


II" 
// 


Mason. 
1884. 


68.000 

32,000 

100,000 

sq.  ft. 
18.9 

£1230. 

1375- 
54" 


68 


// 


3,600 


9'  o" 
23'  4" 


West  Shore. 


A. 


B. 


64,000 
32,000 
96,000 

sq.  ft. 

34- 

128. 

E1084. 

I2I2. I 
55" 

68" 


62,500 
32.000 
94.5a> 
sq.  ft. 

17- 
12&. 

E10841. 
i2ia 


34.000 

30.000 

64,000 

3.000 

10,000 

8'  6" 

22'  996" 

15'  8" 
47'  aW 


•  Weight,  empty,  66,000  lbs.,  leaving  8000  lbs.  for  contents  of  boiler  and  fire-box,  and  two  men. 


408 


CHAP,  XL— THE  LOCOMOTIVE  ENGINE. 


CHAP.  XL— THE  LOCOMOTIVE  ENGINE. 


409 


Table  128. 
Comparative  Dimensions  of  Mogul  and  Ten-wheel  Engines. 


Weight  on  drivers , 
Weight  on  truck.., 
Weight,  total  (lbs). 


Moguls. 


Baldwin 

18x24. 

1873. 


Grate  surface 

1  Fire-box. 
Heating  surface  \  Tubes. . . 

j  Total.... 

Barrel  of  boiler 

Diameter  of  drivers 


••••••« 


Tender  : 
«,...(  Empty. 

'*>*•      (Total 

^         ..    3  Water  (galls.) 
Capacity  j  Coal  (Ibi)  .... 

Wheel-basb  : 

Driving  

Total  engine 

Tender 

Engine  and  tender 


66,000 
11.000 
77,000 

sq.  ft. 

16. 

103. 

948. 

105  X. 
50" 
5^" 


Brooks 

18  X  24. 

1883. 


72^500 
13,500 
86,000* 

sq.  ft. 

17- 

114. 

1141. 

"55- 

53" 


B.  &0. 

19  X  34. 

1883. 


N.  S. 

Wales. 

(Baldwin) 

18x26 

1884. 


87,400 


60" 


3,300 


'5 
23' 


3,880 


15'  6" 

33'  o" 


79.000 
17,000 
96,000 

sq.  ff. 
»7 

I1066. 
J 189. 

55" 
60H" 

31.500 
41,200 
72.700 
3,600 
10,000 

15'  o" 
33'  2" 
14'  6" 

46'    2Vi" 


Ten-whekl. 


Baldwin 

18x26. 
1873. 


58,000 
20,000 
78,000 

sq.  ft. 
M-4 
94- 

1014. 

1108. 
50" 
54" 


3,300 


Brooks 

19x34. 

1883. 


73,100 
21,400 
94i5oot 

sq.'ft. 

23.6 

128.4 
1422.4 
1550.8 

52" 

5594" 


3,880 


13 


2S'  6" 


14'  o" 
«5'3" 

■45' 7'' 


•  Weight,  empty,  78,000  lbs.,  leaving  8000  lbs.  for  contents  of  boiler  and  fire-box. 
t  Weight,  empty,  84,300  lbs.,  leaving  10,200  lbs.  for  contents  of  boiler  and  fire-box. 

The  Baltimore  &  Ohio  Mogul  carries  140  lbs.  of  boiler  pressure,  affording  a  maximum 
average  cylinder  pressure  of  some  119  lbs.  (85  per  cent  of  boiler  pressure).  At  this  rate 
the  cylinder  tractive  force  is  17,184  lbs.,  or  about  \  weight  on  drivers.  In  most  American 
engines  it  is  about  J,  and  in  some  as  low  as  0.30. 

The  tendency  in  recent  years  has  been  strongly  toward  increase  of 
wei^'ht  and  boiler  power  with  the  same-sized  cylinders,  as  Tables  127  to 
I30^and  Table  142  bring  out  very  clearly.  Three  concurrent  causes  have 
brought  this  about:  (i)  The  material  increa.se  in  steam  pressure,  which 
makes  a  smaller  cylinder  do  much  more  work  ;  (2)  the  higher  average 
speed  of  trains,  which  necessitates  larger  boiler  power  to  maintain  it ;  and 
(3)  the  fact  that  the  more  perfect  track  has  justified  and  the  lower  rates 
required  loading  engines  up  to  the  last  limit  of  their  tractive  power,  and 
it  was  necessary  to  have  as  much  as  possible  under  all  conditions  of  rail 
and  weather. 


Table  129. 

Comparative  Dimensions  of  the  Original  and  Present  Standard  Con- 
solidation Locomotive  of  the  Pennsylvania  Railroad,  and  of  the 
West  Shore  Standard  Consolidation. 


Class  I. 
1876. 


Size  of  cylinders 

Weight  on  drivers 

"    truck  

Total  wheel  base 

Driving-wheel  base 

Diameter  of  drivers 

Working  pressure 

Boiler: 
Inside  diam.  smallest  boiler-ring... 

•'T  u.„  S  No.  and  size  (outside) 

TubcsJLengih 

i  Length 

Fire-box^  Width 

(Depth 

•Grate  surface 

{Fire-box 
Tubes 
Total 

Smallest  inside  diameter  chimney. . 
Height  top  of  rails  to  top  of  chimney 

Tender  : 

1  Empty 

'Weights  Load 

(Total 

capacuy]S";.  .■.•.•.•.;•.•.•.•.■.•.:;: 

Wheel-base 


Engine  and  Tender 

Total  wheel-base 

Length  over  all 


20  X  24" 

79,400  lbs. 

12,240  lbs. 

21'  6" 

13'  8" 

50" 
125  lbs. 

53%" 

12'  11" 
96" 

34^'' 
42  to  61" 
23  sq.  ft. 
92  "  " 
E  1,166  "  " 
1,258  "  " 
20" 
14'  11" 


22.770  lbs. 
3-^.000    " 
55,770    '• 
3.000  galls. 
8,000  lbs. 
15'  4" 


47'  7" 
56'  9%" 


Class  R. 

1886. 


Increase. 


20  X  24' 
100,600  lbs. 
14.025 


(1 


21' 


// 


9 
10 
ji 


13' 

SO- 
140  lbs. 


59" 

183,  2^" 

13'  ^W 
107" 

42" 

57  to  591^" 

31.2  sq.  ft. 

167  "   " 

E  1,564  "  " 

1,731  "  " 
18" 
15'  o" 


23,800  lbs. 
33.000    " 
56.800    " 
3.000  galls. 
8,000  lbs. 
15'  4" 

48'  9" 

58'  M' 


None. 
27      p.  C. 
14.6    " 

^" 

2" 

None. 
12  p.  c. 

10.5  p.  c. 

32.6  " 

11.5  p.  c. 
21.8    " 

35.6  p.  c. 

8I.S  " 


4-5  P-  C. 

None. 
1.8  p.  c. 

None. 


I'  2" 

2'  iW 


West  Shore. 

1883. 


-.1' 


20  X  24" 
88,000  lbs. 
16.000    " 

21'  7" 

14'  o' 
50'' 
140  lbs.  (?) 


55" 
169,  2^" 

13'  4%" 
95%" 
34H" 

23  sq.  ft. 
120  "  " 
E  1,340  "  " 
1,460  "  " 

29,000  lbs. 
35,000  '* 
64.000  " 
3,000  galls. 
10,000  lbs. 
15'  8" 


47'  7" 
56'  8>^" 


The  following;  are  some  further  details  in  respect  to  the  changes  in  the  latest  Pennsyl- 
vania Consolidation  from  the  earlier  design  : 

Cylinders. — Unchanged:  diameter  of  piston-rod,  size  of  ports,  travel  and  outside 
'lap  of  valves,  size  of  slide-blocks.  Piston-head,  i  in.  thicker ;  cylinders,  2  in,  farther 
apart  (7  ft.  2  in.)  ;  inside  lap.  none  (in  place  of  ^  in.)  ;  lead,  ^  for  \  in.;  steam-pipe,  19.6 
for  18  sq.  in.;  each  blast-nozzle,  13.8  for  11. 2  sq.  in. 

Journal.— All  increased  materially.  Driving-axles,  from  6i  x  7J  to  7x8!;  truck- 
.axles,  from  4J  X  71'^  to  5  X  8  •  ;  crank-pin,  from  4^  and  5  to  5  and  6  in.  Coupling-rod 
and  journals  unchanged.,  3J  in. 

Boiler.— C/nchanged :  material  (steel ;  wrought-iron  tubes),  distance  between  centres 
•of  tubes  (3i  in.);  thickness  fire-box  platefe  Q  in.  outside  ;  /,  in.  inside),  tube-plates  (i  in.). 
Barrel-plates,  i  and  »  in.  for  g  in.;  butt-joints,  welted  inside,  for  lap.  Water  grate  for 
■shaking  grate. 

Tehder.— Unchanged :  tank,  19  ft.  x  43  in.  high. 

The  West  Shore  Consolidation  was  designed  by  the  late  Howard  Fry,  one  of  the  most 
-eminent  of  American  mechanical  engineers,  and  was  designed  to  include  all  the  latest 
improvements  up  to  its  date. 


!    I 


4IO 


CHAP,  XL— THE  LOCOMOTIVE  ENGINE. 


CHAP,  XL— THE  LOCOMOTIVE  ENGINE, 


41  r 


Table  130. 

Comparative  Dimensions   of  Engines  more   Powerful  than  the  Con- 

soLiDATiON  Type. 


Size  of  cylinders 

Weight  on  drivers  . . 
"  truck  ... 
Total  wheel-base  . . . 
Driving  wheel-base. 
Diameter  of  drivers. 
Working  pressure . . 


Mastodon  Type. 
(8  drivers  ;  4  truck-wheels.) 


Central 
Pacific. 


BOILEK  : 

Inside  diam.  smallest  boiler-ring. 
T  K-.  3  No.  and  size  (outside). . . . 
Tubes^Lengih 

4  Length 

Fire-box K  Width 

(Depth 

Grate  surface. 


1  Fire-box . . 

"A 


Heating  surfaced  Tubes 

I  Total 

Smallest  inside  diameter  chimney. . 
Height  top  of  rails  to  top  of  chimney 

Tender : 

(  Empty  . 
Weights  Load... 

( Total  . . 
-,        .,    j  Water 
Capacity-!  Coal.. 
Wheel-base 


Engine  and  Tbndkr  ; 

Total  wheel-base 

Length  over  all 


19  X  30'' 
106,050  lbs. 
16.050   '* 

15'  9f 
54" 
135  lbs. 


54" 

166,  M' 

12' 

39>6  t?58U" 
25.74  sq.  ft. 
182  "   " 
I   1,076  "   " 

X.258 ;;  " 
20" 

15'  6^" 

26,000  lbs. 

37.000    I' 
63,000    " 
3,000  galls. 
i2,ooo  lbs. 
15'  o94" 

53' »«" 

64'  o^' 


Lehigh 
Valley. 


20  X  26" 

83,432  lbs. 

19.264    '* 

23'  a" 

13^^  o%" 

125  lbs. 

51" 
199,  2" 

11'  6'^ 
34" 
43^t0  52>^" 
32  sq.  ft. 
179  "   " 

1 995  •; :; 

17" 
14'  7" 


23,400  lbs. 

S3.8i8    " 
2,575  palls. 
8,960  lbs. 


46'  9" 
55'  4" 


"  El  Guber- 

nador" 

(Cent.  Pac). 

(10  drivers; 

4  truck-wh'ls) 


21  X  36" 
121,600  lbs 
32.400    ** 
28'  11" 

19'  7" 
57" 
140  lbs 


Decapod 

(Baldwin). 

(10  drivers; 

2  truck-wh'lsV 


22  X  26" 

128,000  lbs. 

16,000    " 

24'  4" 


(?) 


56%'' 

178. 2H" 

12'  o'' 


»7 


o" 
45" 


50,650  lbs. 
35,000    '' 
85,650    " 
3,000  galls. 
10,000  lbs. 


64'' 
268.2" 
12'  gW' 
10'  i^' 

39^" 


65'  5' 


80,000  lbs. 
3,500  galls. 


These  four  engines  are  as  yet  the  most  powerful  in  the  world.     A  Fairlie  engine 
weighing  about  85  gross  tons  and  having  two  six-wheel  driving-trucks,  each  with  17X23 
cylinders,  with  a  Bissell  (pony)  truck  at  each  end,  is  running  on  the  Iquique  Railway, 
in  Peru.     Other  heavy*locomotives  are  given  in  Table  137. 

The  Central  Pacific  Mastodon  (the  original  of  the  type)  has  hauled  20  loaded  cars, 
weighing  422  tons,  up  a  long  grade  of  116  ft.  per  mile.  By  Table  170  it  should  haul  421 
tons  At  8  miles  per  hour  it  is  reported  to  have  shown  an  average  pressure  of  124  lbs. 
per  square  inch  in  the  cylinders.  "  El  Gubemador,"  cutting  off  at  five-sixths  stroke,  at  a 
speed  of  6%  miles  per  hour,  showed  an  average  of  115  lbs.  with  130  lbs.  boiler  pressure, 
or  88  per  cent,  which  is  much  nearer  to  boiler  pressure  than  is  often  possible,  and  de- 
velops the  enormous  tractive  power  of  32,039  lbs.,  or  just  39  lbs.  more  than  one  fourth 
th«  weight  on  drivers.  As  this  is  about  the  very  utmost  the  cylinders  can  do,  it  indicates 
that  the  cylinders,  large  as  they  are,  might  with  advantage  be  larger,  or  the  boiler  pres- 
sure  higher. 


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CHAP.  XI. —  THE  LOCOMOTIVE  ENGINE. 


Table  133. 

Weights  in  Detail  of  an  Old  Illinois  Central    Passenger    Engine, 

i6  X  22  Cylinders. 

[Abstracted  from  a  record  taken  by  Mr.  M.  N.  Forney.] 


Boiler  sheets,  rivets  and  stay-bolts 

Braces,  crown-bars,  etc   

Tubes  and  copper  thimbles  .... 
Rin^fordry-pipe,furn'e-door,eic 

Dome  

Dry-pipes 

Throitle-valve.  etc       

Steam  and  exhaust  pipes 

Petticoat-pipe   

Blower 

Sm<  >ke-box  door  

Smokestack 

•Grate     

Ash-pan 


Weights — Lbs. 


Brass. 


Total  Boiler 


Prames 

Boiler-braces 
Bed-casting  . 


Total  Frames 


■Cylinders 

Sie;im-chest  

Valves 

Pistons 

Cross-liead  guides.... 

Connecting-rods  

Crank-pins     

Driviny-wheel  boxes. 

Valve-ge.ir 

Reverse-lever  

Pumt)S     

Purap-check  valvfS. . . 


Total  Machinery. 


Drivinjj-wherl  centres..  . 

••      tires 

*•     axles  

Truck-wheels 

"      axles  

"      frames,  boxes,  etc 

"      check-chains 

Driver  sprin'.,'s.  steel 

*•      attMchments 

Truck  springs  


Total  Running  Gear. 


40 
75 
38 

13 
10 


16 
9 


301 


no 

36 
18 


13 

117 


113 


3 
436 

39 


883 


7« 


Wrought 
Iron. 


6,299 
1,635 

3»034 
90 

24 
\o-\ 
no 

II 

52 

38 

45 
452 
>75 
314 


12,382 


3.553 

628 

29 


4,309 


6S 

80 

83 

137 

681 

609 

166 

6 

740 

231 

253 
13 


3.04a 


3.360 

«.033 

"60; 

z,i8i 
131 
416 
506 
337 


7.568 


Cast 
Iron. 


»7 
84s 

93 
193 
377 


336 
300 

1.333 


3.394 


913 


913 


2.795 
805 
133 
363 
340 
42 

430 
984 
»9 
163 
100 


5.972 


5.324 

107 
1.884 

1,058 


8.373 


Wood,  etc. 


13 


13 


136 


136 


640 


10 


650 


Total. 


6,399 

1.635 

3.034 

147 

944 

346 

3x6 

398 

52 

54 

390 

652 

1,508 

3M 


15.989 


3,552 
638 

941 


5.i2» 


3,106 
921 
333 

389 
933 
768 
166 
548 

',724 
343 
853 
I5» 


10,033 


5,964 
3.360 
1,140 

1,884 
604 

2,3" 
»3J 
416 

5t6 

337 


16,663 


CHAP.  XL— THE  LOCOMOTIVE  ENGINE. 


Table  \ZZ,— Continued. 


Safety-valve 

Steam  gauges  and  cocks. ... 
Cylinder  cocks  and  fittings. 

Injector 

Sand-box 

Bell  and  clapper  \\'. 

"    stand \\ 

Hand-rail '!.''.'.'. 

Running-board '.'.'.'.'.'.. 

Wheel-covers 

Cab  and  foot-board    ... 

Pilot ;;: 

Head-light  bracket ....  .',*.'.' ,' 
Lagging  and  sundries 


Total  Fittings. 


Tender  tank  

Fittings  for  ditto .'....!.. 

Frame  '''' 

Truck-wheels '.'.'.'.'.'.. 

Axles  and  collars !.'!."!!." 

Axle-boxes '*,",'.' 

Bearings  and  fittings  for  ditto. 

Springs 

Trucks  and  other  parts 

Brakes 


Total  Tender 


Boiler. 

Frame 

Machinery  ... 
Running  gear. 
Fittings 


Total  Engine 

Tender 

Total  Engine  and  Tender. . . , 


■ 


Weights — Lhs. 


Brass. 


53 
73 
10 
66 

45 
80 
68 

63 
60 

139 

4 


Wrought 
Iron. 


15 
114 


26 
26 

57 
21 

144 

9 

10 

44 

lOI 

337 

565 

757 

II 

329 


790 


»9 


2.437 


64 


83 


3,515 

37 
1,124 

1,272 

29 

880 

1.330 

143 


8.330 


Summary. 


201 


882 

72 

790 


1.945 


83 


2,028 


12,382 
4.209 
3.042 
7.568 
2.437 


29,638 


8,330 


37.968 


Cast 
Iron. 


13 

50 
283 


52 


120 

446 

77 

68 


r,ii5 


103 

722 

3.952 

536 
32 

1,596 
46 


6,987 


3,394 
912 

5,972 

8.373 
1,115 


19,766 


6,987 


26,753 


Wood,  etc. 


334 


1,083 
320 

49 

874 


2,660 


3 
2,327 


12 


670 
106 


3."8 


12 


136 

650 

2,660 


3.458 


3."8 


6,576 


415 


Total. 


86 

99 

79 

»37 

472 

89 
130 
107 

495 

596 

2,098 

1. 154 
143 

1.317 


7.002 


3,515 
163 

4.173 

3»952 

1,272 

536 

880 

3-596 

295 


18,518 


15.089 

5. 121 

10,032 

16,663 

7.002 


54-807 


18.518 


73.325 


"^^  "*  hoLl*  fi'lJ'K  *'^'*^'!,'  ^°''  "^^'^^^  °^  *^"^'"«  '°  working  order,  for  contents  of 
boiler,  fire-box,  and  two  men  in  cab,  about  contents  oi 

And  for  contents  of  tender,  coal ; ,:  •  • 

water  (x6oogaiis.)::.::::::::::::::::;:::;;::  n^^^' 

Giving  for  total  weight  of  engine  in  service ~  ^    „ 

And  lor  total  weight  of  tender 60,807 

40.018 

Approximate  total  engine  and  tender  in  service  Zs — 

100,835 


6,000 


21,500 


No.  0/  separate  pieces,  large  and  small  (not 
including  nails) 


)In  engine. 
In  tender. 
Tnfal 


.      .  4.904 

tender 1,366 

Total 0,270 


The  proportion  0/ brass  is  now,  in  general  practice,  much  less  than 


in  the  above  engine. 


4i6 


CHAP.  XI.— THE  LOCOMOTIVE  ENGINE. 


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CHAP.  XL— THE  LOCOMOTIVE  ENGINE. 


Table  135. 

Length  of  Service,  Mileage,  and  Life  of  Locomotives  on  Pennsylvania 

Railroad  (P.  R.  R.  Division)  to  January  i,  1885. 

Passenger  Locomotives. 


5 

O  •  •  •  •  < 

7 

8 

9 

10 

XI.... 
12 

13...- 
14.... 

15 

x6. . . . 
17. ... 
18.... 
19.... 
20.... 

21 

22 


Number  of  Locomotives. 

Total  Mileage  (i  =  looo  miles). 

Average 

Miles  per 

Loco,  per 

Year. 

Years 

IN 

Service. 

Total. 

In  Ser- 
vice. 

Con- 
demned. 

Highest. 

Lowest. 

Average 
per  Loco. 

8 

9 

10 

II 

12 

13 

14 

15 

16 

17 

18 

2 

7 
3 
8 

6 

3 
II 

7 
9 
5 
4 

2 

7 

I 

7 
3 
I 

9 

7 
8 

4 
3 

0 
0 
2 

I 

3 
2 

2 
0 
I 

I 
I 

382 

345 
294 
389 
563 
428 

613 

589 
780 

688 
637 

344 
248 
264 
247 
307 

319 

286 

397 
351 
431 

488 

247 

363 
302 

282 
316 

391 
369 
401 

483 
491 

536 

559 

45.372 
33  566 
28.165 
28.702 

32.573 
28.349 

28.657 
32.204 
30,689 

31  519 
31.067 

13 

65 

52 

13 

780 

412 

31,707 

Freight  Locomotives. 


I3i. 


33 
23 
10 

13 

27 

15 
12 

43 
44 
36 
26 
21 
16 

17 
2 

4 
3 
4 

349 


33 
23 
10 

13 
24 

II 
7 

29 

32 

15 

14 

12 

8 

12 

O 

I 

I 

o 


245 


o 
o 
o 
o 
3 
4 
5 

14 
12 
21 
12 

9 

8 

5 

2 

3 
2 

4 


197 
220 

279 
289 

314 

317 
416 

454 
440 

426 

561 

532 

485 

430 
400 

519 
464 
431 


104 


561 


130 

147 
192 
240 
225 
201 
202 
206 

235 
244 
271 
271 
324 
308 

351 
378 
354 
387 


161 
176 
250 
262 

273 
260 

287 
302 
318 
339 
378 
392 
397 
371 
375 
438 

393 
411 


130 


32.263 

29.391 
35-705 
32.715 
30,349 
25  973 
26.063 
25.172 

24.425 
24.215 
25.204 

24  529 
23  337 
20  620 

19-758 
21.905 

18.733 
18.684 


301 


22.331 


The  above  locomotives  were  intended  to  give  a  fair  average  of  engines  of  aU  ages  and 
cl  Jes  of  service,  and  cover  about  60  per  cent  of  the  whole  number  m  service  The  loc(> 
J^Xves  haTng  the  highest  mileage  (780,18.  miles,  passenger;   561,139  -^les,   fr-ght) 


CHAP.  XL— THE  LOCOMOTIVE  ENGINE. 


419 


were  both  still  running  and  in  good  order.     In  the  original  abstract  the  miles  run  were 
given  to  units,  but  have  been  abbreviated  to  the  nearest  thousand 

Running  of  engines  first  in  first  out  was  first  introduced  in  1878,  six  years  before  date 
^f  table  and  abnormally  increases  the  average  mileage  of  the  younger  engine7  dative ly 
with  a^      •     ^"'"""  '"  ^'^^'  ^'^^^  ^^  ""^^  ^^'^-^  ^'  ^---^n  of  Uly  itagl 

Special   Performances.-^«^«,  273,  479,248  miles  in   ten  years-    $81,642  for 
repairs,  or  X.74  cents  per  mile  run;  .51,552  miles  before  being  off  its  wheels  fSgenerl 
repairs.     Engine.,,    504,30:  miles  in  ten  years  ;  $6534.45  for'repairs.  "  ^n  s IL 

Tent  ""^'  '"''"'  "  ""'^^  ^^"^  "^  ^^^  "^^^^'  --P^  --  -  the  result  of  an  ac^i 

dent.     Engtne  1047,  41,510  miles  in  three  months,  or  461  miles  per  day. 


Average  mileage  of  72  passsenger  engines,  1882,   . 
175  freight  engines,  1882, 


Highest.      Lowest.  Average 
79,258        30,039        45,936 
50,711         30,000        36,584 


.vlvt^"p^.°'  ?r  ^'  ''"'  °^  '"^^  >^^^^^Z^  of  the  working  parts  of  engine^  on  the  Penn- 
sylvania Railroad  occur  immediately  on  starting  from  a  stop 

A  paper  before  the  German  Society  of  Mechanical  Engineers  showed  that  out  of  ,g 
engines  (presumably  a  fair  average)—  "^^ 

10  of  shortest  life  were  broken  up  after 

10  of  longest  life  were  broken  up  after 

15  were  in  use  less  than  20  years,  and  average  of  all  'was 


.    6.5  years. 
.  28.5     " 


The  average  mileage  of  German  locomotives  (Table  69)  is  11,870  mUes  per  year  indi- 
•eating  a  very  short  locomotive  life  in  miles. 


Table  136, 
Approximate  Life  of  Various  Parts  of  the 


Locomotive. 


Part. 


I^ocomotives  as  a  whole,  American 

"        "       English  (and  Eu. 
rope  generally) 

Tenders,  T2in]a 

**        Frames,  wood 


Authority. 


Life  in 
Years. 


Life  in 
Miles. 


•  «•••  •••■ 


Boilers,  as  a  whole  {ejc  partial  renewals) 
**  English  (prob.  an  av.  of  all  parts) 
"  U.  S.  "  "  ••  •♦ 
••  "    (bad  water) , 


Fire-box   steel,     bituminous   coal     fuel 
(wood,  two  thirds  greater) 

Firebox  steel,   anthracite  coal  (iron    or 
copper  fire-box,  about  one  third  only).. 

Firebox    steel   {anthracite    fuel,     50,000 
miles  less,  passenger) 

Fire-hox   steel   (anthracite    fuel,    50,000 
miles  less,  freight) 


M.  M.,  L.  S.  &M.  S.  Ry 

}r.  P.Williams 

L.  S.  &M.  S.  Reports.... 
M.  M.  Association..  ..... 

L.  S.  &  M.  S.  Reports. . . . 

McDonnell,  M.  Inst.  C.E. 

M.  M.,  L.  S.  &M.  S 

Various  sources 


22  to  24 

30 

zo 
7 


10  to  14 


M.  M.,  L.  S.  &M.  S 

M,  M.,  Ph.  &  Reading... 

M.  M.  Association 

M.  M.  Association 


xo-f- 
8  + 


700,000 

450,000 
to  500,000 

800,000 

250,000 

800,000 

to  1,000,000 

320,000 
to  350,000 

450,000 

300.000 
to  350,000 

z8o,ooo 

z  20,000 

300,000 

250,000 


CHAP.  XL— THE  LOCOMOTIVE  ENGINE, 


CHAP.  XL—LOCOMOTIVE  RUNNING  GEAR. 


421 


420  ^ 

Bad  water  estimated  to  reduce  these  last  averages  about  ^-.000  mU^.  -^  increasecost 
of  maintenance  $750  per  year,  or  .*  to  3  cents  per  mUe  7' ^/^f^^^^^^^,^^ J'^^  !; 

^l  r/Txc  J^lTpel  ;ea;  o^  Lds^Uh  L  water.  Z  thence  down  to  none  with 
after  deposit  of  scale.    Nearly  aU  fractures  (about  seven  eighths)  are  m  side  sheets,  vertic    , 

^"S:"lT^^--Good  water.   England,  every  three  weeUs       ^^^^^^^ 
abo^one  month,  but  much  oftener  with  bad  water      T^^c^ness  o/sU.i,  almost  univers 
ally  :  tube-sheet.  /,  to  i";  sides,  back,  and  crown,  ft  ;  barrel,  ,  . 

Mileage  Life. 

j  74.000 

I  to   i6i,ooo 

j  120,000 

\  to  167.000 

360,000 


Fireboxes  coPJer.—Gt.  No.  and  L.,  S. C. 
&  D.  Rys.,  English  (pass,  and  freight).. 

Tubes,  iron,  various  English  railways. . . . 

"  •'       entirely  new  sets 


McDonnell 

McDonnell 

,oyrs.,L.S.& M.S.  Reps 


Years. 

6  to  7 
«5 


more 


'      ordinarily  taken  for  entirely  new  sets  at  half  ^^^1;^^:^^^^^^ 
piecings  at  end  in  addition,  and  removal  o^^^^  J_^  ^^ 

rovrn:;b^oiSVtor^^^^^^^ 

7ubes  not  essentially  different ;  require  cleaning  less  frequently. 

.-Average  of  English  returns,  passenger,  fair  ^^^^  }^'J]^^\ 


Tabes,  *rrt«.     ,    ,.      ,   ,  

about  one  hall  only) J 

Maximum  reported  (McDonnell,  average  of  10  years) \ 

•.      T    c   A^  vr   c:  anrt  T     M  &  I.  (max.  before  removal).. 
Axles,  iron  (.drivers). -\^.  S.  &  M.  S.  and  J ..  M.  a  1.  vi«*  , 

♦»  "     (crtfw^).— English ' 


,000. 


4t         »*     truck.— L.  S.  &  M.  S 

n«Arinss  (^r/T'*rj).— Various  railways,  per  A"  wear 

CesTr^o-,  D  ,  L.  &  W.,  8..oco  ;  lowest,  Philadelphia  &  Reading,  X4 
Tlrls  .1/  -5'  6"  average  of  U.  S. ;  65,000  per  turning  ;  3  turnings 

in  h;aTyserv^ce,  with  small  drivers,  near  a^^^^^^^^ 

English  reports  very  nearly  the  same,  viz. -j  ^/ g,. -j 

l>riving-wheel  centres.-L.  S.  &  M.  S.  Reports 

Cylinder8.-Same  as  engine.  .    „    ^  . 

Frame.-"  A  question  of  accident"  (M.  M.  Assoc.). 

*  ra™*'*       "^^  ^*  TT  Q    oR"  to  10"  wheels).    M.  M.,  Ph.  &  Kdg. 

Truck-wbeel8.-(About  av.  of  U.  S..  28    to  30    wncc«; 

Teiider-wheel..-( About  average  of  U.  S.,  33"  wheels). 

vITves'-^ommon  slide-valve  between  facings  (M.  M.  Assoc.) 

"        -Good  balanced,  several  patterns,  between  facings  (M.  M.  Ass'n).... 
scrap  value,  old  English  l-omotives  (copper  fire-bo.,  brass  tubes),  about 
p.  c.  of  original  cost  of  materials. 


Mileage 
Life. 
200,000 
290, ooo- 
to   437i000 

300.000- 

150.000- 

to   225,000 

100,000 

30.000 
56,000 


to 


aoo.ooo 
100,000 

196,600 

106,000 

to   150.000 

z,ooo,ooo 


34.O0O 

50.0004- 
30,000 

75.000 
to  100,000 


10 


The  locomotives 
18  to  ao  months. 


of  the  Pennsylvania  Railroad  go  into  shop  for  general  repairs  once  in. 


Table  137. 
Miscellaneous   Extra   Heavy  Locomotives. 

(A  list  published  in  the  National  Car- Builder.) 


Road. 


Kind. 


Reading 

Pennsylvania 

Baldwin  Loc.  W'ks. 
Boston  &  Albany. . . 
Pennsylvania 


Passenger  Locomotives. 
Fast  express. 


Class  K. . 


Tank  locomotive. 


Reading 


A.,  T.  &  Santa  F^ 
Central  Pacific 


Freight  Locomotive. 

Consolidation 

Twelve  wheels  coupled 

Consolidation,  tank 

Mogul,  tank 


Weight. 


Total. 


96,200  lbs. 

92,700  " 

85,000  " 

80,000  " 

§  120,400  " 

102,000  " 

101,000  " 

X  115,000  •• 


On  Drivers. 


*  64,250  lbs. 

*  65,300    " 

1 35  to  45,000  lbs, 
1 56,000  lbs. 


88,500  lbs. 
101,000  '* 
X  100,000  " 
88,000   " 


Driv- 
ers. 


68  in. 

78  " 

78  •' 

66  " 

60  " 

50  " 

46  " 

48  " 

48  " 


Cylin- 
ders. 


21 X  22  in. 
18  X  24  " 

18x24  " 
18x22  " 

17x24  " 


20  X  24 
20  X  26  '* 
17  X  24  " 

16X24    " 


*  On  four  wheels.       t  On  two  wheels.       X  Estimated.    §  Reported  weight. 

THE  RUNNING  GEAR. 

504.  The  distinctive  peculiarities  of  the  running  gear  of  American 
locomotives,  as  compared  with  foreign,  are  two:  the  swivelling  TRUCK 
in  front  (in  England  called  "  bogie"),  and  the  equalizing  levers  by 
-which  the  load  is  kept  uniformly  distributed  on  the  four  or  more  drivers, 
and  the  effect  of  any  chance  irregularities  in  the  track  reduced  to  a 
minimum.  The  first  was  invented  by  John  B.  Jervis  in  1834,  before  the 
trial  of  the  Rocket  had  taken  place ;  the  second  was  invented  by  Ross  M. 
Winans,  who  also  invented  the  double-truck  railway  car  which  has  be- 
come all  but  universal  in  this  country,  only  a  few  years  later.|| 

605.  Both  of  these  inventions,  with  much  else  that  was  novel  and 
meritorious,  had  their  origin  in  the  necessities  of  the  earlier  years  of 
American  railways,  which  required  that  the  locomotives  should  be 
adapted  to  ready  passage  over  sharp  curves  and  imperfectly  surfaced 
track  and  road-bed.     Both  of  them  are  now  gradually  making  their  way 

\  A  crude  form  of  double-truck  car  was  shown  to  have  been  used  in  Quincy, 
Mass.,  before  Winans  invented  it,  so  that  Winans  was  unable  to  support  his 
claim  for  patent;  but  he  reinvented  it  independently,  and  really  deserves  the 
credit  for  conceiving  of  and  introducing  it  as  the  normal  type  of  car. 


m 


422 


CHAP.  XL— LOCOMOTIVE  RUNNING  GEAR. 


CHAP.  XL— LOCOMOTIVE  RUNNLNG  GEAR. 


423 


into  England  and  throughout  the  world  ;  and  both  of  them,  beyond 
doubt,  will  eventually  become  universal,  since  they  are  almost  equally 
advantageous  on  good  roads  and  on  poor  roads,  the  only  difference  being 
that  on  poor  track  they  are  absolutely  indispensable,  while  on  good  track 
they  are  not  indispensable,  but  merely  advantageous.  In  great  part,  we 
owe  to  them  two  advantages  which  experience  appears  to  indicate  that 
the  American  locomotive  possesses:  It  can  (at  least  it  unquestionably 
does)  haul  greater  loads  in  proportion  to  weight  on  drivers,  and  it  is  less 
readily  disorganized,  so  that  it  can  run  in  practice  (at  least  it  does)  a 
great  many  more  miles  in  a  day  and  a  year  (see  Tables  68,  69). 

The  extent  of  this  advantage  should  not  be  exaggerated.  It  does  not 
clearly  appear  that  on  first-class  track  (on  which  alone  English  locomo- 
tives can  be  run  at  all  to  any  advantage)  the  cost  of  locomotive  repairs 
per  mile  run  is  noticeably  different  for  either  type,  although  the  cost  per 
ton  hauled  is  enormously  in  favor  of  American  engines.  Nevertheless  it 
still  remains  true,  that  wherever  American  locomotives  have  fairly  come 
in  competition  with  those  without  their  distinctive  features,  as  in  Canada. 
Mexico,  South  America,  and  the  Australasian  colonies  (in  nearly  all  of 
which  the  right  of  decision  has  rested  in  English  officials),  they  have  in- 
variably obtained  the  preference,  with  exceptions  that  prove  the  rule. 

506.  The  original  type  of  American  locomotive,  still  distinctively 
known  as  the  "American"  type,  has  two  drivers  coupled,  spaced  8  ft.  to  8 
ft.  6  in.  apart  so  as  to  include  the  fire-box  between  them,  with  a  four-whee) 
truck  in  front.  Until  about  twenty  years  ago  this  type  was  all  but  uni- 
versal in  both  passenger  and  freight  service,  but  the  name  is  now  rapidly 
losing  its  appropriateness.* 

507.  At  the  present  time  there  are  the  following  types  in  common  use 

in  America. 

1.  American  (Table  127).  4  drivers.  4  truck  wheels ;  still  approved 
for  light  service,  but  passing  out  of  use  for  ordinary  freight  and  heavy 

passenger  service. 

2.  Mogul  (Table  128),  6  drivers.  2  truck  wheels  (pony  truck) ;  one  of 

*  Complete  illustrations  of  every  detail  of  the  ordinary  form  of  "  American" 
engine,  with  outline  drawings  of  others,  may  be  found  in  the  "Catechism  of 
the  Locomotive,"  by  M.  N.  Forney,  and  drawings  and  descriptions  of  many 
examples  of  all  the  types  of  locomotives  here  named  in  "  Recent  Locomotives  ' 
both  published  by  the  Railroad  Gazette  of  New  York.  The  catalogues  of  the 
Baldwin  and  the  Rogers  Locomotive  Works  also  contain  views  and  many  of 
the  details  of  all  ordinary  types  of  locomotives,  with  much  other  interesting 
matter      All  the  above  works  are  valuable  ones  for  the  engineer  to  own. 


the  earliest  modifications  of  the  "  American"  locomotive  and  largely  used, 
but  in  rather  less  favor  than  formerly. 

3.  Ten-wheel  (Table  128),  6  drivers,  4  truck  wheels;  generally  pre- 
ferred to  the  Mogul,  and  at  one  time  bidding  fair  to  become  the  standard 
type  for  heavy  freight  service,  but  now  hardly  tending  to  multiply,  except 
as  a  substitute  for  the  American  for  heavy  passenger  service. 

4.  Consolidation  (Table  129),  8  drivers,  2  truck  wheels ;  a  compara- 
tively recent  innovation,  invented  by  Alex.  Mitchell,  superintendent  of 
the  Lehigh  Valley  Railroad,  in  1872.  It  has  very  rapidly  won  its  way 
into  public  favor,  and  is  now,  it  is  hardly  too  much  to  say,  the  standard 
American  locomotive  for  heavy  freight  service,  and  is  fast  coming  into  use 
for  all  but  the  lightest  service. 

507.  These  are  the  only  types  which  can  be  said  to  be  in  general  use 
for  road  service,  but  in  addition  there  are  the  following  in  approved  but 
more  limited  use: 

5.  Mastodon  (Table  130).  eight  drivers,  four  truck  wheels  a  very 
recent  design  introduced  by  Mr.  A.  J.  Stevens,  of  the  Central  Pacific 
Railroad,  in  1881,  and  said  to  be  rendering  most  excellent  service.  Some 
have  been  built  for  the  Lehigh  Valley.  It  has  not  as  yet  (1886)  been  in- 
troduced to  any  extent  on  other  roads,  but  it  is  exceedingly  probable 
that  it  will  be.  While  not  very  largely  increasing  the  load  on  the 
drivers,  which  is  not  feasible,  the  four-wheel  truck  and  greater  load 
thereon  not  only  makes  the  engine  run  better,  but  enables  the  boiler  to 
be  enlarged. 

6.  Forney,  a  type  invented  by  Mr.  M.  N.  Forney  some  twenty  years 
ago,  having  the  tender  and  engine  combined  on  one  frame,  the  tender 
running  in  front  and  its  truck  serving  in  lieu  of  an  engine  truck,  so  that 
the  weight  of  the  engine  itself  is  carried  wholly  on  the  drivers. 

508.  The  advantage  of  the  Forney  type  is  that  it  gives  more  tractive  power 
(adhesion)  for  the  same  size  of  engine,  by  placing  the  entire  weight  of  the  latter 
on  the  drivers.  Its  disadvantage  is  that  the  boiler  of  no  locomotive  engine 
can  generate  steam  enough  to  utilize  its  whole  weight  for  adhesion,  unless  at 
slower  than  ordinary  freight  speeds,  or  in  service  requiring  very  frequent 
stops,  as  will  be  seen  from  par.  551.  For  such  service  only  is  the  engine  well 
adapted,  and  for  such  service  only  has  it  come  into  use.  As  this  service  is 
the  exception,  the  quite  extensive  use  which  the  type  has  recently  been  given 
still  leaves  it  an  exceptional  type.  It  has  been  urged  for  use  in  general  ser- 
vice, but  is  not  well  adapted  for  it  in  the  respect  mentioned. 

509t  Other  types  of  engines  are : 

7.  Double- Ender,  with  two  "pony"  trucks,  one  at  each   end,  or 


11*1 


424 


CHAP,  XL-LOCOMOTIVE  RUNNING  GEAR. 


CHAP,  XL.—LOCOMOTLVE  RUNNLNG  GEAR. 


425 


sometimes  with  one  "pony"  and  one  four-wheel  truck;  used  chiefly  for 

short-run  local  service.  . 

8  TANK  engines;  a  type  not  confined  to  any  espec.al  form  of  run- 
ninggear,  but  available  for  any  locomotive,  whenever  it  .s  des.rab  e  to 
have  very  great  adhesion  for  short  runs.  As  th,s  adhesion  can  only  be 
utuLd  at  very  slow  speeds,  without  exceeding  the  bo.ler  power,  there  :s 
no  economy  or  advantage  in  placing  a  tank  on  the  engme.  except  as  a 
temporary  resource,  unless  for  very  slow  speeds;  and  hence,  naturally. 
veTsmaU  drivers,  carrying  nearly  the  whole  weight  of  the  engme.  are 
usual  with  tank  engines. 

510.  This  type,  carried  one  step  further,  results  i"- 
g   FAIRLIE  Engine;  two  boilers  placed  back  to  back  wth  a  smgle 
frame   and  carrying  on  their  back  the  entire  supply  of  both  fuel  and 
wa    r'     The  two  "trucks"  on  which  the  whole  is  carried  are  drwmg- 
wheel  bases,  each  carrying  their  own  cylinders,  which  are  supphed  w,th 
Ttelm  through  a  swivelling  joint.     It  is  siiU  less  possible  for  engmes  o 
hlsType  Ui^n  for  tank  engines  to  utilize  their  great  adhesion  without 
exceed^g  their  boiler  power,  except  at  the  slowest  speeds.    Consequently 
they  have  only  found  acceptance  for  work  on  very  heavy  grades  where 
Irelt  tractive  power  is  necessary  and  slow  speed  no  objection,  and  for 
flch  service  onlv  are  they  suitable.     The  type  is  the  invention  of  the 
late  Robert  F.  Fairlie,  the  "apostle"  of  the  now  moribund  narrow-gauge 
movement,  and  was  pushed  by  him  energetically  for  many  years   but 
without   success,  except  as   respects   localities   such   as  descried  (_s 
for  example  the  Mexican  Railway  described  in  Appendix  C),  where  the 
type  has  done  and  is  doing  good  service,  although  very  costly  to  maintain 
611.  Finallv,  in  certain  extreme  cases,  where  still  greater  a<ll.es.on  is 
necessary  and  still  less  speed  desired,  there  is  a  device,  already  referred  to 
(par.  495  .  by  which  the  paying  load  is  carried  on  a  platform  slung  be- 
tween  two  tank  engines,  and  so  utilized  for  adhes.on,  and  when  even 
these  devices  have  not  sufficed  to  give  necessary  adhesion  °"  very  heavy 
grades,  reliance  upon  insistant  weight  to  give  necessary  adhesion  1  .s 
been  abandoned  altogether,  except  as  an  auxiliary  resource,  and  recourse 
had  to  other  devices  noted  in  par.  495. 

S12.  In  addiiion  to  the  previous  types  mentioned,  there  are  for  yard  use 

only — 

10.  Four-wheel  Switching  Engines. 

11.  Six-wheel  Switching  Engines. 

Both  of  these  are  made  either  tank  or  with  tender,  usually  the  latter^     They 
are  admirably  adapted  by  their  great  tractive  power  for  yard  work,  which 


•demands  great  power  even  for  short  trains,  in  order  to  get  them  under  way 
easily,  and  ihey  are  only  used  for  such  service.  Neither  their  boiler  power 
nor  running  gear  is  adequate  for  high  speed,  and  in  fact  engines  with  trucks 
are,  as  a  rule,  preferred  even  for  yard  service. 

613.  In  all  these  various  types  the  load  on  the  drivers  is  equalized  by 
side  levers  connecting  the  springs,  whereas  in  foreign  locomotives  it  is 
not  customary  to  do  more  than  give  a  separate  spring  for  each  wheel. 
The  effect  of  this  equalizing  is  that  in  all  engines  of  the  "  American"  type, 
and  less  perfectly  in  the  other  American  types  of  engines,  the  loco- 
motive is  carried  in  effect  upon  three  points,  the  centre  of  the  truck  and 
the  centre  of  the  equalizing  system  on  each  side  of  the  boiler,  in  three- 
legged-stool  fashion,  which  ensures  perfect  contact  of  wheel  and  rail, 
and  uniform  distribution  of  pressure,  on  all  inequalities  of  track.  For  the 
same  reason  that  a  three  legged  stool  always  stands  solidly  on  any  surface 
however  rough,  while  one  with  four  or  more  legs  will  only  stand  solid 
on  a  plane  surface,  the  total  weight  is  always  evenly  and  fairly  distributed 
between  the  wheels,  however  rough  the  track. 

In  foreign  engines,  on  the  contrary,  which  are  not  equalized,  the  con- 
sequence of  this  or  some  other  and  unexplained  difference  of  detail  or 
of  administration  is  that  there  is  very  great  irregularity  in  the  pressure 
of  the  wheels  on  the  track.  The  exhaustive  experiments  of  the  late 
Baron  von  Weber  on  maintenance  of  way  showed  the  pressure  on  the 
rail  varying  all  the  way  from  zero  to  twice  the  average  load.  That  the 
elimination  of  this  irregularity  of  load  by  adding  equalizers  should  have 
a  certain  effect  to  increase  the  tractive  power  seems  reasonable,  and  that 
or  other  cause  (perhaps  only  greater  effort  to  utilize  to  the  utmost  the 
power  of  the  locomotive)  has  had  that  effect. 

514.  All  the  diverse  types  of  engines  for  road  service,  both  American 
and  foreign,  while  differing  in  almost  every  other  detail  of  their  running 
gear,  agree  in  this — that  in  every  case  (except  four-  and  six-wheel  switch- 
ing engines)  there  is  either  a  truck  or  some  substitute  therefor  to  per- 
form the  office  of  pilot  for  the  driving-wheel  base.  Experience  has 
abundantly  shown  that  such  a  pilot  is  necessary  for  safety  at  high  speeds, 
or  on  rough  track, and  advantageous  at  all  times.  The  different  methods 
for  accomplishing  this  end,  in  the  order  of  their  introduction,  are  as 
follows : 

1.  A  fixed  axle,  parallel  with  the  driving-wheel  axle,  but  carrying  a 
lighter  load  ;  the  normal  foreign  type. 

2.  The  ordinary  American  four-wheel  truck,  consisting  of  four  wheels 
on  two  parallel  axles,  the  whole  swivelling  on  a  centre-pin  O,  Fig.  102. 


426 


CHAP.  XI.— LOCOMOTIVE  RUNNING  GEAR. 


CHAP.  XI.— LOCOMOTIVE  RUNNING   GEAR. 


427 


I 


«•— 


3.  The  sayne  truck  with  a  swing  motion,  the  mechanical  details  of 
which  are  in  substance  similar  to  Figs.  loi,  103,  permitting  the  truck  to 
deviate  somewhat,  laterally,  from  the  axis  of  the  driving-wheel  base,  as 

Oa,  Fig.  100. 

4.  The  "pony"  or  Bissell  truck  (so  named  from  its  inventor),  consist- 
ing of  only  a  single  pair  of  wheels  on  a  single  axle,  but  with  its  axle 

attached  to  a  radius  bar  (constructed  in  prac- 
tice as  a  double  V-shaped  bar,  as  shown  by 
the  solid  lines)  so  that  the  pair  of  wheels 
*'*  swivel  around  a  point  O,  Fig.  98.  6  to  8  feet 
in  the  rear,  thus  having  the  effect  to  compel 
the  single  axle  to  always  remain  parallel  with 
the  driving-axles  on  tangents,  while  permitting 
it  to  assume  a  radial  position  on  curves. 

615.    All  these  four  plans   have   approxi- 
mately the  same  object,  to  relieve  the  driving- 
^.^   wheel  flanges  of  the  task  of  guiding  the  driv- 
ing-wheel base  on  curves,  and  to  leave  them 
only  the  simpler  duty  of  holding  them  on  the 
rails  against  the  effect  of  chance  irregularities 
of  motion.    To   do  this,  if   it  be   effectually 
done,  it  is  plain  that  a  heavier  duty  must  be 
thrown  upon  the  flanges  of  the  forward  wheels 
than  properly  appertains  to  the  load  carried  on 
them,  and  apparently  these  diverse  plans  will 
accomplish  the  end  with  very  unequal  degrees- 
of  efficiency,  and  cause  very  unequal  derailing  moments  in  the  forward 
wheels.     Nevertheless,  each  and  all  of  them  have   been  approved  by 
experience  as  adequate  for  the  end  in  view,  nor  has  experience  shown  any 
very  great  difference  in  the  coefficient  of  safety  of  each.     By  investigat- 
ing theoretically  the  mechanics  of  the  locomotive-wheel  base,  we  shall 
see  why  this  should  be  so,  and  at  the  same  time  gain  an  important  insight 
into  the  feasibility  of  using  various  types  and  sizes  of  locomotives  on 
different  alignments.  The  result  of  such  an  analysis,  which  follows  below, 
is  presented  in  Fig.  107,  page  433. 

516.  The  work  to  be  done  by  the  pilot-wheels  is  in  all  cases  the  same— to- 
prevent  the  front  outer  driving-wheel  flange  from  grinding  against  the  rail  and 
compel  it  to  stand  away  from  the  rail,  or  at  least  relieve  its  pressure.  To  do 
this,  force  or  pressure  must  be  applied  at  some  point  on  the  axis  of  the  driving- 
wheel  base  sufficient  to  cause  it.  in  effect,  to  continuously  rotate;  because  it 


Fig.  98. 


compels  the  wheel-base  to  change  its  direction  to  follow  the  curve  sooner  than 
it  naturally  tends  to  do  so. 

The  force  (pressure)  in  pounds  necessary  to  cause  this  rotation  is  the  same, 
however  fast  or  slow  the  motion  of  rotation  takes  place  (the  work  done  in  foot- 
pounds per  second  only  varying),  and  varies  only  with  (i)  the  load  on  drivers, 
(2)  the  coefficient  of  friction,  which,  for  reasons  we  shall  shortly  see,  we  will 
take  at  one  third,  and  (3)  the  length  of  the  wheel-base.  The  rotation  may  take 
place  either  by  throwing  the  front  axle  inward  or  the  rear  axle  outward,  or 
both;  but  without  going  into  unnecessary  and  doubtful  details  as  to  which  is 
most  probable,  which  would  but  little  affect  the  final  result,  the  resisting  mo- 
ment of  the  driving-wheel  base  to  rotation  may  be  estimated  as  follows: 

Two-axle  driving-wheel  base,  of  length  =  /  and  total  load  =  W;  letting 
r=  diagonal  distance  from  centre  of  wheel-base  to  each  wheel: 

Resisting  moment  M=  WrX  coefficient  of  friction  (say  \). 
Three-axle  wheel-base,  of  length  =  /and  total  load  =  W : 

Resisting  moment  M  =  (^  iVr-\-^lVr')  X  coefficient  of  friction. 
Four-axle  wheel-base  : 

Resisting  moment  M  =  ^IV {r-{-r')  X  coefficient  of  friction. 
The  values  of  r  and  t'  are  readily  computed  from  the  gauge 
and  the  length  of  wheel  base. 

This  resisting  moment  is  overcome  in  any  form  of  loco- 
ihotive- wheel  base  by  a  force  applied  at  some  point  O,  Figs. 
98,  100,  acting  with  a  leverage,  which  let  =  Z,  varying  with  the 
pattern  of  engine;  and  the  amount  of  this  force,  O,  is  readily 
determined  by  the  formula 

517.  This  statement  of  the  action  of 
these  forces  is  incomplete  in  this,  that  a 
motion  of  rotation  of  the  driving-wheel 
base  can  only  be  produced  by  the  action 
of  a  couple,  and  not  by  any  single  force. 
Actually,  therefore,  it  is  essential  that 
one  or  the  other  wheels  should  serve  as 
a  fulcrum,  to  enable  the  force  O,  Fig.  99, 
by  which  the  truck  causes  the  driving- 
wheel  base  to  rotate,  to  act  ;  but  which 
wheel  it  would  be,  or  whether  it  would 
be  any  one  single  wheel  for  more  than 


Fig.  99. 


Fig. 


100. 


a  few  instants  at  once,  we  cannot  assert  with  certainty,  nor  would  the  action  or 


BmmmmmHtr^  - 


428  C/fAF,  XL-LOCOMOTIVE  RUNNING  GEAR. 


CHAP.  XL— LOCOMOTIVE  RUNNING  GEAR. 


429. 


amount  of  the  force  0  be  very  greatly  affected  by  any  possible  differences  in 

^^'^n"hrEnglish  type  of  wheel-base,  three  parallel  axles,  the  two  rear  being 
driving  axles,  this  force  O  is  of  necessity  all  supplied  by  the  flange  of  the  outer 
leading-wheel.  In  the  American  type  of  wheel-base.  Figs.  99.  100.  it  .s  of  neces- 
sity  all  supplied  by  the  centre-pin  of  the  truck  ;  but  it  is  to  be  remembered,  as 
respects  the  wheel-bases  with  more  driving-axles,  like  Fig.  98.  that  u  ,s  not 
essential  that  the  driving-wheel  flanges  should  be  wholly  relieved  of  all  work  m 
guiding  the  wheel  base,  but  only  that  they  should  be  so  greatly  relieved  that 
such  flange  pressure  as  remains  to  them  shall  not  be  injurious. 

518.  The  lateral  force  at  0,  Figs.  98.  100.  being  given,  the  more  important 
question  remains-the  amount  of  additional  lateral  strain  thrown  by  it  on  ihe 
leading  wheel  a,  Fig.  99-  I"  every  locomotive,  as  they  are  actually  constructed, 
this  wheel  is  in  most  danger  of  mounting  the  outside  rail  on  curves.  The  flange 
pressure  of  this  wheel  may  be  determined  as  follows  :  ,     ,     ^. 

In  the  American  type,  Figs.  99.  100,  the  action  of  the  forces  on  the  leading 

truck  is  as  follows  :  ,  •  1     .u 

As  a  result  of  guiding  the  truck  itself,  considered  as  a  separate  vehicle,  the 
reaction  of  the  rail  against  the  front  outer  flange  a  must  be  enough,  as  we  have 
seen  (par.  302),  to  cause  three  of  the  wheels,  a,  b,  c.  Fig.  99.  to  rotate  around 
^  as  a  centre;  or,  calling  the  load  on  each  truck- wheel  «/.  and  the  coefficient  ot 
friction  i  (instead  of  i.  as  for  the  driving  wheel  base,  on  account  of  the  lighter 
load),  we  have  for  the  force  /,  Fig.  99, 

The  wheel  c  normally  stands  away  from  the  rail,  as  shown  in  Figs.  99  an^ 
20,  and  resists  being  crowded  up  against  the  outside  rail  with  a  force  =/- 
enough  to  slide  the  three  wheels  b,  c,  d.  ^        ^       a    j  x:„ 

519.  The  force  O  is  equally  divided  between  the  two  axles  ab  and  cd.  Fig. 
99.  so  that  we  have,  in  any  engine  truck  of  an  American  engine  : 
Pressure  of  leading  wheel  a.  Fig.  99.  against  outside  rail  =  \  force  ^+  orce/. 
Pressure  of  rear  wheel  c  against  outside  rail  =  \  force  O  -  force/. 

The  latter  is  true  because  the  force /on  the  rear  axle  is  a  negative  or  resist- 
ine  force  If  \0  be  greater  than/,  the  wheel  will  be  crowded  up  against  the 
rail,  but  Ihere  will  always  be  a  force  = /tending  to  cause  it  to  leave  the  rail  so 
thai  the  net  pressure  against  the  rail  will  be  only  the  difference  between  the 

'''V2'orWhen  the  truck  is  a  swing-motion  truck  the  distribution  of  the  force. 

is  in  no  way  affected.      A  certain  amount  of  lateral  motion  takes  place  first- 

>that  is  all-sufficient  to  bring  about  the  equilibrium  of  forces  sketched  in  Fig. 

loi.  as  one  might  take  out  the  slack  of  a  chain  before  it  comes  to  a  bearing, 

and  then  the  force  O  acts  as  before.  .   .     ,    »  ^.o^tiral 

Right  here  we  touch  upon  the  leading   theoretical,  and  in  fact  practical, 


objection  to  the  swing-motion  truck,  although  its  true  cause  is  not  always  ap- 
preciated. We  have  seen  (par.  516)  that  the  force  O  is  a  constant,  regardless 
of  the  radius  of  curvature.  Consequently,  whenever  this  force  is  called  into- 
action  at  all,  the  same  amount  of  lateral  deflection.  Oa,  Figs.  100,  loi,  lo2»  will 
take  place,  or  tend  to  take  place,  unless  stopped  by  the  driving-wheel  flange: 
coming  in  contact  with  the  rail,  which  it  is  the  object  of  the  truck  to  prevent. 


Fig.  ioi. 


Fig.  102. 


521.  This  is  not  at  all  what  is  desired,  since  it  correctly  adapts  the  wheel- 
base  to  motion  on  only  one  curve,  that,  namely,  on  which  the  distance  Oa,  Fig. 
102,  =  the  offset  to  the  curve  at  O  from  a  tangent  to  the  curve  at  c.  This  must  be- 
on  a  comparatively  sharp  curve  if  the  very  object  of  the  swing-motion  (to  enable 
the  locomotive  to  pass  sharp  curves  easily)  is  to  be  attained.  On  easier  curves 
the  amount  of  deviation  which  the  swing-motion  permits  is  as  much  too  great 
as  that  of  the  fixed  centre-pin  is  too  small.  On  all  easier  curves  the  wheel-base 
will  tend  to  assume  a  position  something  like  Fig.  102.  which  is  still  less  favor- 
able  than  the  normal  position  of  an  American  engine  wheel-base,  without  the 
swing-motion,  outlined  in  Fig.  100.  It  is  true  that,  owing  to  the  splay  given  to 
the  links  of  the  swing-motion,  there  is  a  certain  amount  of  resistance  to  any 
lateral  motion,  however  slight;  but  this  is  not  sufficient  to  restrain  the  tendency 
lo  assume  the  position  shown  in  Fig.  loi,  and  hence  has  little  remedial  effect. 


430 


CHAP,  XL—LOCOMOTIVE  RUNNING  GEAR. 


CHAP.  XL— LOCOMOTIVE  RUNNING  GEAR. 


431 


522.  For  these  reasons  the  swing-motion,  although  very  largely  used,  has 
never  shown  the  advantage  over  the  fixed  centre  which  it  probably  would  if  the 

lateral  deviation  were  in  fact  proportioned  to  radius 
of  curvature,  as  it  is  often  assumed  to  be.  As  orig- 
inally designed  by  Mr.  Bissell  (for  **  pony"  trucks) 
it  was  not  open  to  this  objection;   two  inclined 
planes  being  used,  in  the  manner  shown  in  principle 
in  Fig.  103,  which  offered  the  same  lateral  resist- 
ance however  much  or  little  motion  took  place. 
But  for  practical  reasons  (rapid  deterioration   of 
bearing  surfaces  and  impact  when  bearings  return 
to  the  centre)  this  form  has  passed  out  of  use,  per- 
haps in  part  for  lack  of  giving  due  weight  to  the 
theoretical  advantages  which  it  undoubtedly  pos- 
jf  sesses. 

I  523.  The  manner  in  which  the  two-wheeled 

/  Bissell  or  "  pony"  truck  (Figs.  104,  105)  relieves  the 

Fig.  103.  driving-wheel  base  of  lateral  strain  is  quite  differ- 

ent, and  much  less  clear.  Apparently  it  ought  not  to  assist  at  all.  except  to 
the' very  slight  extent  (especially  on  easy  curves)  by  which  the  resistance  of  the 
swing-motion  (Fig.  lOi),  which  is  directly  over  the  axle,  resists  lateral  motion; 

for  it  is  free  to  swivel  around 
its  bearing  at  O  (Figs.  104  and 
98),  regardless  of  the  remain- 
der of  the  wheel-base.  It  is 
known  to  have  in  fact,  how- 
ever, a  very  material  effect 
upon  the  motion  of  the  wheel- 
base,  and  theory  very  readily 
indicates  to  us  why  this  should 

be. 

The  "pony"  truck  natu- 
rally tends  to  roll  forward  in 
a  right  line,  parallel  to  itself, 


Kl^a 


Fig.  105. 

as  in  Fig.  104.  The  rigid  driving-wheel  base  behind,  and  not  its  own  flange  or 
its  coning,  as  we  shall  see,  compels  it  to  move  in  a  curve,  to  do  which  the 
driving-wheel  base  must  exert  a  stress,  O,  Fig.  104,  in  the  opposite  direction 
to  the  arrow,  of  sufficient  magnitude  to  produce  motion  in  the  direction  ak. 
Fig.  105,  and  thus  slide  one  or  the  other  of  the  wheels  continuously  on  the  rail, 
compelling  the  leading  axle  to  move  in  a  curved  path  instead  of  a  straight  one. 
The  resistance  of  the  wheels  to  this  sliding  creates  one  or  the  other  (not  both) 


of  the  two  forces  represented  by  the  longitudinal  arrows  in  Fig.  104,  and  for 
the  force  O,  resulting  therefrom,  we  have 

O  =  (load  on  one  wheel  X  coef.  frict.)  X  f  L!^'  ^     ,. 

/  (Fig.  104) 

624.  Lest  the  wheels  should  run  toward  the  outside  rail,  and  from  coning  or 
•otherwise  adapt  their  diameters  to  naturally  travel  in  a  curve,  we  have  this 
further  precaution: 

To  enable  both  the  pony  truck  and  the  transverse  axis  of  the  driving-wheel 
base  to  assume  radial  positions,  the  radius-bar  of 
the  pony  truck  should,  from  well  known  properties 
of  the  circle,  pivot  at  the  point  O  (Fig.  106),  mid- 
way between  c  and  the  "  pony"  axle.  If  shorter  than 
this,  as  at  o.  Fig.  106  (as  it  always  is),  the  driving- 
wheel-base  will  throw  the  rear  end  of  the  radius- 
bar  over  through  a  certain  distance  (ak.  Fig.  105) 
toward  the  outside  rail,  and  thus  create  in  it  a 
tendency  to  run  toward  the  inside  rail  and  away 
from  the  outside  rail.  This  tendency  is  increased 
by  the  fact  that  it  is  the  rear  and  not  the  centre  of 
the  driving-wheel  base  which  tends  (par.  294  and 
Fig.  20)  to  assume  a  radial  position,  the  front 
outer  driving-wheel  tending  of  itself  to  crowd 
^hard  against  the  outer  rail. 

625.  These  two  causes  together  ensure  that 
the  pony  axle  shall  always  have  a  continuous  ten- 
dency to  run  toward  the  inside  rail  and  away  from 
the  outside,  and  if  the  radius-bar  be  made  too 
short  this  tendency  becomes  so  decided  that  inju- 
rious wear  results.     Thus,  in  a  Consolidation  en-  pio.  106. 

gine  of  the  Norfolk  &  Western  Railroad  the  radius-bar  was  originally  only 
4  ft.  2  in.  long,  and  created  so  strong  a  tendency  to  run  to  the  inside  rail  that  it 
was  lengthened  to  5  ft.  6  in.  long,  with  very  beneficial  results.  Even  then  the 
point  O  was  some  9  ft.  ahead  of  the  centre  of  the  wheel-base,  c,  Fig.  106,  so  that 
it  was  still  much  shorter  than  was  apparently  required  to  enable  the  wheel-base 
to  adapt  itself  most  perfectly  to  the  curve. 

No  very  strong  tendency  in  the  pony  axle  to  run  toward  the  inside  rail 
is  necessary,  but  only  just  enough  to  ensure  the  driving-wheel  base  shall  in 
fact  modify  its  natural  path  in  the  way  outlined,  by  however  little,  since  if  any 
force  whatever  (O,  Fig.  104)  needs  to  be  applied  to  cause  the  pony  axle  to 
roll  in  the  curve  it  must  necessarily  be  adequate  to  slip  the  wheels  on  the 
rails:  the  stress  necessary  to  slip  them  a  little  is  as  great  as  to  slip  them  a 
good  deal. 


432 


CHAP.  XI.— LOCOMOTIVE  RUNNING  GEAR. 


CHAP.  XI.—LOCOMOTIVE  RUNNING  GEAR. 


433 


From  this  it  will  be  seen  that  xll  =  g  (Fig.  104)  the  lateral  force  at  0  neces- 
sary to  alter  the  path  of  the  leading  wheels  is  just  half  diS  great  as  if  these  were 
a  fixed  axle  at  O,  in  the  English  style  (because  there  is  only  one  wheel  to  slide 
instead  of  two),  with  the  added  advantage  that  the  pony  axle  is  approximately 
radial  and  guided  by  the  wheel-base  behind,  so  as  to  relieve  the  pony  flanges 
of  strain,  and  thus  add  greatly  to  safety. 

In  addition  to  the  force  O,  Fig.  104.  the  swing  motion  of  the  pony  truck  sup- 
plies any  desired  amount  of  additional  lateral  force,  directly,  whenever  the 
engine  is  running  on  curves  sharp  enough  to  develop  it  fully. 

526.  For  the  forces  acting  on  the  leading  outer  wheel  of  any  locomo- 
tive wheel-base.  then,  if  it  is  in  fact  to  perform  the  office  of  guiding  the 
complete  wheel-base  on  curves,  we  have  these  conditions:  There  is  a 
vertical  component  equal  to  the  load  on  the  wheel,  and  there  is  a  hori- 
zontal component  equal  to  the  forces  determined  for  all  the  various  types 
in  pars.  516  to  525.  These  forces,  as  computed  for  a  great  variety  of  light 
and  heavy  engines  of  all  types,  have  been  plotted  in  Fig.  107,  which  rep- 
resents graphicallv  the  comparative  degree  of  safety  of  various  types  of 
locomotives  for  passing  curves ;  and  the  surprising  dejiree  of  uniformity 
which  they  show  in  a  measure  tends  to  confirm  the  correctness  of  our 
conclusions,  since  experience  has  shown  that  there  is  in  fact  no  marked 
difference  in  safety  between  the  engines  themselves. 

Note  to  Fio.  107.— The  diagram  shows  in  magnitude  and  direction  the  resultant  of 
the  horizontal  and  vertical  forces  acting  on  the  front  outer  truck-wheel  of  locomotive 
wheel-bases  of  all  common  types  on  curves  of  any  radius  (the  same  being,  except  for 
unknown  variations  in  the  coefficient  of  friction,  uniform  for  all  radii). 
The  comparative  safety  may  be  considered  as  varying— 

First.  With  the  direction  of  the  resultant,  as  being  more  or  less  inclined  to  the 
"  horizontal;  those  most  inclined  being  the  safest,  other  things  being  equal,  since  the  re- 
sistance to  the  flange  mounting  the  rails  is  then  greatest. 

Secondly,  and  chiefly.  With  the  MAGNITUDE  of  the  resultant,  or  total  pressure  of  the 

wheel  against  the  rail. 

All  American  engines,  embracing  a  great  variety  of  designs  and  weights,  will  be  seen 
to  lie  within  the  small  quadrilateral  marked  out  by  the  points  i.  3,  10,  15.  The  more  com- 
mon English  types  cause  a  far  greater  pressure  against  the  rails,  but  as  a  compensating 
advantage  have  more  nearly  vertical  resultants.  ^^ 

Details  as  to  all  the  locomotives  shown  may  be  found  either  in  ♦'  Recent  Locomotives, 
Forney's  "Catechism  of  the  Locomotive"  (Railroad  Gazette),  or  Barry's  "Railway  Ap- 
pliances" (Spon). 

Manner  of  Constructing  the  Diagram. 

The  vertical  ordinates  represent  the  load  in  pounds  on  the  front  outer  wheel. 

The  horizontal  abscissa  represent  the  lateral  stress  in  pounds  acting  on  the  wheel, 
which  consists  of  {a),  with  four-wheel  trucks  only,  the  flange  pressure  necessary  to  cause 
rotation  in  the  truck,  and  (b)  half  the  force  (9,  Figs.  99  and  104,  required  to  be  appUed  at 


V  * 


434  CHAP,  XL-LOCOMOTIVE   TRACTIVE  POWER. 


CHAP.  XL— LOCOMOTIVE   TRACTIVE  POWER. 


435 


the  centre-pin  of  the  truck  (or  all  of  it  in  the  case  of  two-wheel '  *  pony  »  trucks)  to  produce 
rotation  of  the  driving-wheel  base. 

The  various  types  of  locomotives  shown  are : 


Mastodon.  \  i— Central  Pacific. 

(4-wheel  truck.)     1  2— Lehigh  Valley. 

Consolidation.  \  3— Baldwin. 

(Pony  truck.)         \  4— Pennsylv'a  (Class  1). 

Ten-wheel.        <  5— Baldwin. 
(4-wheel  truck.)     \  6— Pennsylvania. 


f  9 — Baldwin. 
Tr.— Pennsylvania. 


Mogul. 
(Pony  truck.) 


(  7 — Baldwin. 
(  II — 


American. 

(4-wheel  truck.) 


Heavy  Mogul. 


English. 
(No  truck,  lead 
ing  axle.) 


12— English  fast  passenger 
14 — Pennsylvania  fast  pas- 
senger. 
15— Old   (light)   fast  pas- 
senger. 

reight  type. 
Passenger  type. 


)    8— Pre 
^-  ^  13-PaJ 


V 


TRACTIVE   POWER. 

527.  The  friction  between  the  driving-wheels  and  rails  which  prevents 
them  from  slipping  and  enables  them  to  propel  the  train  is  a  static  or 
mer"  y  resisting  fdction.  as  distinguished  from  dynamic  friction  or  that 
Twh^ch  motion  takes  place  between  the  surfaces  in  contact,  w.th  result- 
L  destruction  of  energy.  Its  cause,  beyond  all  question,  is  an  absolute 
inferlocking  of  the  roughnesses  or  projecting  fibres  of  the  surfaces  in 
contact  as  cogs  might  Interlock.  That  this  is  essentially  true  of  all 
frictTon  between  metallic  surfaces,  under  the  most  favorable  circumstances, 
iTs  curio^^^^^^^^  by  experiments  of  Mr.  Beauchamp  Tower  *  on  the 

most  finely  polished  and  completely  lubricated  journals:  a  mere  change  m 
the  direc  fon  of  revolution  resulted  in  a  noticeable  but  temporary  increase 
n  the  coefficient  of  friction,  for  which  so  careful  and  competent  an  ob- 
ervercouM  ascribe  no  other  cause  than  that  the  fibres  were  stroked  one 
way  by  continuous  revolution,  as  fur  might  be,  and  that  on  motion  being 
reversed  the  fibres  opposed  each  other 

528.  Our  best  existing  evidence,  by   far.  of  the  general  ^^^^wmcn 

govern  static  friction  between  rail  and  wheel  - -"^^^^^ '"J^/.^P^^ 
by  Capt.  Douglas  Galton.  giving  the  results  ^^  JP^.^""1^"    ^7/,g' 
efficiency  conducted  by  him  and  by  Mr.  Geo.  Westinghouse  m    1876 
T^ee  experiments  are  quite  unique  in  the  completeness  and  accur^^^^^^^^^^ 
the  apparatus  used,  and  (what  is  still  more  important)  ^"/he  Uioj^^^^^ 
ness  a'n'd  technical  knowledge  with  which  the  ^^^^^^^^J^l^^^^^    '^^ 
they   positively  contradict  the  assumption   someumes^made.  that  tne 

♦Trans.  Inst.  Mcch.  Engrs. .  1885.     See  Appendix  B. 


coefficient  of  friction  between  rail  and  wheel  is  greater  at  low  speeds 
"on  account  of  less  time  for  new  surfaces  to  interlock."  * 

An  impression  that  the  adhesion  is  less  at  speed  has  been  derived,  in 
some  instances,  from  dynamometer  records,  which  shows  far  less  tractive 
pull  between  stations  than  in  starting.  This,  however,  results  merely 
from  the  fact  that  the  cylinders  are  not  able  to  exert  their  full  power  at 
speed,  and  has  no  real  connection  with  the  adhesion. 

No  error  of  moment  can  arise,  therefore,  from  assuming  that  the 
resistance  of  the  wheels  to  slipping  is  sensibly  constant  at  all  speeds.  It 
is  only  at  slow  speeds  that  the  precise  amount  of  adhesion  becomes 
important.! 

That  the  coefficient  of  adhesion  is  the  same  at  all  train-speeds  has  not  been 
experimentally  proven;  but  however  fast  the  motion  of  the  locomotive,  so  long 
as  the  drivers  do  not  slip,  the  adhesion  is  equally  static;  and  the  only  reason 
why  the  adhesion  should  be  less  at  high  speeds  is  that  the  fibres  are  afforded 
less  time  to  completely  engage  with  each  other.  That  this  difference  may  have 
some  slight  effect  is  possible,  but  as  the  available  cylinder  power  falls  far  more 
rapidly  with  increase  of  speed,  it  is  a  fact  which  is  not  important,  even  if  true. 

529.  When  slipping  has  once  begun,  however,  the  conditions  are 
very  different.  Chiefly  from  the  Galton- Westinghouse  experiments 
before  referred  to.  which  are  confirmed  from  other  sources  and  by  uni- 
versal experience,  we  may  derive  the  following  conclusions  as  to  the  gen- 
eral laws  which  govern  friction  between  rail  and  wheel ;  all  of  which  cor- 
respond closely  with  the  results  of  modern  investigations  of  other  kinds 
of  friction. 


*  "The  Pennsylvania  Railroad  Company,"  by  James  Dredge:  Appendix  on 
Brake  Trials.     The  exact  language  of  Capt.  Galton  on  this  point  is: 

•*  The  amount  of  frictional  resistance  which  determines  the  point  at  which 
the  rotation  of  wheels  is  checked  varies,  it  is  true,  in  the  different  experiments. 
The  ratio  which  it  bears  to  the  weight  upon  the  braked  wheels"  varies  from  .29 
to  .35.  averaging  .25.  "  But  it  [the  variations]clearly  represents  simply  the 
adhesion  between  the  wheel  and  the  rail,  and  varies  only  with  this,  and  not 

with  the  speed. 

"  Thus  at  60  miles  per  hour  the  amount  of  frictional  resistance  which 
checked  the  rotation  of  the  wheels  was  about  2000  lbs,  exhibiting  an  adhesion 
of  about  .191  per  cent;  at  15  miles  per  hour,  2160  lbs.  or  .196  per  cent.  As 
these  two  values  are  so  nearly  equivalent,  it  would  appear  that  the  effort  is 
much  the  same  at  all  speeds." 

f  D.  K.  Clark,  a  usually  careful  authority,  states  (p.  724,  "  Man.  Mech. 
Engr."),  '*  As  the  speed  is  increased  the  adhesion  is  reduced,"  as  a  result  of  his 
own  tests  of  locomotives.  The  author  cannot  but  believe,  however,  that  this 
is  an  over-hasty  conclusion  by  that  able  and  usually  trustworthy  writer. 


IP 


436  CHAP.  XL— LOCOMOTIVE    TRACTIVE  POWER, 


1.  The  coefficient  of  static  friction  between  rail  and  wheel  is  not  sen- 
sibly  affected  by  the  velocity  of  motion  (as  above). 

2.  It  is  very  greatly  affected  by  the  insistent  weight,  increasing  rapidly 

therewith. 

3.  It  is  very  greatly  affected  by  the  condition  of  the  surfaces  as  re- 
spects moisture  or  other  equivalent  for  a  lubricant,  even  when  the  eye 
can  detect  no  difference,  and  is  very  considerably  affected  by  unknown 
causes,  so  that  it  can  rarely  be  determined  twice  alike. 

4.  It  is  greatest  when  the  rails  are  very  dry  or  (probably  for  the  rea- 
son that  the  minute  mineral  and  metallic  particles  which  act  as  rollers  are 
washed  away)  very  wet,  moisture  or  frost  having  the  most  injurious  effect. 

5.  The  coefficient  of  dynamic  or  sliding  friction  is  very  greatly  less 
than  static  friction,  and  very  greatly  affected  by  velocity,  in  inverse 
ratio  thereto.  At  the  instant  when  slipping  begins,  the  velocity  of  the 
rubbing  surfaces  being  very  small,  it  is  sensibly  the  same  as  static  friction, 
but  as  the  velocity  becomes  greater  it  falls  very  rapidly,  until  it  is  hardly 
one  third  or  one  fourth  as  great  as  the  static  friction. 

Tables  112,  113,  page  290,  show  the  general  results  of  these  tests,  and 
the  evidence  on  which  the  above  conclusions  are  based,  more  clearly 

than  words.  . 

From  these  laws  it  necessarily  results  that  when  slipping  of  the 
drivers  once  begins  the  resistance  to  further  slipping  (coefficient  of  fric- 
tion) should  almost  instantly  fall,  and  hence  that  the  wheels  should 
almost  instantly  begin  to  "spin;"  i.e.,  the  surplus  energy  of  the  drivers. 
no  longer  required  to  turn  the  wheels  against  a  great  resistance,  but 
only  ag'ainst  a  small  resistance,  must  necessarily  go  somewhere,  and  is 
stored  in  the  wheels  in  the  form  of  velocity,  sometimes  making  them 
••spin"  so  violently  (when  steam  is  not  shut  off  soon  enough)  as  to  wear 
holes  in  the  rails  one-eighth  to  one-half  inch  deep.  This  spinning  is  not 
an  evidence  of  overloading,  since  (par.  483)  «n  any  well-designed  engine 
letting  in  the  full  power  of  the  cylinders  will  in  any  case  give  a  greater 
tractive  energy  than  the  wheels  can  transmit.  The  proper  course  when 
it  occurs  is  to  shut  off  steam,  let  the  drivers  come  to  rest,  and  start  more 
gradually.  If  engines  are  to  be  loaded  up  to  their  full  capacity,  only  the 
greatest  care  can  prevent  this  phenomenon  occasionally  occurring,  and 
it  does  occur  constantly  in  practice,  in  starting  trains,  although  rarely 
when  in  motion,  except  when  the  train  is  almost  at  a  stand-still. 

630.  A  lonjx  list  of  actual  performances  of  locomotives  in  ser- 
vice is  given  in  Table  138,  and  from  this  and  the  further  data 


CHAP.  XL— LOCOMOTIVE    TRACTIVE  POWER.  437 


^'Z^  to  0.37 
(i)  ^'Zl 


(i)  0.25 


(i)  o-  20 


below  it  is  clear  that  the  following  average  coefficients  of  adhe- 
sion may  be  assumed  with  sufficient  exactness  as  corresponding 
closely  to  the  results  of  American  practice.  European  practice 
(par.  537  and  Table  139)  shows  much  lower  ratios  of  adhesion  : 

Min.  (load  on 
TT1   •  !•      •       r  *  drivers  =  1. 00). 

1.  Ultimate  limit  of  adhesion  in  practice,  under  con- 

ditions  in   all   respects   favorable,  and   with 
loads  per  wheel  exceeding  10,000  lbs.,    . 

2.  Working  limit  of  adhesion  when  sand  is  used, 

3.  Working  limit  of  adhesion   in  ordinary  summer 

weather,  and  maximum  limit  with  loads  of 
less  than  10,000  lbs.  per  wheel, 

4.  Working  limit  of  adhesion  on  slightly  moist  or 

frosty  rail,  being  the  apparent  average  of  ad- 
hesion which  limits  the  weight  of  trains  in 
winter  (as  to  which  see  par.  632), 

5.  After  the  wheels  have  once   slipped,  the  co- 

efficient rapidly  falls  (see  Table  112)  to  less 

^^^" (iV)o.io 

531.  The  first  of  these  limits  was  realized  by  Zerah  Colburn 
as  early  as  1853,  and  with  light  locomotives  \io,ooo  lbs.  per 
driver),  in  his  still  famous  tests  on  the  Erie  Railway,  and  re- 
peatedly since.  In  a  large  number  of  recorded  instances  trains 
have  been  hauled  in  regular  service  which  demanded  nearly  or 
quite  one  third  adhesion,  but  only  as  exceptional  performances. 
A  long  list  of  notes  as  to  such  trains  might  be  given. 

532.  The  second  limit  (when  sand  is  used)  is  less  fully  deter- 
mined, but  various  dynamometer  records  of  the  effect  of  sand  to 
increase  tractive  power  indicate  that  it  increases  the  working 
limit  of  coefficient  to  about  \  under  all  conditions  of  track  or 
weather;  that  is  to  say,  it  makes  the  adhesion  on  a  bad  rail  as 
high  as  on  a  good  one.  On  a  good  rail  it  does  not  appear 
that  the  coefficient  of  adhesion  is  appreciably  increased,  but 
what  is  gained  by  the  sand  is  to  retard  the  tendency  to' slip. 
Direct  evidence  on  the  subject  is  scarce,  and  there  is  no  doubt  a 


"liil 


.:''(!:' 


438  CHAP.  XL-LOCOMOTIVE    TRACTIVE  POWER. 


No.  of 
Record. 


I. 

3. 

3 
4 
5- 

6. 

7- 
8 

9 
lo. 

II 

12 

X3- 


X5  • 

x6  - 

17. 

18.. 

19.. 

ao. . 

31. 

32. 

«3- 


84- 

95 
s6. 

37. 


s8. 


89 

30 

31 

3a 

33 

34 

II::::; 

37 

38.... 

39.... 


Cylin- 
ders. 
Inches. 


13x22 
14x22 

15x22 

16x24 
tk 

X7X24 

t  k 

tt 
ii 

18x24 


19x34 


16x24 
kk 
<t 
(i 

17x24 

(t 
«i 

18x34 


Table 

Performance  of  American 

(Including  all  the  Records  of  Performance  given 

American 


CHAP.  XL— LOCOMOTIVE    TRACTIVE  POWER. 


Weight  of  Engine. 
[All  Tons,  2000  lbs.] 


En- 
gine. 


Ten- 
der. 


16x24 

44 

36-15 

17x24 

38.0 

18x24 

44 

40.0 

kk 

44 

tl 

11 

it 
ii 

ii 

ii 

tl 

42.0 


35-5 
ii 
ii 
ti 

37-5 

ii 

ii 

ii 

39  o 
ki 

II 
it 


On 
Drivers 


28.0 

4k 

24.0 

«k 

29.5 

4. 

24  5 
kk 

31.0 

25.0 

330 

25.0 

44 

it 

35-0 

25.0 

ii 

ik 

tl 

tl 

37.0 

26.0 

4. 

ip.o 

20.0 

21. 5 
ik 

23.0 
*k 

ii 

it 

24-5 


Tractive 

Power, 

at^ 

Adhesion. 

Lbs. 


Character  of 
Performance. 


8,750 

9.500 

kk 

10,000 

10,750 
ti 

11,500 

kk 
it 
■it 

13,350 


Single  performance 

kk  -engiueers  say. 

Regular  (?) .- •• 

Single  perf.  "  with  ease.  '. 
Regular  service 


Grade, 
Feet 
Per 

Mile.* 


tl 

II 


Second  trip 

Regular 

*•  Frequently.'' 

Regular'?)       

'•  No  difficulty." .-, 

Can't  exceed  10  m.  p.  h. 


72  +  a 

52.8 

71.0 

237.0 

43.0 

65.0 

47-7 
70.0 
40  o 

63  9  +  2 
160.0 


*  The  additions  to  the  grade  in  this  column  are  an  allowance  for 

Ten-wheel 


26.0 
ii 

26.0 

ik 

26.0 
ki 

it 

It 

it 

it 

It 

it 

26.0 


27.  X 

ki 

38.5 

it 

30-5 

ii 

tl 
tl 

it 
II 

II 

tl 


33.0 
"'it 


13.550 

.4 

141250 

4. 

15.250 

it 

tl 
it 
II 

41 

It 

16,000 


"Have  taken." 

Pass,  exceed  20  m.  per  hour 
Single  trip 


Maximum  load 

Regular       "     

Daily  and  easily.' 


Maximum  Load 
it 

Usual  load 

it       it 

"  Have  pulled.'' 


484-8 

53  +  5 

77  +  3 

150-^-13 

79+3 

62  +  4 

21  -H  5 

126 

76 

126 

76 

76  +  6 

lox  —  8 


Mogul 


25-5 

It 
II 

14 

25-5 
It 


36.0 
II 

tt 

44 


30.0 
It 
It 
It 

31-5 
II 

41 
II 

33;0 
44 
44 


15,000 


15*750 
It 

14 

41 

16,500 
tl 

44 
44 


Equiv't  work  every  day. 

do.    (gained  speed  in  test) 

Regular  trains 

Irregular    "     

"  Have  hauled." 


Largest  regular  load 

Comparative  test  •• 

"  Equal  serv.  every  day.  '. 
Intended  as  daily  duty.     . 


Momentum  grades,  reg.  ser, 


83 +  21 

40.5 
53- 

44  ± 
It 

70  +  6 
85  +  10 

53 
60 

70 
53 -a« 


439 


138. 

Locomotives  in  Practice. 

in  the  Catalogue  of  Baldwin  Locomotive  Works.) 

Engines. 


Resist- 
ance. 
Lbs. 
Per 
Ton. 

Train-Load. 

Excess  of  Actual 

No.  of 
Record. 

Actual. 

Accord- 
ing to 
Table 
170. 

Load  over  Table. 

Name  of  Road. 

No. 
Cars. 

Kind  of 
Load. 

Tot.  I'd, 
inc.eng. 

Tons. 

Per 
Cent. 

1 

3 

3 

4 

5 

6 

7 

8 

9 

10 

XI 

X3 

13 

36.03 

28.0 

34-9 
97.8 

23.91 

32  62 
26.0 
34-52 
23-15 

33  0 

68.6 
ik 

12 

15 
15 
18 

3 

23-5 

16 

41 
20 

33-4 

20 

4 
5 

Loaded  flats. . 
ik           ki 

Loads 

Green  wood  . 

Passenger 

( 
17.9  tons...  -J 

Loads 

1 1  tons 

2i§4  tons 

Not  ascert'd.. 
k.          .^ 

Passenger.... 
it 

k .  • . 

276 

330 
362 
422 
112 
480  1 
to  516  j 

354 
847 
503 
662 
468 

143+ 
163+ 

243 

k4 

339 
273 
102 

450  •{ 

330 
443 
333 
497 
350 
178 
178 

33 
87 
23 
149 
10 

30 
to  66 

24 
404 
170 

165 
118 

-35 
-15 

13-5^ 

35-8^ 

6  8^ 

54-6^ 
9.8^ 

6.7^ 
to  14.6 

7-3^ 
91-55^ 
Sio% 
33-2^ 

33-7^ 

—  19.6% 

-  8.4^ 

Macon  (Ga.)  &  B. 

W.  Ala. 
Macon  &  Br. 
Sp.,U.&C.(S.Ca.). 

j-  Atl.  &  W.  Pt. 

Atl.  &  Charlotte. 
Kansas  Pacific. 
Mo.,  K.  &  Tex. 
Long  Island. 
Ate,  T.  &  S.  ¥6. 
Cumb.  &  Penna. 

k.                              tk 

the  effect  of  curvature,  as  noted  below  this  table,  on  next  page. 
Engines. 


14- 

16. 

»7- 
18. 
19. 

30. 
21. 
23. 

23- 
24- 

^5- 
36. 

27 


29.21 

30.0 

34 

38-3 

14 

69.36 

39-15 

18 

44 

15 

330 

48 

17.85 

40 

55  73 

•  • 

38-79 

•  • 

55-73 

.  • 

38.79 

39.06 

22 

43-23 

22 

Eng.,  pass... 
Heavy  loads. 


21  tons , 


Empties. 
Loads . . . 


18  tons, 
ik 


577-2 
387.8 

462 
450 

372 

372 

207.4 

452 
410 

496-3 
945-2 

205 

389 
389 
463 
855 

331.2 
448-8 
189 
to  292  f 

274 
393 

274 

3155 

393 

472 

409 

472 

370 

(-62) 
o 
2 

63 
21 

33 
90 

57 
56 


-77 

63 

102 


24.9^ 

-13-7^) 
o 

x.o% 
16.1^ 

5.3J 

7-2^ 

10.4^ 
20.8^ 
14.2^ 


- 19.85^ 

15-3^ 
37.8JS 


Del..  L.  &  W'n. 

Norway. 

West.  Md. 

C.&  Fogelsv.(Pa.) 

Youghiogheny. 
ik 

B.,  N.  Y.  &  Phila. 

k.  ii 

Lehigh  Valley. 

kk  i4  ' 


St.  L.  &  San  Fran. 
it  it 


Engines. 


38. 

^. 

30. 

31- 

32. 

33- 

34- 
35- 
36. 
37- 
38. 

39- 


40.3 

45 

234 

28 

28.0 

31 

ii 

25 

34.7 

28 

tt 

i    9 

(45 

36.8 

»7 

44.0 

37 

28.08 

28 

28.1 

. . 

34-5 

30. 13 

.  40 
I45 

Empties.  ...< 

Load  of  coal., 
Loads. 


Loaded  . 
Empties. 
23  tons. . 

t5  tons  . 
oaded  . 


:::} 


>-  Loaded  . .  -j 


.390 -4 
395.8 

\    ^^^1 

573-3 

605 

481 

536 

561 

536 

679 

637 

665 

637 

452 

428 

418.5 

358 

709 

588 

665 

587 

544-1 

479 

825  1 
910  f 

820 

17 

23 

o± 
-45 
25 
42 

28 

24 
60 
121 
78 
65 

o± 


5-4^ 

0 

-8  A% 

A.1% 

6.6% 

4-4^ 

5-6^ 

16.7^ 

20.5^ 

13.2^ 

^zM 

0 

Sharpsville. 
ti 

Western  Ala. 

k  *  kk 

T.  H.  &  Ind'olis. 


E.  T.,  Va.  &  Ga. 

E.  Kentucky. 

F.  &  Pere  Marq. 
Mo.,  K.  «&  Tex. 


C.  &  Talc.  (Chili). 


ill!  I 


440 


CHAP.  XI.^LOCOMOTJVE    TRACTIVE  POWER, 


Table  138. — 
Consolidation 


No.  of 
Record. 


40. 


41. 

4a 

43- 

44. 
45- 
46. 

47- 
48. 

49 
50. 

5«- 
53 

53- 

54 

55- 

56 

58. 

59- 
60. 
61. 
6a. 
63. 
64. 
65. 


Cylin- 
ders. 
Inches. 


20x24 
tt 
«> 
tt 
ti 
t( 
it 
ti 
i< 
(t 
ti 
it 
it 
it 
ti 
it 
it 
ti 
it 
it 
it 
ii 

31x24 
»i 

Ii 

it 


Wbight  of  Engine. 
Tons,  2CXX)  lbs. 


En- 
gine. 


45-8 

ii 
ii 
tt 
it 
tt 
ti 
it 
It 
II 
It 
It 
ii 
it 
It 
it 
it 
It 
It 
it 

60.0 

ii 

tt 
tt 


Ten- 
der. 


36.3 
26.0 

4» 
ti 
it 
ii 
ii 
ii 
it 
tt 
tl 
(I 
It 
ii 
ii 
II 
ii 
ti 
ti 
It 
tt 
ti 

0.0 
II 

11 

tl 


On 
Drivers 


39  7 

44.0 

It 
It 
it 
it 
it 
It 
11 
It 
ii 
it 
it 
ii 
t. 
It 
ii 
tl 
ti 
it 
tt 

50.0 
tl 

ti 

it 


Tractive 
Power, 

Adhesion. 
Lbs. 


19.850 

32,000 
II 

Ii 

t« 

it 

it 

tt 

it 

tt 

tt 

it 

it 

it 

tt 

it 

t« 

tt 

tl 

tt 

it 

it 

95,000 
tl 

It 

it 


Character  of 
Performance. 


Grade. 
Feet 
Per 

Mile. 


Regular  service. 


>i 
II 


do.  (fair  average  work.)  . 


Regular  load 

Occasional  load .... 

Trial  trip  

Daily  service 

Using  sand 

Regular  service  (?). 

Maximum  load 

Usual  •'     

Maximum    "     .... 

Usual 

Maximum 

Usual 

Average  of  5  years. 


it 
ii 


Daily  service. 


ti 

11 


II 
tl 

it 


Maximum. 


0  +  6 

96 
145  -}- 10 

116  --  xo 

64  -  -  28 

96  4-  »o 

45  +  3 
171 

23 
126 

II 

If 
96-t- 10 

96 

130 

68.6 

67.6 

53-4 
105.6 
184.8 
316.8 


The  caboose  is  included  in  the  gross  loads  given  when  used  on  train,  although  not  in- 
cluded in  list  of  cars.  ^     T,  ,J    .     T 

The  assumed  ratio  of  adhesion  used  in  this  volume  (as  also  by  the  Baldwin  Locomo- 
tive Works)  is  M-  The  percentage  by  which  the  calculated  load  taken  from  Table  170 
exceeds  or  falls  below  the  computed  load  may  be  estimated  by  the  following : 

An  assumed  adhesion  of  1  would  increase  the  calculated  load  334  per  cent. 


(( 


tl 


(I 


«»  t      •«     decrease 


it 


20 


i( 


The  principal  cause  of  the  fluctuations  between  the  actual  and  computed  loads,  how- 
ever lies  in  the  fact  that  the  reported  gradients  are  not  the  actual  de-facto  gradients  for 
operating  purposes,  but  are  increased  in  effect,  in  some  instances,  by  uncompensated  curva- 
ture or  stopping-points  on  the  maximum  grade,  and  diminished  in  others  by  the  use  of 
momentum  to  assist  in  surmounting  them.  No.  8  (Kansas  Pacific)  and  No.  9  (M.,  K.  &  T.> 
are  conspicuous  instances  of  the  latter,  the  loads  reported  as  hauled  being  beyond  all 
probability  for  de-facto  grades  of  the  given  rate.  Nos.  2,  4,  10,  11,  14,  and  27  are  prob- 
ably less  conspicuous  instances  of  the  same  use  of  momentum  \.o  practically  reduce  grades 
below  the  profile  rate.  In  Nos.  27,  39.  61  this  was  expressly  stated  to  be  the  case,  and 
(the  length  of  the  grade  being  given)  the  corresponding  de-facto  grade  per  mile  was  com- 


CHAP.  XI.'-LOCOMOTIVE   TRACTIVE  POWER. 


441 


Continued, 
Engines. 


No.  of 
Record 


40 

41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 
61 
63 
63 
64 
65 


Resist- 
ance. 
Lbs. 
Per 
Ton. 


zi.o 

44  36 
66.71 

55  72 
4*  85 

48- 15 

26.18 

72.8 
II 

16.71 
55-73 

36 -79 

48  15 

ii 

44-36 
57-24 
34-14 
33  76 
26.56 
48. 
78. 
128. 


Train-Load. 


Actual. 


No 
Cars. 


Kind  of 
Load. 


^^^'•''li  Loaded 
I  90.31  S 


23 

26 

15 
40 

33 
35 
47 
32 

100 

35 

25 

140 

100 

40 

35 
100 

30 
29 
30 
40 


7 
9 


Loaded  . 
Empties. 
Loaded  . 


it 

ii 


Empties 

Load,  4-wh. . . 

4-wh.,  coal.... 
II        II 

Empty  4-wh.. 

41  Ii 

Load,  4-wh... 

ti         II 

Empty  4-wh. . 

Load,  4-wh... 

i5-ton  load. .. 
ii        Ii 

. . . 

Loads 


Loads . 


Tot.  I'd, 
inc.eng. 


1720  I 
1886  f 

438.4 
298.6 
405.2 
478 
375-7 
393-7 
1100 
264 

309 
1 144 

445-5 
340.2 
610. 1 
458.8 
498.1 
445-5 
457-8 
392.8 
752 
776 
1005 
542  5 
318.5 
210.5 

254 


Accord- 
ing to 
Table 

170. 


1804 
496 

330 
394 
513 
456 
456 
840 
302 
302 
13*0 
394 
394 
600 
600 
487 
487 
496 

384 
644 

653 
828 
520 
320 
195 
195 


Excess  of  Actual 
Load  over  Table. 


Tons. 


o± 


-58 

-31 

9 

—35 

—80 

-62 

260 

-38 

7 

—  176 

52 

-54 
10 

-141 
II 

-41 
-38 

9 
108 

123 

177 

22 

—  I. 

16 

59 


Per 

Cent. 


■11.7^ 

-  9-4^ 
2.3^ 

-  6.6^ 

■17-4^ 

-13.7^ 

31.05C 

-12.6jf 

2.3^ 

-13-3^ 

13-1^ 

-13.7^ 

-23-5?^ 
2.3^ 

-  8.4;« 

-  7-7^ 
2.45« 

16.8^ 
18.8^ 
21.4^ 

4-2jt 

o 

8.2^ 

30-3^ 


Name  of  Road. 


Ph.  &  Erie. 

Dom  Pedro  II. 

Tyrone  Br.,Penn. 
Ii  II 

Lehigh  &  Susq. 
Lehigh  Valley. 

i.  ii 

Missouri  Pacific. 

Cumb.  &  Penna. 
ii  ii 

Central  N.  J. 
Lehigh  Valley. 


ti 
it 
It 
it 


it 
It 
«t 
ii 
it 


Chic,  Burl.  &Q. 
tl  ii 

II  II 

Ate,  T.  &  S.  Ftf. 


it 
it 


it 
tl 


puted  and  used  in  computations,  the  reduction  being  indicated  by  a  —  sign  in  the  column* 

of  grades. 

On  the  other  hand,  most  of  the  instances  in  which  the  reported  performance  is  less  than 
Table  170  calls  for  are  to  be  explained  by  high  speed  or  by  uncompensated  curvature, 
except  under  Consolidation  engines,  where  the  character  of  the  trains  (chiefly  4-wheel  coal 
cars)  had  no  doubt  equal  or  greater  effect  to  diminish  the  load. 

Curvature  was  assumed  to  add  only  1  ft.  per  mile  (0.38  lb.)  per 
degree  of  curvature  up  to  10°  curves,  and  2  ft.  per  mile  per  degree  for  sharper  curves,  when 
expressly  stated  to  constitute  an  addition  to  the  grade,  and  this  addition  is  indicated  by 
the  sign  -|-  in  the  column  of  grades.  A  very  low  rate  was  assumed  in  order  that  tiie 
comparison  of  actual  and  theoretical  loads  might  be  more  certainly  trustworthy. 

From  the  above  table  we  may  conclude  that  if  the  given  grade  be  the 
de-facto  grade  for  operating  purposes,  with  all  effects  of  curvature  and  velocity  elim- 
inated, an  assumed  adhesion  of  one  fourth  the  weight  on  drivers  and  a  rolling 
friction  on  tangent,  at  15  miles  per  Jiour,  ofS  lbs.  per  ton  {the  latter  being  somewhat 
more  than  ample)  will  give  very  approximately  TUTS,  safe  operating  load  IN  REGU- 
LAR SERVICE.  . 

A  long  list  of  further  records  of  performance  the  writer  omits  to  save  space.  Quite  a 
number  of  them  show  more  than  %  adhesion  realized  as  an  average  of  long  runs,  but 
not  as  every-day  {>erforraances. 


ft 


442  CHAP.  XI.^LOCOMOTIVE   TRACTIVE  POWER, 


certain  deduction  to  be  made  from  the  apparent  gain  because  of 
the  increased  tractive  train  resistance  caused  by  the  sand  on  the 

rails 

633.  The  third,  and  most  important  limit,  that  of  ordinary 
working,  is  warranted  by  the  all  but  universal  evidence  of  mod- 
ern experience,  as  sufficiently  proved  by  Table  138,  which  gives  a 
long  record  of  actual  performances  with  locomotives,  taken  chiefly 
from  the  very  abundant  data  given  in  the  catalogue  of  the  Bald- 
win Locomotive  Works,  and  including  all  the  records  therein. 
The  ratio  of  \  is  used  by  them  as  the  basis  for  computing  the 
table  of  capacity  on  various  grades  given  in  their  catalogue,  and 
thus  in  a  measure  guaranteed  by  them,  and  the  high  character 
and  great  experience  of  that  firm  entitles  this  fact  to  far  more 
than  the  usual  weight  which  would  be  accorded  to  manufac- 
turers* evidence. 

534.  Many  causes  combine  to  make  the  apparent  mdications 
•of  practice  very  variable.  One  of  the  most  important  is  that 
the  nominal  ruling  gradient  is  not  the  real  or  -  virtual"  one, 
being  in  some  cases  higher  than  the  virtual  grade,  because  the 
rulin'^g  grades  are  short  and  surmounted  in  part  by  momentum  ; 
and  in  others  (and  far  more  commonly)  lower  than  the  virtual 
grade,  because  of  the  necessity  of  stops  on  unreduced  gradients, 
or  of  unreduced  curvature  on  the  ruling  grade,  thus  materially 
increasing  the  nominal  maximum:  so  that  if  we  assume  the  grades 
of  the  profile  to  be  the  virtual  grades,  the  trains  hauled  will  ap- 
pear to  be  only  such  as  are  due  to  \  adhesion,  or  even  less. 

On  very  low  gradients  this  is  especially  true;  and,  moreover, 
another  cause  comes  in— the  difficulty  of  starting,  making  up, 
and  handling  very  long  trains.  From  this  it  results  that  we 
very  rarely  indeed  hear  of  trains  being  hauled  on  very  easy 
grades  such  as  are  beyond  all  question  within  the  power  of  the 
locomotive  under  conditions  which  are  as  fair  actually  as  they 
are  nominally.  But  when  these  errors  are  eliminated  it  will  be 
found  that  in  all  cases,  in  good  American  practice,  the  actual 
ratio  of  adhesion  is  ^  whenever  it  is  attempted  to  load  the 
engines  to  their  full  capacity. 


CHAP.  XL— LOCOMOTIVE    TRACTIVE  POWER. 


443 


635.  The  fifth  ratio  of  adhesion,  \,  apparently  applies  to 
winter  loads,  and  will  actually  give,  in  most  cases,  the  loads 
which  are  hauled  in  practice  in  winter.  It  is  usually  assumed 
that  this  difference  is  due  to  the  fact, that  the  ratio  of  adhesion 
is  less  in  winter  than  in  summer,  but  it  appears  probable  that  in 
reality,  as  we  shall  see  (par.  632),  it  is  due  to  an  increase  in  the 
rolling  friction,  both  because  of  greater  axle  friction  and  because 
of  the  poorer  condition  of  the  track. 

636.  In  the  former  edition  of  this  treatise  \  instead  of  \  was  as- 
sumed as  the  ordinary  working  ratio  of  adhesion.     This  was  deduced 

Table  139. 

Comparative  Ratios  of  Adhesion  of  American  and  Foreign 

Locomotives. 


Conditions. 


Maximum  at  slow  speeds  and  under  favor- 
able conditions 


Working  maximum 

Ordinary  apparent  adhesion, 


Ratio  of  Adhesion. 


Foreign  Engines. 


i  or  0.25 

(      ^  or  0.20  to 
\     i  or  0.17 

\  or  0.14 


American  Engines. 


tor  0.33 
i  or  0.25 
^  or  o .  20 


Many  European  engineers  assume  f,  or  even  less ;  but  many  American  engineers,  in 
like  manner,  assume  \. 

From  a  summary  by  Mr.  O.  Chanute,  in  "  Haswell's  Pocket-Book,"  we  may  abstract 

the  following  data  as  to  early  and  European  tests  of  adhesion  : 

Ratio  of  Adhesion. 

Mr.  Wood  on  early  English  railways  (per- J  Slm^ormTd^y  rails! ::::::::::  V<^ 

haps  the  earliest  tests  on  record) |  Very  greasy  rails    0.04 

B.  H.  Latrobe  on  B.  &  O.  R.  R.    1838 Safe  working  limit 0.13 

(Maximum 0.20 

Modern  European  practice •<  Minimum o.ii 

Soemmering  line 0.16 

Italian    Alpine   road,    subject    to    frequent      Maximum  in  open  cuttings 0.12 

mists *l  Maximum  in  tunnels o.io 

Dry  weather -j  oJo^^ciSS 

Damp  weather \   °'  j^* 

Prench  experiments.  1862-67  by  Messrs.  Vuil-  J  |      ■  39 


lemin,  Guebhard,  and  Dieudonn^. 


Wet  weather. 


39 
0.078 
0.164 

Light  rain 0.09 

Rain  and  fog    0.14 

Heavy  ram 0.16 


The  last  records  are  of  dubious  value.  Mr.  Chanute  gives  a  table  of  average  European 
and  American  practice,  which  differs  somewhat  from  the  above,  but  seems  open  to  ques- 
tion in  several  details. 


M 


444 


CHAP.  XL-'LOCOMOTIVE   TRACTIVE  POWER. 


by  comparison  of  the  actual  loads  hauled  on  various  nominal  grades  by 
the  same  engine.  Besides  the  causes  just  mentioned,  however,  which  tend 
to  make  this  process  inaccurate,  within  the  nine  years  from  1876  to  1885 
a  very  great  change  has  taken  place  in  the  average  train-loads  hauled  on 
American  railways,  as  shown  in  Tables  30  to  33.  and  others.  Much  of 
this  is  due  to  the  use  of  heavier  engines,  but  a  great  part  of  it  is  due  to 
greater  care  to  load  engines  to  their  full  capacity. 

537.  The  adhesion  of  English  and  other  foreign  locomotives  is  ordi- 
narily stated  at  less  than  of  American  by  a  considerable  percentage. 
Table  139  approximates  closely  to  the  difference  which  appears  to  exist. 
How  much  of  this  represents  an  actual  difference  of  capacity  and  how 
much  is  due  merely  to  difference  of  administration,  it  would  be  impos- 
sible to  say ;  but  there  is  no  room  for  doubt  of  the  fact  that  foreign 
engines  haul  lighter  trains,  as  a  rule,  than  American  engines  of  the 
same  weight,  or  that  European  engineers  state  the  limit  of  their  ad- 
hesion at  less  than  that  given   by  American   engineers  for  American 


engines. 


""ines. 

538.  If  we  may  assume  that  the  loads  hauled  by  the  same  engine  on 
any  two  grades  are  affected  only  by  the  difference  in  the  grades  (which 
ordinarily  we  cannot,  except  very  approximately),  we  may  at  once  deter- 
mine from  the  records  of  these  loads  the  rolling  friction  and  ratio  of 
adhesion,  as  follows ; 

Let  L  and  L'  =  the  gross  load  (including  its  own  weight)  hauled  by  the  same 
engine  on  any  two  grades,  i'  and  ^'. 

Let  X  =  the  total  resistance  per  ton  on  the  lowest  grade  g,  and  d  -  the  an 
ference  in  resistance  per  ton  on  grades  ^  and  /  (being  that  due  to  gravity  only, 
and  equal  to  the  resistance  from  gravity  on  a  grade  of/  - g). 

Then 


whence 
Then  we  have 


Lx  =  L'(x-{-d), 
L'd 


Rolling  friction       =x-  resistance  from  gravity  only  on  grade  g. 

Traction  of  engine  =  xL 

traction 

Ratio  of  adhesion    =  "^t^  ^„  driZ^' 

But  while  these  formula  are  theoretically  correct,  results  determined  by 
them  are  to  be  accepted  as  reliable  only  with  great  caution.  If  the  reported 
low  grade  loads  are  too  small,  as  they  usually  are.  the  effect  will  be  to  greatly 
increase  the  apparent  rolling  friction.  ^      .     r-      ^^ 

539.  Owing  chiefly  to  some  misinterpreted  experiments  made   in  France 


CHAP.  XL— LOCOMOTIVE    TKACTLVE  POWER. 


445 


^ome  years  ago  by  a  M.  Rabeauf,  a  chief  engineer  of  the  Corps  des  Ponts  et 
Chaussies,  there  has  for  some  time  been  some  available  authority  to  show  that 
there  may  be  such  a  thing  as  **  imperceptible"  or  continuous  slip  in  the 
driving-wheels  of  locomotives  in  motion.  Such  a  thing  is  really  impossible, 
but  the  impression  that  it  occurs  has  become  widespread,  and  mere  assertions 
in  support  of  it,  or  allusions  to  it  as  a  well-known  fact,  exist  without  number. 
The  experiments  referred  to,  from  which  this  wholV' imaginary  discovery  seems 
to  have  originated,  were  described  in  a  paper  in  the  Annates  du  Genie  Civil 
(1876),  in  which  the  record  was  given  of  tests  of  a  fast  passenger  engine  for  the 
Northern  Railroad  of  France,  having  four  coupled  drivers  6  ft.  10  in.  diameter, 
carrying  2Jb\  tons  on  a  grade  of  0.5  per  cent  (26  ft.  per  mile),  with  good  rail  and 
weather,  and  121  lbs.  per  square  inch  boiler  pressure.     The  repc^rt  continues: 

• 

"  Under  these  conditions  the  locomotive,  which  was  tested  alone  (hauling 
no  train  behind  it),  attained  a  speed  on  the  down  grade  of  74^  miles  an  hour, 
corresponding  to  303  revolutions  of  the  drivers  per  minute.  Now,  the  regis- 
tered number  of  revolutions  was  360,  corresponding  to  88.8  miles  per  hour — a 
slip  of  19  per  cent. 

"Surprised  at  these  results,  the  writer  repeated  the  same  observations  on 
a  certain  number  of  locomotives  of  different  types,  comparing  the  speed 
with  the  revolutions  of  the  drivers.  It  was  generally  found  that  the  slip  was 
slight  on  an  up  grade,  but  very  apparent  on  a  down  grade,  ranging  from  13  to 
25  per  cent.     It  increased  rapidly  with  the  speed." 

This  evidence  appears  pretty  conclusive,  especially  as  other  articles  and 
paragraphs  to  the  same  effect  have  appeared  from  time  to  time,  accompanied 
by  various  reasons  why  the  centrifugal  force  of  the  counterweights,  and  what 
not,  must  have  the  effect  of  producing  it. 

540.  As  a  result  of  these  tests  it  was  concluded  that  "  common  locomotives" 
were  'actually  unsuited  for  speeds  of  60  to  75  miles  per  hour,"  because  the 
slippage  was  as  much  as  20  per  cent.  In  a  specific  instance  (the  Uetliberg  road) 
referred  to  in  the  paper  it  was  said  that  on  grades  of  7  per  cent  (370  ft.  per 
mile;  less  by  i  per  cent  than  is  now  successfully  operated  in  Colorado,  and  less 
by  3  per  cent  than  was  successfully  operated  on  temporary  lines  by  the  late 
Benj.  H.  Latrobe)  "the  slip  of  the  driving-wheels  was  found  so  considerable 
that  the  gear  system  was  found  more  economical."  in  spite  of  the  slow  speed. 

541,  On  the  other  hand,  tests  of  various  American  passenger  locomotives  at 
speeds  at  from  75  miles  per  hour  down,  made  by  Prof.  Chas.  A.  Smith,  Mr. 
Albert  F.  Hill,  and  Messrs.  Henry  Abbey  and  Oscar  H.  Baldwin  (see  Engineer- 
ing, Aug  ,  1885),  to  mention  no  others,  have  uniformly  indicated  that  no  such 
phenomenon  occurs  with  American  locomotives  under  any  circumstances. 

There  is  an  undoubted  possibility,  so  far  as  this  evidence  alone  is  concerned, 
that  the  phenomenon  might  not  occur  with  American  locomotives,  and  might 
occur  with  differently  constructed  foreign  locomotives;  but  in  addition  to  the 
:grave  reasons  for  questioning  the  physical  possibility  of  the  assumed  phenom- 


CHAP.  XL— LOCOMOTIVE    TRACTIVE  POWER. 


AA^  , 

enon,  as  being  contrary  to  what  is  known  in  other  ways  of  the  laws  of  fiiction^ 
it  is  not  difficult  to  see  how  the  alleged  slipping  may  have  occurred  and  yet 
have  been  in  no  respect  "imperceptible"  slip,  nor  different  in  any  way  ixora, 
ordinary  slipping,  which  is  perceptible  enough. 

542,  When  a  locomotive  is  only  moving  itself,  especially  if  running  down 
a  grade,  and  so  having  little  work  to  do,  and  when  all  possible  power  is  put  on' 
to  run,  in  literal  truth  "  as  fast  as  the  wheels  can  turn,"  whether  the  wheels  are 
slipping  or  not  will  make  no  very  conspicuous  difference  in  their  speed  of  revo- 
lution; while,  on  the  other  hand,  the  work  required  of  the  locomotive,  simply 
to  keep  up  speed,  will  be  so  small  that,  when  the  wheels  once  begin  to  slip,  the 
loss  of  power  will  not  be  so  great  as  to   prevent  the  acquirement  and  mainte- 
nance of  very  high  speed,  although  they  will  continue  to  slip  indefinitely,  never- 
theless.    On  the  other  hand,  with  a  traifl  of  even  one  car  behind  the  engine  no 
high  speed  could  probably  be  maintained  under  such  conditions,  for  the  mini- 
mum power  to  maintain  the  speed  would  then  be  so  great  that  the  speed  would 
be  immediately  checked,  and  make  it  clear  to  the  senses  that  the  wheels  were 
slipping.     Whenever  the  locomotive  was  running  up  any  considerable  grade  it 
would  be  still  less  possible;  and  the  cautious  statement  quoted  above,  that  it 
was  "generally  found"  that  "the  slip  was  slight"  on   an  up  grade,  probably 
means  that,  as  a  matter  of  fact,  no  absolute  evidence  of  any  slip  was  detected, 
or  the  figures  for  it  would  have  been  given. 

543.  To  make  the  true  explanation  of  the  phenomenon  clearer:  Suppose, 
when  the  wheels  of  a  freight  engine  were  slipping,  while  it  was  standing  still, 
that  the  engine  were  simply  uncoupled— instead  of  shutting  off  steam  in  the 
usual  fashion.     If  the  grades  were  not  too  unfavorable  the  engine  would  prob- 
ably start  ahead,  the  wheels  still  slipping;  and  if  all  the  steam  were  put  on,  on 
a  favorable  down  grade,  a  velocity  of  "  74^  miles  per  hour"  might  possibly  be 
obtained,  with  an  "imperceptible  slip"  of  20  per  cent.     These,  or  something 
like  these,  are  probably  the  conditions,  and  the  only  conditions,  under  which 
the  phenomenon  has  ever  been  observed,  and  they  correspond  to  nothing  in  the 
worst  extremes  of  practical  operation.     The  only  thing  really  proved  by  such 
"tests"  is  that  even  the  wheels  are  slipping  in  ordinary  fashion  they  will  kick 
hard  enough  against  the  rails  to  make  an  unloaded  engine  move  down  a  grade 
at  a  very  lively  pace;  which  illustrates  how  easy  it  is  to  draw  wrong  conclusions 
from  observed  facts. 

544.  The  effect  of  the  CENTRIFUGAL  FORCE  OF  THE  COUNTERWEIGHTS 

of  the  locomotive  to  modify  the  pressure  of  the  wheels  on  the  rail  is  con- 
siderable, and  especially  on  bridges  very  important,  but  as  respects  its 
effect  on  the  adhesion  it  is  less  important,  if  indeed  it  can  be  said  to  be 

of  any  importance. 

The  counterweights  are  weights  added  to  balance  the  piston  and 
other  reciprocating  parts,  and  thus  prevent  serious  disturbance  of  the 


CHAP.  XL— LOCOMOTIVE    TRACTIVE  POWER. 


44r 


Fig.  108. 


motion  of  the  engine.  They  are  either  cast-iron  weights  between  the 
spokes  of  the  drivers  or  lead  poured  into  hollows  in  the  wheel-centre^ 
and  have  the  effect  to  make  the  wheel  lop-sided.  When 
the  counterweights  are  in  the  position  a.  Fig.  108,  their 
centrifugal  force  will  be  so  much  added  to  the  weight  car- 
ried by  the  wheel,  and  increase  its  pressure  on  the  rail  by 
so  much.  When  they  are  in  the  position  a',  at  the  top  of 
the  wheel,  the  centrifugal  force  will  decrease  the  pressure 
on  the  rail.  When  they  are  in  the  position  d  and  d'  the 
centrifugal  force  will  have  no  vertical  effect. 

As  respects  freight  engines,  especially  when  the  engine  is  working 
hard  enough  to  be  in  any  danger  of  slipping  the  wheels,  the  speed  is 
ordinarily  so  slow  that  the  centrifugal  force  of  the  counterweights  is  all 
but  imperceptible.  As  respects  passenger  engines,  the  counterweights 
can  at  worst  exert  no  appreciably  injurious  effect  upon  the  adhesion,  for 
the  reason  that  the  possible  boiler  tractive  power  decreases  with  speed 
very  much  faster  than  it  can  be  diminished  by  any  possible  effect  of  the 
counterweights. 

545.  But  while  this  phenomenon  has  no  measurable  effect  upon  the  adhe- 
sion, and  is  not  likely  to  have  a  very  serious  effect  upon  the  track,  it  may  and 
does  have  such  effect  on  bridges.  The  sharp  variation  which  takes  place  in 
the  load  on  the  rails  has  no  effect  on  the  riding  of  the  engine,  since  it  does  not 
act  through  the  springs.  But  it  does  give  to  the  rail  what  has  been  not  inaptly 
termed  a  "hammer-blow;"  and  its  effect  on  bridges  (especially  on  over  light 
bridges;  see  Chap.  XXIII.)  is  visi- 
ble in  the  striking  diagrams  repro- 
duced in  Figs.  101-108,  which  show 
how  very  greatly  the  oscillations 
of  bridges  are  increased  when  the 
period  of  revolution  of  the  drivers 
happens  to  coincide  with  the  period 
of  oscillation  of  the  bridge. 


JRWwrvvwvYy 


IT:  173. 


Figs.  109-1 16  are  from  observations 
on  the  vibration  of  bridges  by  Prof.  S. 
W.  Robinson.  They  show  the  vertical 
and  lateral  vibrations  of  the  panel 
point  nearest  the  middle  of  its  lower 
chord  during  the  entire  passage  of  the 
train. 

The  upper  line,  AB,  shows  the  ver- 
tical movements,  and  the  lower  one, 
MNy  the  lateral  movements.     The  lowest  one,  XY^is  a.  line  of  reference. 


^r»v^l^^w^nn^^^o^ 


—M ^-- 


Figs,  ioq,  ho.— Effect  of  Passage  of  Fast  Pas- 
senger Trains  (40.8  and  42.1  Miles  per  Hour) 
OVER  Through  Pratt  Truss,  148  Ft.  Shan. 


As  a  train 


448  CHAP,  XL-^LOCOMOTIVE    TRACTIVE  POWER, 


CHAP.  XL— LOCOMOTIVE  POLLER. 


449 


T^ 


Figs.  iii-«i6.— Vibrations  Produced  in  the 

SAME  BrIDCB  by  THE  PASSAGE  OF  VARIOUS 

Freight  Trains  at  Various  Speeds. 

Vertical  Scale  three  fourths  of  actual  move- 
ment. 

[Through  Pratt  Truss  Bridge,  New  York, 
Pennsylvania  &  Ohio  Railroad,  near  Leav- 
ittsburg,  O.,  141  feet  span,  24  feet  deep,  9 
panels,  15  feet  8  inches  each.  Kind  of  engine 
and  train  and  speed  given  in  each  diagram. 
The  scale  below  "  Length  of  Train"  shows 
the  revolutions  of  the  drivers.] 


T  ^1  L  »_jai.i-i-i-iJj.J.  i-»-L-i  j-Li-.LL.i-i.  ^ 


approached  the  indicator  was  started,  making  the  straight  lines  to  the  left  oi  AM  and  ^. 
As  the  train  struck  the  bridge  lateral  motion  of  the  pencils  began,  and  it  will  be  seen  that 
in  all  cases  the  deflection  was  greatest  within  a  second  or  two  after  the  locomoUve  had 
entered  upon  the  bridge,  or  about  when  the  whole  of  the  engine  and  tender  was  fairly  on 
the  bridge,  and  long  before  it  had  reached  even  the  middle  point  of  the  bridge. 

The  hollow  in  the  diagrams,  which  immediately  follows,  showing  a  reaction  from 


this  extreme  depression,  indicates  clearly  that  the  latter  is  a  dynamic  effect,  the  sudden 
depression  caused  by  the  entrance  of  the  load  setting  the  bridge  in  motion  downward  so 
quickly  that  its  momentum  carries  it  down  far  below  what  even  much  greater  static  strains 
are  able  to  maintain.  It  is  probable  that  bridges  of  longer  span  and  greater  weight  would 
show  this  effect  much  less  markedly. 

The  length  of  train  and  also  a  scale  (on  the  right  line  between  A  and  B)  on  which  the 
revolutions  of  the  drivers  are  indicated  has  been  added  to  the  originals. 

It  will  be  seen  that  in  every  instance  the  vibrations  of  greatest  magnitude  are  almost 
exactly  synchronous  with  the  drivers'  revolutions,  but  as  the  vibrations  decreased  they  be- 
come less  so,  and  when  the  vibrations  become  a  mere  wavy  line  there  is  no  observable 
connection  whatever  with  the  drivers'  revolutions. 

.  The  difference  in  the  effect  of  passenger  and  freight  trains,  or  of  different  construc- 
tion and  speed,  as  shown  by  comparing  Figs.  115-16  with  Figs.  109-10,  is  very  noticeable 
and  curious. 

THE  LOCOMOTIVE  BOILER. 

546.  To  burn  more  than  80  lbs.  of  coal  per  square  foot  of  grate  per 
hour  is  sure  to  decrease  the  efficiency  of 
combustion,  although  as  much  as  100  lbs. 
may  be  burned  under  favorable  conditions, 
with  fair  economy.  When  combustion  is 
pushed  beyond  this,  as  it  not  unfrequently 
is,  sometimes  even  so  far  as  to  apparently 
double  it,  it  is  all  but  certain  that  a  large 
proportion  of  the  additional  coal  supply  will 
be  ejected  at  once  from  the  smoke-stack, 
unconsumed.     As  much  as  20  per  cent  of 

the    entire    coal    put    into    the    fire-box   has    Fig.   117.— Lump   of   Unconsumed 
,,  ,      .     ^,       ^^^i,«  K^v    nnA        Anthracite  Coal,  Natural  Size, 

been  actually  caught  in  tne  smoKe-oox,  ana      ejected  from  the  Smoke-stack 

.      -^     «.U„4.   «,Uon    m r»r^   tVl an     l  in  OF  AN  EXPRESS  LOCOMOTIVE    WITH 

It  IS  quite  certain  that  When  more  tnan  130      ^^^^   ^^^^^    ^^    ^^    ^^^^    ^^ 
to   ICO  lbs    oer  square   foot  are  "burned"      through  the  Open  Window  m 

10    i^u   lus.    pci     34    a                             ,             ,      .  THE  Second  Car  in  THE  Rear. 

nearlv  the  whole   of  the  excess   of  supply  is  (This  lump  was  picked  up  by  Mr. 

•'^             ,             ^   t-1          /r\        T?-         ,«        -4.1,  Geo.  W.  Parsons,  who  handed  It  to 

thus  ejected  (see   lable  140).       fig.  117.  Wltn  the  writer,  still  hot.    The  most  sali- 

its  accompanying  note,  gives  a  rather  exag-  J«  »i;ffb„T'SiS?iy'""o^rar'^er 
gerated  instance  of  what  is  continually  tak-   S'a^^^SJd^bmln'.l'umerabi^ 

incT  Tulare       The   minimum    waste   of   coal  in     smaller  ones.     The  lump  was  near- 
ing  pidCC.       1  lie    .  j^  ^  ^^^^      j^  partially  ignited   its 

this  way  is  probably  5  per  cent.  specific  prraviiy  would   have  been 

.  c         ^         much  reduced,  and    it  would  have 

647,   The   ordinary  evaporation  Ot   water    been  more   easily  carried    out    by 

per  pound  of  coal  burned  is  hardly  more   S^^he  p'ciae'^?""'"'"  "■°''"  "^ 

than  6  lbs.  in  this  country,  and  sometimes 

only  5  lbs.,  or  even  less,  although  it  rises  to  8  or  9  lbs.  in  some  cases, 

29 


('  , 


t. 


I; 


450 


CHAP.  XI.-^LOCOMOTIVE  BOILER. 


and  very  frequently  if  not  usually  does  so  abroad,  where  the  evaporation 
is  more  economical  than  is  common  here,  owing  in  great  degree  to  the 
combustion  being  less  pushed  by  the  hauling  of  heavy  loads,  and  in  part, 
probably,  to  more  skilful  firing.  Theoretically,  a  fair  ordinary  coal  (of 
14000  heat-units— not  by  any  means  the  best— see  Table  140)  ought  to 
ev'aporate  something  over  12  lbs.  from  water  at  60°  Fahr.  to  steam  at 
120  lbs.  pressure. 

Table  140. 
Heat-units  in  Various  Fuels. 


Pure  carbon  — , 

Pennsylvania  anthracite. . . 
Pittsburg  bituminous 

Illinois  coal  (pure  quality) 


Heat-units. 


Evap.  Power  (lbs.  water) 
from  and  at  313*. 


English  coal  (average).. 

English  coke  (average). 

Crude  petroleum 

Lignite 

Asphalt 


Dry  wood  (all  kinds) 


8,000  I 

10,000  s 

14,858  \ 
13,860  f 

14,150 1 
13,300  \ 


91834  \ 

I4»449  ) 


14,500 
i4»5oo 
14.200 

9,000 

14.330 

»3.550 
30,340 
11,678 

16,655 
7,79« 


X4-34^ 
X5-5a J 


(        13.73 t 


10.18  I 
14.96  f 


15.0a 
15.03 
14  69 

9.30 
-4.83 

14.03   lbs. 

aO.33    ** 
13. 10  •• 

«7.a4  " 
8.07  " 


The  heat  required  for  evaporation  •'from  and  at  212"  (i.e.,  the  conversion  of  water  at 
ai2»  into  steam  at  212-  or  atmospheric  pressure)  being  i.oo,  the  heat  required  to  turn 
water  at  normal  feeding  temperatures  into  steam  of  usual  working  pressures  is  as  foUows: 


Feed- 

Steam  Pressure  above  Atmosphere— Lbs 

• 

water. 
•  Fahr. 

20 

40 

60 

80 

100 

120 

140 

160 

40* 

6o» 

8o» 

lOO* 

1.193 
1.173 
1.151 
X.131 

1.303 
1.183 
1.161 
1.141 

1.309 
1.188 
1. 167 
1.147 

1. 314 

I  193 
1.173 

1.153 

1.319 
1.198 
1.177 
1.157 

1.333 

1.303 
I.181 
I.161 

1.336 
1.205 
1.184 
1.164 

1.339 
1.308 
1.187 
1.167 

(Abstracted  from  a  large  table  in  "  Steam-Making,"  by  the  late  Prof.  Charles  A.  Smith.) 

The  lowest  rates  of  evaporation  occur  with  the  highest  rates  of 
combustion,  and  vice  versa  ;  and  ordinarily  it  is  not  possible  to  evaporate 
more  than  600  lbs.  of  water  per  square  foot  of  grate  per  hour  (say  80  lbs. 
coal  X  7i  lbs.  evaporation  ratio,  or  100  lbs.  x  6)  for  any  length  of  time. 


CHAP,  XI,— LOCOMOTIVE  BOILER, 


451 


More  may  be  done,  but  it  cannot  be  relied  on,  and  500  lbs.  of  water  per 
square  foot  of  grate  would  come  nearer  to  a  moderate  working  maximum. 
548.  The  ordinary  load  on  drivers  per  square  foot  of  grate  ranges 
from  2500  to  4000  for  ordinary  types,  as  shown  in  Tables  127-130;  3000 
lbs.  being  rather  low  for  passenger  engines  of  the  American  type  and 
for  Consolidation  engines,  and  4000  rather  low  for  Mogul  and  Ten-wheel 
engines.  The  larger  proportion  of  grate  surface  in  the  Consolidation 
type  may  be  considered  as  in  part  a  concession  to  the  difficulty  in  firing 
such  engines. 

649.  The  steam  used  in  the  every-day  working  of  locomotives  (in- 
cluding the  entrained  water  carried  along  with  the  steam  mechanically)  to 
•do  33,000  fi.-lbs.  of  net  effective  work  is  somewhat  under  30  lbs.,  never, 
probably,  running  very  much  higher  than  that,  and  rarely  quite  as  low 
as  to  25  lbs.,  even  under  the  most  favorable  circumstances;  that  being 
the  lowest  fair  assumption  for  steam  used  at  slow  speeds  on  long  grades 
or  at  other  specially  favorable  points,  except  that  for  very  short  distances 
•considerably  more  than  that  may  be  shown,  owing  in  part  to  drawing  on 
the  small  reserve  of  power  in  the  boiler  (par.  553  and  Table  144). 

650.  Then,  as  the  production  of  steam  is  600  lbs.  per  square  foot  of 
grate  per  hour,  and  the  consumption  per  horse-power  per  hour  is  rarely 
better  than  25  lbs.  and  often  much  worse,  we  have  ^^  =  24  horse-power 
as  the  maximum  ordinary  capacity  of  one  square  foot  of  grate  area. 
Tables  146  and  147  will  indicate  that  this  is,  on  the  whole,  a  rather 
favorable  showing  for  what  can  be  actually  realized.  But  to  determine 
the  very  highest  maximum  which  can  be  claimed  in  the  way  of  locomo- 
tive performance,  we  may  appropriately  refer  to  Mr.  Wm.  Stroudley's 
paper  on  the  locomotive  performance  of  the  London,  Brighton  &  South 
Coast  Railway  (Trans.  Inst.  C.  E.  1885),  where  we  find  that  an  average 
of  about  600  indicated  horse-power  was  maintained  for  6  or  8  miles  in 
succession  by  an  engine  with  17.04  square  feet  grate  area,  with  an  aver- 
age horse-power  for  the  whole  run  of  50  miles  of  528.5,  corresponding  to 


Indicated  H.  P.  per  sq.  ft.  grate 


maximum 


600 


=  35-3  H.  P. 


average 


528.5  _ 


17 


=  31.1 


(( 


2iet  effective 


<« 


(10  per  cent  less),  say,  32  and  28  H.  P. 


In  round  figures,  30  effective  horse-powers  per  square  foot  maybe  said 
to  be  the  ultimate  limit. 

651.  The  horse-power  which,  if  it  could  be  produced,  might  be  trans- 


452 


CHAP,  XL— LOCOMOTIVE  BOILER. 


mitted  through  the  drivers  for  propelling  the  train  is  very  much  greater 
than  this  except  at  the  slower  speeds,  so  that  at  the  slower  speeds  onljr 
is  it  possible  to  utilize  the  full  adhesion,  as  may  be  determined  thus : 

Per  Square  Foot  of  Grate  Area. 

Usual  load  on  drivers,  as  per  Table  141.      3.000  to  4.000  lbs. 
Equivalent  tractive  power  for  \  adhesion,      750  to  1,000  lbs. 

Table  141. 

Load  on  Drivers  Per  Square   Foot  of  Grate  Area  for  the  Various 

Locomotives  given  in  Tables  127-130. 


Table  127.— American  Engines. 


Date. 


X873  .. 
1884... 
1884  .. 
1884... 
1884... 
1884... 

1884  . . 


Road  or  Maker, 
and  Cylinders. 


Mason,  17x24 

No.  Pacific,  17x24.. 
Brooks,  17x24 

C,  B.  &0.,  17x24- 

♦'        "       18x24. 

Mason,  18x24 

West  Shore  -j  3  *   • 


Lbs.  per 
sq. 


s.  pel 
J.  ft. 


Table  128.— Mogul  Engines. 


Date. 


a.440 
3.390 

2,920 

3.050 
3.070 
3.590 

i,88o* 

3.670 


1873... 
1883... 
1884... 


Road  or  Maker, 
and  Cylinders. 


Baldwin,  18x24 — 

Brooks,  i8  X  24 

Baldwin  (N.S.Wales),i8x26 


Lbs. 
sq. 


r 


4,120 

4,270 
4.650 


Table  129.— Consolidation  Engines. 

aox  24  cylinder*. 


Table  128.— Ten-wheel  Engines. 


1873  . . 
1883... 


Baldwin,  18x26 
Brooks,  19  X  24 


1875-6 

1886... 

1883... 


Penna.  "Class  I".. 

"       "  Class  R". 

West  Shore  


3.450 
3,210 
3.830 


Table  130.— Mastodon  Engines. 


Central  Pac,  19x30. 
Lehigh  V.,  20x26... 


4,120 
2.570* 


♦  These  engines  have  specially  large  grates  to  permit  of  slow  combustion. 


Then  the  horse-power  per  hour  per  square  foot  of  grate  area  which 
will  or  might  be  transmitted  through  the  drivers,  if  their  utmost  adhesioa 
be  utilized,  will  be — 

_    load  on  drivers  )  _    5280 ^  ^     ^^  -^^  ^^jj^g  ^^  hour. 

Max.  H.  r,  -  T^eff .  adhesion  (  33.000  x  60 

By  this  formula  Table  142  was  computed,  which  indicates  at  once  a 
truth  of  the  first  importance-that  it  is  absolutely  impossible  to  produce 
enoucrh  power  in  the  boiler  to  utilize  more  than  a  small  fraction  of  the 
available  tractive  power  at  any  of  the  higher  speeds,  and  it  is  only  as  we 
fall  below  1 5  miles  per  hour  that  it  becomes  possible  for  even  freight 
engines  to  do  so. 


CHAP,  XI.— LOCOMOTIVE  BOILER, 


453 


Table  142. 

Horse  power  of  Net  Effective  Work  required  to  be  Continuously 
Generated  Per  Square  Foot  of  Grate  Area  to  FULLY  utilize 
the  Entire  Tractive  Force  of  Various  Engines  at  Various  Ve- 
locities. 

Adhesion  assumed,  \.     Reduce  by  one-fifth  part  to  correspond  to  \  adhesion. 


Pounds  on  Drivers 
Pbr  Square  Foot  of 


Horse-power  to  be  supplied  Per  Square  Foot,  at 
Velocities  in  Miles  Per  Hour. 


Grate  Area. 

10 

15 

20 

30 

40 

«,ooo    1 

Minimum 

for 

American  engines. 

Freight  types. 

1333 
16.67 
20.00 

23 -33 
26.67 

30.00 

20.0 
25.0 
30.0 

26.67 

40.0 

:     50.0 
60.0 
70.0 
80.0 
90.0 

53-33 
66.67 
80.00 

93  33 
106 . 67 

120.00 

«.500 

33-33 

3.000    . 

40.00 
46.67 

53-33 
60.00 

3.500 

350 

4,000 

4.500    . 

40.0 
450 

50 


66.67 

83 -33 
100.00 
116.67 

133-33 
150.00 


The  black  line  marks  the  limit  at  which  it  ceases  to  be  physically  possible,  under  the 
most  favorable  circumstances,  for  the  boiler  to  produce  sufficient  steam  to  utilize  the  full 
adhesion,  allowing  30  horse-power  per  hour  per  square  foot  of  grate  (an  ordinary  maximum 
being  24  horse-power)  and  for  \  adhesion.  To  add  a  similar  line  corresponding  to  \  ad- 
hesion, draw  the  line  at  37.5  horse-power  instead  of  30  horse-power,  as  indicated  by  dotted 
Ime,  making  little  change. 


652.  There  is,  however,  one  more  resource  for  eking  out  deficiency 
of  boiler  power — to  draw  upon  the  reserve  in  the  boiler  itself,  either  by 
pumping  in  no  feed  water  for  the  time  being,  or  by  allowing  the  pressure 
to  fall  somewhat  while  the  excessive  demand  continues,  or  both. 

Neither  of  these  resources  amounts  to  much,  although  both  assist  very 
slightly.  As  respects  variations  of  pressure  ;  as  the  pressure  of  steam  rises 
or  falls,  the  sensible  temperature  of  the  steam  rises  or  falls  very  rapidly, 
but  the  total  heat  per  pound  of  steam  is  little  affected — so  little  that  the 
total  heat  was  at  one  time  supposed  to  be  constant  for  all  pressures.  This 
is  shown  in  Table  143.  «"  ^he  following  page  : 

553.  A  very  small  excess  of  demand  for  steam,  therefore,  will  cause 
the  pressure  to  fall  very  rapidly,  and  as  there  are  only  20  to  30  lbs.  of 
live  steam  stored  in  the  boiler  at  any  one  time,  what  is  gained  by  letting 


1  1* 


454 


CHAP.  XL—LOCOMOTIVE  BOILER, 


CHAP.  XL— LOCOMOTIVE  BOILER, 


455 


Table  143. 
Weight  of  and  Heat  in  Steam  at  Various  Pressures. 


Pressure, 

Lbs.  per 

sq.  in. 

above 

atmosphere. 


O 
20 

50 
100 
120 
140 
160 


Hkat-units.* 


Sensible.        Total. 


212.0 

259-3 
281.0 

33S.O 
350.1 
361.0 
370.8 


Weight 

per 
cu.  ft. 

Lbs. 


II78.I 

.038 

II92.5 

II99.I 
I2I6.5 
1220.2 

.086 

.120 
.263 
.308 

1223.5 
1226.4 

.350 
.393 

Full  tables  giving  these  properties  of  steam  for  each  point  of  pressure  will  be  found 
in  D  K  Clark's  "  Manual  for  Mechanical  Engineers,"  and  in  many  other  treatises.  The 
pressures  given  above  the  atmosphere  should  be  0.3  lb.  greater,  and  the  total  pressure 
measured  from  a  vacuum  15  lbs.  greater.  These  figures  rest  purely  on  experiment,  from 
which  accurate  fonnulae  have  been  deduced. 

Table  144. 

Available  Energy  in  Heated  Water  and  Steam  of  Locomotive 

Boilers, 
Between  normal  temperature  of  steam  and   2I2-   Fahr.,  or  that  available  in  case  of 
explosion.    For  practical  working  the  available  stored  energy  is  very  much  less  than 
this.     See  top  of  next  page. 
[Abstracted  from  a  paper  on  "  Boiler  Explosions."  by  Prof.  R.  H.  Thurston,  Trans.  Am.  Soc. 

M.  E.,  Vol  VI.,  Paper  CLXII.l 


Area  of — 

,            Weight  of— 

Stored  Energy  Available— 

Grate. 

Heat'g 
surface. 

Boiler. 

1 

Water. 

Steam. 

Water. 

Steam. 

Total. 

sq.  ft. 
IS 

30 
23 
30 

sq.  ft. 

875 
1,200 
1,070 
1,350 

lbs. 

14,020 
20,565 
19,400 
25,000 

lbs. 

6,330 
6,450 
5,260 
6,920 

lbs. 

19.02 

25.65  1 
21.67 

31  19 

ft.-lbs. 
1  =  1000 

64,253 
64,452 
52,561 
69,149 

ft.-lbs. 

I  =  1000 
2.385 
3,226 

2,7U 

3»9io 

ft.-lbs. 

I  =  1000 

66.638 

67,678 

55.278 

73.059 

mile-lbs 
1  =  1 
12,621 

12,818 

10,469 

13,837 

♦  The  heat-unit  must  be  carefully  distinguished  from  a  mere  degree  of  temperature,  from 
which  it  differs  much  as  ^foot-pound  differs  from  a  pound  or  a  foot,  or  as  an  area  differs  frorar 
a  distance.  The  little  diagrams  on  the  next  page  (Figs.  118,  tiq,  and  120)  will  make  this  clearer 
A  heat-unit  is  a  quantity  of  heat.  What  is  called  temperature  is  merely  an  altitude  of  heat  A 
high  altitude  of  temperature  is  consistent  with  a  very  small  quantity,  if  the  body  be  small,  or 
even  if  the  body  be  large  and  its  capacity  for  absorbing  or  holding  heat  small.  Different 
materials  differ  greatly  in  this  respect. 


Assumed  steam  pressure,  125  lbs. 

This  table  gives  the  entire  energy  in  the  steam  and  water  between  212"  and  353<»,  or 
the  amount  of  work  which  would  be  done  if  the  pressure  were  allowed  to  faU  to  zero 
and  there  were  no  back  pressure  or  other  losses  in  the  cylinder.  It  will  be  seen  to  be 
about  equal  to  the  ordinary  working  tractive  power  of  a  powerful  engine  for  about  one 
mile.  Perhaps  one  half  of  this  stored  energy  is  a  practically  available  resource  in 
operating  emergencies. 


pressure  drop  from  140  lbs.  to  $0  lbs.  is 
simply  this,  say,  for  the  second  engine 
given  in  the  preceding  Table  144  : 

In  Steam  Space:  Only  8.8  instead  of  25.6 
lbs.  of  steam  are  required  to  fill  the  steam 
space,  releasing  some  17  lbs.  of  steam. 

In  Water  Space:  The  fall  of  sensible 
temperature  from  361°  to  281°  releases  80 
heat-units  per  pound  of  water,  and  80  x  | 
(specific  heat  of  iron)  heat-units  per  pound 
of  boiler,  being  sufficient  to  convert  into 
steam  a  weight  of  water  equal  to  about 
■^  of  the  total  weight  of  boiler  and  con- 
tained water,  or  for  the  given  engine  728 
lbs.  of  steam. 

This   makes  a  total  gain    of   only  745 


I 

I 


■20Fh 


fOFi-- 


Areas 


I 


lOff.       "^pf.       30ff,     '^OFt! 


« 

\ 
% 


I 
.J. 


Fig.    X18. — Relation    of    Areas    to 
Altitudes  and  Lengths. 


a 
I 


lbs.  of  steam,  or  37^  lbs.  per  square  foot  ."^ 
of  grate,  which  is  about  what  a  square  ^ 
foot  of  grate  should  evaporate  in  3f  min- 
utes, at  the  rate  of  600  lbs.  per  hour.  0 


kx 


I 


Foot  Pounds 
■20Fh-^ -: J— - 

I     of  WORK.t 

yopf-\ i \—' 

I  Weicrhfs 

ToWs     20 /bs  30 lbs  -w/i6i 


554.   As    respects    letting   the    supply  of    Fig.  119 —Relation  of  Foot-pounds 
water  fall  off.  here  also  the  gain  is  COmpar-     °^  ^okk  to  Distances  and  Weights. 


atively  slight,  because  the  heat  used  to 
raise  the  temperature  of  the  water,  say, 
from  60°  to  the  boiling-point  at  120  lbs. 
pressure,  350°,  is  only  290  heat-units  per 
pound  of  water,  or  one  third  f||-|)  as 
much  as  is  needed  to  change  the  water 
into  steam  after  it  has  reached  that  limit. 
Therefore,  even  if  we  allow  as  much  as  10 
per  cent  of  the  whole  water  in  the  boiler 

to   evaporate   without   replacing   it,  which    Fig.    120.— Relation    of    Hf.at-units 
,    .  .       ,  1  1.      ^  to  Temperature  and  Mass. 

Will  lower  It  about  3  m.,  we  only  save  heat 

enough  to  evaporate  ^  of  the  whole  water  in  the  boiler,  or  215  lbs., 


I 


o     I  :  ■  I 

<o  r-^- — \ 4 ^•- 

I       I        I 

.3o°F-\ \ ;- 

o    !      Heat  Units. 

fio  r--; 1- 4 

\/o'rS i.-.~.| 

I  \ Mass  A 

•  I  • 

to  lbs     ZOlhS      30//>S    40169^ 


CHAP,  XI.— LOCOMOTIVE  BOILER. 


45<^ 

being  somewhat  over  lo  lbs.  per  square  foot  of  grate,  or  about  what  is 

evaporated  in  one  minute.  „   .      ,        •    ^« 

655.  Nevertheless  it  helps ;  but  that  the  help  is  small,  is  clear  in  an- 
other way  from  Table  143.  which  gives  the  total  available  energy  in  the 
boiler  and  contents  if  the  boiler  pressure  were  allowed  to  fall  to  zero,  and 
the  steam  thus  produced  used  without  loss  (other  than  the  heat  in  the 
steam  at  212°)  in  the  cylinders. 

It  will  be  seen  from  Table  143  that  an  engme  which  is  workmg  fairly 
hard  (as  hard  as  it  can  continue  to  work  indefinitely),  and  evaporating 
600  lbs.  per  square  foot  of  grate,  will  evaporate  a  whole  boilerful  of  water 
in  from  20  to  40  minutes.    This,  again,  shows  that  the  available  reserve 

Table  145. 

Estimated  Approximate  Distribution  of  the  Loss  of  Heat  in  American 
Locomotive  Boilers  to  its  Various  Contributing  Causes. 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER. 


457 


Theoretical  evaporation  o£  fairly  good  (14,000  H.  U.) 
coal 

Actually  evaporated  in  fair  average  practice,  with 
such  coal 


Maximum. 


Lbs.      I  Per  cent. 


12. 07 
9.06 


Leavinff  as  wastage  to  be  accounted  for,  which 
may  be  divided  between  the  various  sources 
of  loss,  as  follows  : 

1  Heat  carried  off  in  the  gases  of  combustion  (ex 
tremes  of  smoke-box  temperature  taken  at  392 
and  724°) 

•.  Lost  in  the  ash 

,    Getting  up  steam  and  banking  fires  (about  10  per 

^*        cen?,  but  not  included  above,  and  so  ueglccted.) 

4.  Unconsumed  coal  ejected  by  the  blast 

5.  Imperfect  combustion 

6.  External  radiation.   

7.  Entrained  water  (a  real  loss  but  apparent  gain). 

8.  Lost  through  safety-valve 

Total  loss  as  above  estimated ■ 


3. ox 


Minimum. 


Lbs. 


Per  cent. 


xoo. 


75. 


25- 


X.3X 


T2.07 

6.04 
6.04 


TOO. 


50- 


zo. 

0.+ 


.36 


«.44 
— O.I3 

o.ia 


3. ox 


19. 

—  I. 
X. 


25- 


3.43 


x.ai 
.60 

i.8x 

— o.6x 

0.61 


50. 


6.04 


so. 

0.+ 


xo. 

5- 

15. 

-5. 

5- 


50. 


These  extremes  are  rarely  reached  in  the  same  engine,  but  the  maximum  is  onlr 
reJhrf^der  favorable  and  the  mtoimum  under  unfavorable  condmons  for  economical 

""^^"m'arine  practice  nearly  all  the  above  sources  of  loss  except  the  first  are  avoided.  An 
efficiency  of  fr'omTtoV'per  cent  of  the  theoreUcai  evaporation  is  therefore  no  longer 

exceptional. 


in  the  boiler  is  a  pretty  small  affair,  and  the  normal  generation  of  steam 
we  have  seen  (Table  142)  to  be  quite  unequal  to  utilizing  the  full  tractive 
power  at  any  high  speed. 

556.  The  boiler  is  not  an  uneconomical  generator  of  power.  In  the 
last  types,  from  75  to  90  per  cent  of  the  potential  energy  which  goes  into 
it  in  the  form  of  fuel  leaves  it  in  the  form  of  steam.  Nor  is  the  locomo- 
tive boiler,  in  spite  of  its  great  efficiency  in  proportion  to  weight,  inferior 
to  other  types  in  economy,  the  very  best  of  stationary  and  marine  boilers 
alone  excepted.  Without  going  into  details,  for  which  space  cannot  be 
taken.  Table  145  gives  the  substance  of  the  facts  in  relation  to  its  ordi- 
nary working  when  not  burning  over  80  to  100  lbs.  of  coal  per  hour. 
When  combustion  is  pushed  harder,  the  loss  from  unconsumed  coal 
■ejected  by  the  blast  is  much  heavier. 

THE  CYLINDER  POWER. 

557.  Since  we  have  seen  that  the  locomotive  boiler  is  quite  unequal 
to  supplying  steam  enough  to  utilize  the  full  adhesion  at  high  speeds,  it 
results  in  no  serious  loss,  and  need  occasion  no  surprise,  that  the  cylin- 
der, which  is  a  mere  transmitting  agency,  is  in  actual  practice  and  as 
actually  constructed  unequal  to  transmitting  such  an  amount  of  power, 
even  if  it  could  be  generated.  As  the  speed  rises  above  the  lower  work- 
ing speeds  for  which  the  locomotive  was  designed  there  is  a  very  great 
reduction  of  cylinder  efficiency  as  measured  by  the  average  pressure  in 
the  cylinders,  cut-off.  opening  of  throttle,  and  boiler  pressure  being  the 
same. 

558.  The  steam-engine,  even  in  its  most  perfect  forms,  attempts  only 
to  convert  into  work  the  expansive  energy  of  steam,  which  is  a  very 
small  part  of  its  total  energy.  All  that  great  proportion  of  the  heat 
energy  in  the  steam  which  has  been  required  for  the  purpose  of  chang- 
ing it  from  water  into  steam  is  wholly  thrown  away,  even  in  a  theoreti- 
cally perfect  steam-engine.  It  is  hardly  to  be  conceived  of  that  science, 
will  not  eventually  discover  some  radically  different  device  for  convert- 
ing heat  into  work  which  will  be  many  times  more  effective,  but  at  pres- 
ent we  do  not  seem  to  be  even  tending  toward  it. 

559.  All  ordinary  forms  of  steam-engines  are  in  substance  similar  to 
the  engine  of  the  locomotive,  which  in  its  essential  outlines  is  simplicity 
itself,  consisting  only  of  a  piston  vibrating  back  and  forth  within  a  cylin- 
der to  wliich  steam  is  admitted  and  cut  off  at  each  end  alternately  by 
«ome  form  of  automatically-acting  valve — in  the  locomotive,  the  slide- 
valve.    The  steam  is  admitted  for  a  certain  fraction  of  the  stroke  (one 


458  CHAP.  XI.^LOCOMOTIVE— CYLINDER  POWER, 


quarter  to  three  quarters  in  the  ordinary  practice  of  the  locomotive),  called 
\.\\^ period  of  admission;  then  cut  off,  permitting  what  steam  is  shut  up- 
in  the  cylinder  to  expand  and  do  further  work  during  what  is  called  the 
period  of  expansion  ;  and  then  released  or  permitted  to  escape  at  or  be- 
fore the  end  of  the  stroke,  so  that  there  may  be  as  little  as  possible  back 
pressure  to  resist  the  return  stroke. 

While  this  division  of  the  work  done  in  the  cylinder  into  the  period 
of  "  admission"  and  of  "expansion"  is  convenient, yet  during  each  period 
alike  it  is  the  expansive  energy  of  the  steam,  and  that  alone,  which  does, 
what  work  is  done. 

560.  On  the  proper  design  of  the  valve  gear  by  which  the  slide-valve  is 
moved,  and  so  the  admission,  cut  off  and  release  of  the  steam  controlled, 
hangs  nearly  the  whole  question  of  good  or  bad  working  of  the  cylinders,  and 
its  theory  is  a  study  in  itself,  into  which  we  need  not  enter  ;  contenting  our- 
selves with  determining  what  are  the  theoretical  limits  of  efficiency,  what  are 
the  results  actually  obtained  in  good  practice,  and  how  these  results  ought  to- 
be  and  are  affected  by  varying  conditions. 

561.  The  form  of  valve-gear  known  as  the  link-motion  is  in  all  but  univer- 
sal use  on  American  engines,  and  is  used  on  a  large  majority  of  all  foreign 
engines.  It  was  invented  almost  contemporaneously  with  the  locomotive  itself, 
and  a  large  part  of  the  credit  for  it  is  due  to  the  same  man,  George  Stephenson';. 
so  that  it  is  not  unjustly  known  by  his  name,  although  it  is,  properly  speaking, 
the  invention  of  Howe,  a  foreman  in  his  shops.  It  has  not  been  essentially 
modified  or  improved  upon  since  its  invention,  except  as  advancing  experience- 
has  given  better  knowledge  of  the  precise  proportions  which  it  should  have, 
and  it  is  with  justice  regarded  as  one  of  the  most  notable  inspirations  in  the 
history  of  mechanism,  fulfilling  as  it  does  very  simply  yet  remarkably  well  all 
the  complex  requirements  which  a  locomotive  valve-gear  should  have. 

562.  Nevertheless  there  are  certain  desirable  ends  which  it  does  not  fulfil, 
and  in  recent  years  a  number  of  valve-gears  have  been  devised,  some  of  them 
of  a  highly  ingenious  character,  which  are  claimed,  and  probably  with  truth, 
to  possess  certain  practical  advantages  over  the  link-motion,  and  which  have 
met  wide  acceptance  abroad.  It  is  possible,  although  as  yet  hardly  probable, 
that  some  of  these  may  eventually  supplant  the  link-motion,  but  none  of  them 
have  yet  been  shown  to  give  such  radically  different  results  from  the  link-mo- 
tion that  any  of  the  conclusions  we  shall  reach  will  be  affected  thereby,  except 
in  degree. 

563.  Assume  such  a  cylinder  as  that  described  in  par.  559  to  have  a 
connection  opened  with  the  boiler,  at  the  beginning  of  the  stroke,  which 
continues  open  until  the  end  of  the  stroke.  Let  the  connection  with 
boiler  be  then  closed,  and  a  connection  with  the  outside  air  opened,  so 


CHAP,  XI.— LOCOMOTIVE— CYLINDER  POWER. 


459 


I 

I 


Frj-LBSo£.Work, 


stroke , 


as  to  permit  the  inclosed  steam  to  escape,  while  at  the  same  time  steam 
is  admitted  to  the  other  end  of  the  cylinder  and  the  operation  is 
repeated. 

564.  In  this  we  have  a  steam-engine  of  the  simplest  type,  which  was 
also  the  earliest  type,  and  an  indicator-diagram 
of  such  an  engine,  if  it  worked  perfectly  (which 
it  would  not  be  likely  to  do  at  very  high  speed), 
would  resemble  Fig.  121.  The  boiler,  being 
constantly  generating  steam,  may  be  considered 
as,  for  the  time  being,  a  reservoir  of  infinite 
volume,  and  the  expansion  of  the  steam  to  fill 
the  cylinder  will  not  reduce  its  pressure.  Con- 
sequently, the  cylinder  pressure  throughout  the  F'^.  121. 
stroke  will  be  equal  to  the  boiler  pressure,  and  the  diagram  will  be  a 
rectangle,  in  which  the  foot-pounds  of  work  done  will  be  represented 
by  stroke  in  ft.  x  area  of  piston  in  sq.  ins.  x  boiler  pressure  in  lbs.  per 
sq.  in.  The  efficiency  of  even  so  crude  an  engine  as  this  is  considerably 
over  three  fourths  of  what  is  actually  realized  in  fair  average  practice^ 
and  fully  as  much  as  is  realized  under  unfavorable  conditions,  and  may 
be  determined  thus  : 

565.  A  17  X  24  in.  cylinder  has  a  capacity  of  3.1525  cu.  ft.,  and  will  hold 
almost  precisely  one  pound  of  live  steam  at  a  pressure  of  126  lbs.  per  sq.  in. 
above  the  atmosphere — an  ordinary  working  pressure.  The  work  done  by  this- 
steam,  in  foot-pounds,  if  there  be  no  loss  by  condensation  or  other  disturbing 
cause,  will  be 

W17' 

-— -  X  126  lbs.  X  2  ft.  =  57,200  ft.-lbs. 
4 

Dividing  this  amount  of  work  by  the  mechanical  equivalent  of  heat,  we  obtain- 
as  the  useful  work  which  ought  to  be  realized  if  there  were  no  losses  by  back 
pressure  of  steam,  condensation,  or  otherwise, 


57^200 
772" 


=  74.09  H.  U. 


In  addition  to  this  useful  work  the  steam  has,  in  a  non-condensing  engine, 
tione  this  work  against  the  pressure  of  the  atmosphere  on  the  opposite  side  of 
the  piston,  amounting  to  nearly  15  lbs.  per  sq.  in.,  or  about  11. 2  per  cent  of  the 
useful  pressure.  Computed  to  include  work  done  against  this  pressure,  most 
of  which  is  avoided  in  marine  and  other  condensing  engines,  the  total  work 
done  is  equivalent  to  74.09  X  1.112  =  82.91  H.  U. 

Now  the  total  heat  in  this  quantity  of  steam  is  (Table  100)  1191  H.  U.,  so« 
that  all  that  is  utilized  is  : 


.460  CHAP.  XL— LOCOMOTIVE— CYLINDER  POWER, 


CHAP.  XL— LOCOMOTIVE— CYLINDER  POWER. 


46E 


Cutting  off  at  Full  Stroke. 

In  a  perfect  non-condensing  engine,  In  a  perfect  condensing  engine 

74.09  „  b      s       , 

=  0.22  per  cent. 


1191 


82.9 

— -  =  6.96  per  cent. 


Practically  even  this  result  is  7  or  8  per  cent  too  great,  owing  to  the  steam 
wasted  to  fill  the  passages  between  the  valve  and  the  piston,  which  does  no 
work  whatever  unless  the  steam  is  expanded  after  being  cut  off. 

666.  There  being  33,000  X  60  =  1,980,000  ft.  lbs.  in  a  horse-power  per 
hour,  we  shall  have  to  use,  in  order  to  develop  a  horse-power  per  hour  with  an 
engine  worked  in  this  way, 

1.980.000 

"57.200"  ~  "^^  steam. 

And  if  we  had  a  boiler  able  to  utilize  the  full  evaporative  efficiency  of  fairly 

good  coal,  instead  of  only  one  half  to  three  fourths  of  it,  we  should  require 
34.62  ^ 

j2  07  ~  ^'^^  ^^^*  °^  *^°^^  '°  obtain  one  horse-power  per  hour. 

567.  Only  under  the  most  favorable  possible  circumstances  for  ob- 
taining the  last  degree  of  efficiency  out  of  the  locomotive  is  it  possible 
to  obtain  a  horse-power  per  hour  with  2.87  lbs.  of  coal,  or  with  less  than 
25  lbs.  of  steam.  Ordinarily  in  fact,  even  on  long  up  grades  which 
afford  the  most  favorable  localities  for  the  economical  working  of  the 
locomotive,  something  like  30  lbs.  per  horse-power  is  used  (see  Table 
146).  With  ordinary  evaporation  of  6  to  8  lbs.  of  water  per  pound  of 
coal  from  4  to  6  lbs.  of  coal  per  horse-power  per  hour  are  required,  and 
this  is  about  what  is  ordinarily  obtained  from  locomotives,  the  very 
finest  marine  engines  running  down  to  1.3  to  1.5  lbs. 

568.  Many  engines  in  times  past  have  been,  and  in  fact  still  are,  run 
at  nearly  full  stroke,  as  notably  high-pressure  engines  on  Mississippi 
River  steamboats.  In  the  locomotive  this  is  occasionally  done,  but 
usually  the  steam  is  permitted  to  expand  through  about  half  the  stroke. 
The  theoretical  gain  from  doing  this  is  large,  but  the  practical  gain 
small — so  small  that  nearly  all  that  is  gained  by  it  is  to  neutralize  tjie 
various  practical  obstacles  to  realizing  the  full  theoretical  work  of  steam 
at  full  stroke, 

669.  A  theoretically  perfect  condensing  steam-engine  and  boiler  requires 
only  f  lb.  per  H.  P.  per  hour  of  coal,  and  some  8  lbs.  of  water,  at  a  boiler 
pressure  of  120  lbs.  per  sq.  in.,  utilizing  a  scant  26  per  cent  of  the  energy  in  tiie 
coal.     A  theoretically  perfect  non-condensing  engine  utilizes  16,9  per  cent. 

570.  The  very  best  ever  claimed  to  have  been  realized  with  locomotives  is 
in  the  paper  by  Mr.  Wm.  Stroudley  before  referred  to  (par.  550),  where  it  is  stated 
ilhat  in  a  trip  ot  50.4  miles  at  43.3  miles  per  hour  the  average  coal  consumption 


(exclusive  of  coal  for  getting  up  steam,  which  is  about  3  lbs.  per  mile  run)  was- 
24.87  lbs.  per  mile,  and  the  average  horse-power  developed  528.53  (see  Fig. 
123).  This  amounts  to  producing  a  horse  power  with  2.04  lbs.  of  coal  per  hour 
— a  result  which  has  been  approached  elsewhere  under  the  most  favorable  con- 
ditions, but  when  alleged  as  the  result  of  an  ordinary  service  run  over  undu- 
lating grades  it  is  all  but  certain  that  its  remarkably  favorable  result  is  largely 
due  to  serious  errors  in  the  record  ;  in  great  part  probably  originating  in  the 
shortness  of  the  run,  in  which  only  some  1200  lbs.  of  coal  is  alleged  to  have 
been  burned,  or  1.2  cu.  ft.  per  square  foot  of  grate.  The  same  allowance  must 
be  made  for  the  alleged  rate  of  evaporation,  11. 6  to  12.6  lbs.  per  pound  of  coal, 
which,  it  is  risking  little  to  say,  is  from  10  to  20  per  cent  beyond  the  limits  of 
physical  possibility,  in  view  of  the  fact  that  the  gases  in  the  smoke-box  seem 
to  have  had  a  temperature  of  600°  Fahr. 

571.    A  far  better  index  of  average  practical  results  is  that  given  in  Table* 


M 

c 

9 

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t» 
4; 

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a. 
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400 
300 

200 
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Fig. 


122. 


Diagram  showing  Results  of  a  Test  of  a  Baldwin  Locomotive,  by  John  W.  Hill,  M.E... 
DURING  A  Run  between  Cincinnati  and  Hamilton,  24.7  Miles.   (See  Tables  146  and  147.) 

[The  abscissae  represent  the  intervals  between  indicator-diagrams,  which  were  taken  in  as 
quick  succession  as  possible  (40  in  25  miles,  or  ih.  26m.)  and  not  miles.] 

The  mean  effective  pressure  may  be  considered  as  the  equivalent  of  the  tractive  power, 
which  should  theoretically  fall  immediately  to  zero  on  striking  the  down  grade,  if  the  velocity 
were  to  remain  the  same,  but  instead  of  this  was  maintained  about  the  same  for  some  distance, 
with  the  effect  of  greatly  increasing  the  speed  and  horse-power. 

146  and  147,  where  from  4^  to  5^  lbs.  of  coal  per  horse-power  per  hour  were 
required,  rising,  when  combustion  was  so  forced  as  to  expel  unconsumed  coal 


462  CHAP.  XI.-LOCOMOTIVE-^CYLINDER  POWER, 


*rf*' 


1'   T 


•   ¥    •   ♦ 


mil  fin 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER. 


463 


T   T   T 


r'l  I r !  'i,  \\ 


tons.    A  verage  of  WhoU  Ji'un^iu^J^^  °       "  m  ""     ^^'S^^t  of  engine  and  23  carriages,,/.  7 

from  .h=  smoke-stack  (as  it  often  is  in  practice),  to  over  7  lbs.     Fig.  .22  show, 

he  fluctuafons  of  speed  and  tractive  power  during  a  part  of  this  run  in  a  some! 

what  similar  manner  to  Fig.  123.  aomc- 

Table  146, 

Tests  of  a  Baldwin  16  X  24  in.  American  Engine  in  Express  Freight 

Service. 
(D..uc.a  fro.  R„or.  "f  T.„  .,  M    W  „„,   M.  ^_B.,  ;ou.  K„„.  fn«..  .pH,-„.,.  ..^ 


For  details  of  engine  and  train,  see  below.] 


Boiler  Performancb. 


Cincinnati 

to 
Hamilton. 


Apparent  evaporation,  actual 

r     .  '  ,        ,     "    ^^ss  5  p.  c.  primage 

Equivalent  from  and  at  212" 

Actual  evap.  (less  primage)  perVq.'ft 

of  heating  surface,  per  hour. . . 
Coal   burned  per  sq.  ft.  of  grate,  '^x 

hour °_  ^ 

Evap'n  from  and  at  212°  per  hour! 

Estimating  coal  burned  per  sq.  ft.* of 
grate  per  hour  with  natural  draft  at 
25  lbs.,  and  one  horse-power  =  15 
sq.  ft.,  we  have,  for  such  an  engine 
as  above,  for  a 

Healing  surface  per  H.  P.  of 

Ratio  of  effect  of  blast  (  coal  burned 
to    natural    draft, -j 
comparing  by (  heating  surface 


lbs. 

7.44 
7.07 
8.36 

9.96 

83.9 
10,586 


Hamilton 

to 

Twin  Creek. 


Twin  Creek 

to 

Dayton. 


sq.ft. 
3.24 


lbs. 
4-75 
4-51 
5.34 

13.01 

172.0 
13.856 


3.36 
3.32 


■q.  ft. 

2-57 


lbs. 

6.55 
6.22 

7.30 
12.24 

117. 3 
12,918 


sq.ft. 
2.61 


4.34 
4.33 


4.04 
4*o8 


mnnu  I  HI 


I  ! 


/ 


1 


m  M*  i 


•     I 

■:'     j     is!      !        ' 

j  !!i>a»|i«M»|«ii*aM{  ■•■ms  i        ■•««•• 


I 


! 


i        I       "I 


I 


Brighton  &  South  Coast  Railway. 

Speed  in  miles  per  hour  is  indicated  by  the  figures  at  the  top  of  the  diagram  and  by  the 
heavy  solid  line.  Horse-po-wer  is  indicated  by  the  d^aed  line  made  of  points.  Tractive  force 
is  indicated  by  the  light-dotted  line.  The  dotted  lines  along  the  base  show  where  diagraais 
were  taken,  49  in  all.    The  three  arrow-heads  at  the  left  indicate  stops. 

Table  \^6*— Continued. 

Engine  Performance, 


Miles  run  

Speed,  miles  per  hour 

Mean  boiler  pressure 

'•      initial       "  

••      cut-oflf 

"     effective  pressure 

Grade  of  expansion,  incl.  clearance... 

Distribution  of  Power: 

Indicated  H.  P 

Power  absorbed  by  engine  only  above 

all  resistances 

Gross  load 

Extra  friction  due  to  load  (5  p.  c.  of 

gross  load) 

Power  expended  in  moving  train 

Per  cent  of  total  power  absorbed  by 

engine 

Cost  of  Power: 

Steam  per  hour  to  engines 

Steam  accounted  for  by  diagrams  .... 

Per  cent  of  do 

Steam  per  I.  H.  P.  from  boiler 

"     diagrams.... 

Coal  per  I.  H,  P.,  actual 

••  *'         **       at  I  to  9  evap'n... 


24.7 
17.23 
122.0  lbs, 
98.5  " 

.53 
65.0  lbs, 
2.0 

H.  P. 
291.9 

33.4 
258.5 

12.9 
245.6 

15.86 

lbs. 

9.424 -6 
8,017.2 

85 
32 
27 

4 

3 


o 

3 
5 
24 

59 


15.87 

22.67 
124.0  lbs, 
107.     " 

•515 
64.2  lbs. 
2.09 

H.  P. 

368.7 

41-3 
327.4 

16.4 
311. o 

15-63 

lbs. 
12.312 
9,883 
80.3 

33.4 
26.9 

7.03 
3.71 


16.267 
23.0 

123.0  lbs. 
105.5  •' 

.52 
63 . 2  lbs. 
2.03 

H.  P. 

388.5 

44.3 
344-2 

17.2 
327.0 


15.82 

lbs. 

12.415 
10.324 

83 
32 
26 


2 
O 

6 

5.36 
3-55 


These  tests  are  perhaps  as  fairly  representative  of  every-day  American  practice  as  any 
which  exist.    See  details  on  following  page  and  Table  147. 


464 


CHAP.  XL— LOCOMOTIVE— CYLINDER  POWER, 


Details  of  Engine  and  Train  for  Tables  146,  147. 

Baldwin  American  engine,  16  x  24  in.  cylinders,  61  in.  drivers,  15.99  sq.  ft.  grate  area,, 
898.7  total  heating  surface. 

Weight  on  drivers,  44.840;  trucks,  27,380;  total,  72,22olbs. 
Weight  of  tender,  empty,  23,480155.;  load,  24,000  lbs. 

Train,  35  loaded  box  cars  and  caboose,  weighing 782.94  tons. 

Average  of  engine  and  tender 5572    " 

Total  weight  of  train 838.66  tons. 

Engine  in  ordinary  working  order,  out  of  shop  22  months  (55,471  miles),  Pittsburg  No. 
2  coal.     Date  of  tests,  July  28,  1878. 

Evaporation  per  sq.  ft.  of  fire-box  surface,  assuming  60  per  cent  of  the  evaporation  to 
have  been  from  that  surface,  93.53  lbs.  per  hour. 

Friction  of  engine  was  determined  by  series  of  indicator-diagrams  at  each  speed, 
averaging  15.8  per  cent  (including  the  allowance  of  5  per  cent  for  extra  work  due  to  load, 
which  is  probably  too  large),  while  the  weight  of  the  engine  was  only  6.65  per  cent  of  the 
total.  This  work,  however,  includes  atmospheric  head  resistance  as  well  as  rolling  and 
internal  friction. 


572,  A  more  reasonable  presentation  of  what  may  fairly  be  expected  from 
locomotives  under  the  most  favorable  working  conditions  for  developing  power 
economically  is  given  in  a  paper  on  "The  Consumption  of  Fuel  in  Locomo- 
tives," read  before  the  Institution  of  Mechanical  Engineers,  by  M.  Georges 
Mari6,  engineer  of  the  Paris  &  Lyons  Railway,  of  France.  In  these  tests  a 
powerful  locomotive  (21^  X  26  in.  cylinders,  eight  4  ft.  \\  in.  drivers,  carrying 
some  100,000  lbs.;  exact  figures  not  given)  was  loaded  with  a  light  train  of 
167.8  to  183.2  tons,  and  run  up  a  long  grade  on  the  Mont  Cenis  line,  rising 
1709  ft.  in  \-j\  miles,  or  about  a  two  per  cent  average  grade  (the  maximum  being 
2.84  per  cent),  in  one  hour.  The  total  tax  on  the  adhesion  on  such  a  grade  was 
only  some  65  lbs.  per  ton  maximum  and  46  lbs.  average,  or  a  total  average 
traction  of  some  8000  lbs.  With  so  light  a  load  it  was  possible  to  cut  off  at  one- 
fifth  stroke.  The  author's  conclusions  from  the  tests  are  that  with  a  good  loco- 
motive and  a  good  driver  the  consumption  of  fuel  and  water  is  as  follows  : 


Consumption  of  fuel  per  effective  horse-power  per  hour. 
Consumption  of  fuel  per  indicated  horse  power  per  hour. 
Ratio  of  consumption  of  water  to  consumption  of  fuel... 
Ratio  of  dry  steam  produced  to  fuel  consumed 


3.27  lbs. 
2.88  lbs. 
8.88 
8.08 


These  satisfactory  result  are  attributed  to  the  following  causes:  "  (i)  The 
total  heating  surface  of  the  boiler  is  very  large  compared  to  the  grate  surface, — 
96  to  I, — so  that  the  boiler  absorbs  the  heat  of  the  gases  very  completely;. 
(2)  the  cylinders  of  the  locomotive  are  very  large, — according  to  the  late  M. 
Mari6's  system, — so  that  the  grade  of  expansion  is  high  ;  (3)  the  locomotive 
was  very  well  looked  after,  which  is  an  important  point  in  economy  of  fuel." 


CHAP.  XL— LOCOMOTIVE— CYLINDER 


PO  WER. 

» 


465 


Table  147. 

Details  as  to  ia^  Resistances   of   Engine  and  Train   in  the  Tests 

Abstracted  in  the  Preceding  Table. 


In  three  runs  of 

At  speeds  in  miles  per  hour  of. 


The  average  indicated  H.  P.,asdetsrmined  by  the  average 
of  cards  taken  on  both  sides  of  the  engine  simulta- 
neously at  intervals  of  two  minutes,  was  

The  entire  weight  of  the  train  having  been,  engine,  55.72  -f- 
782.94  =  838.66  tons,  we  may  compute  from  the 
above  data  that  the  average  tractive  eflergy  of  the 
locomotive  (including  its  own  internal  friction)  was 

Equal,  average  of  entire  train 

Of  the  above  H.  P.,  however,  it  was  determined  by  actual 
trial  that  the  indicated  H.  P.  necessary  to  move  the 
engine  alone  at  the  given  speeds  was 

And  it  was  estimated  that  when  the  engine  was  working 
hard  there  was  a  further  addition  to  its  internal 
friction  of  5  per  cent  loss  on  work  done,  = 

Making  total  H.  P.  absorbed  within  engine 

Deducting  this  from  the  work  done,  and  deducting  engine 
from  weight  of  train,  we  find  the  average  traction 
exerted  on  the  train  was 

Leaving  as  the  power  required  to  propel  the  engine  itself, 
without  load 

Add  estimated  addition  to  engine  resistance  when  work- 
ing hard  (5  p.  c.) 


C.  to  H.      H.  to  T.  C.      T.  C.  to  D. 

24.7  miles.    15.87  miles.   16.27  milesw 

17.23  22.67  23.0 

Average  of — 
40  cards.       20  cards.       21  cards. 

L  H.  P. . 

291.9  368.7  388.5 


-lbs. 


V 

6,346  6,097  6,334. 

I lbs.  per  ton « 

7-57  727  7-55 

/ 1.  H.  P.,  engine  only » 

33-4  41-3  44-3 


12.9 
46^ 


6.83 

727. 

281. 


Total  continuous  force  in  lbs.  to  move  eng. 

Or  in  lbs.  per  ton  of  engine  and  tender: 

Locomotive  without  load 

Increase  d  ue  to  load 


itself.      1008. 


Total  locomotive  resistance 

Assuming  the  effective  end-area  of  the  engine  for  air  re- 
sistance to  be  100  sq.  ft.,  and  air  resistance  to  be 
\^  lb.  per  sq.  ft.,  at  10  miles  per  hour,  we  have  for 
air  head  resistance  only .  .*. 

Leaving  as  the  tractive  and  internal  resistance  of  the 
engine  without  load 


In  round  figures,  we  may  deduce  from  the  preceding,  for 
locomotive  resistances  in  lbs.  per  ton,  of  engines 
of  the  American  type  (in  which  head-resistance 
would  be  a  larger  proportion  than  in  more  powerful 
engines) 


13.04 
5.06 

18.10 


16.4 
57-7 

-lbs.  per  ton- 

6.57 
—Total  Ibs.- 

683. 

273. 

955- 

-lbs.  per  ton- 

12.26 

4.87 


17.* 
6^ 


6.78 


722. 

280. 
1002. 


148 


17.13 

-Total  lbs. 
857 


12.96 
5  04 

18.00 


265 


579 


4*6  457 
Lbs.  per  ton  of  eng. 

Atmospheric 3.0 

Rolling  friction,  light  ...  5.0 

Internal     "  '*      ...  5.0 

"         "  increase 

due  to  load 5.0 


Total 18.0 

The  average  of  the  train  behind  engine  is,  say 6.75, 

Excess  of  engine  resistance,  lbs,  per  ton  of  engine 11.25 

This  engine  excess,  when  distributed  through  the  entire  train  (of  35  loaded  cars)  makes  a  difiter- 
ence,  as  shown  above,  of  only  (average,  0.74,  0.70,  0.77),  say 94  lb.  per  ton. 

30 


466  CHAP.  XT.— LOCOMOTIVE-CYLINDER  POWER. 


Reference  ,s  also  made  in  the  same  paper  to  some  experiments  made  by 
M  Regray.  Chief  Engineer  of  the  Eastern  Railway  of  France,  on  consumption 
of  fuel  m  express  engines  hauling  express  trains,  showing  3.01  lbs.  per  indi- 
cated  horse-power  as  an  average,  and  2.48  lbs.  as  the  minimum.  These  satis- 
factory  results  are  claimed  by  the  author  to  be  due  in  large  part  to  the  use  of 
large  heating  surfaces  and  large  cylinders:  he  always  built  his  own  locomo- 
tives by  that  rule. 

673.  The  present  tendency  in  this  country,  however,  is  not  by  any  means 
toward  the  use  of  large  cylinders,  but  rather  toward  heavier  engines  and  boilers 
for  the  same  cylinders.     The  comparison  given  in  Table  148  shows  this  very 

Table  148. 
Increase  in  Total  Weight  of  Engines  having  the  Samesized 

Cylinders. 
Baldwin  Locomotive    Works. 


Class  of  Engine. 

American , 

Mogul 

Consolidation 


Cylinders. 


16  X   24 

17  X  24 

16  X   24 

17  X  24 

18  X  24 

19  X  24 

20  X  24 


Weight  in  Working  Ordbk.     i  =  1000  Lbs. 


On  Drivers. 


73. 


42 

45 
51 
54 
58 
61 

87 


86. 


46 
52 
54 
57 
64 
70 
95 


Inc. 


4 
7 
3 
3 
6 

9 

8 


On  Track. 

Total. 

73- 

86. 

Inc. 

1 

73. 

86. 

Inc. 

23 

26 

3 

65 

72 

7 

25 

28 

3 

70 

80 

10 

16 

18 

2 

67 

72 

5 

18 

21 

3 

72 

78 

6 

19 

24 

5 

77 

88 

II 

20 

24 

4 

81 

94 

13 

9 

13 

4 

96 

108 

12 

Rhode  Island  Locomotive   Works. 


CHAP.  XL— LOCOMOTIVE— CYLINDER  POWER. 


467 


Table  148. — Continued. 

Taunton  Locomotive    Works. 


16"  X  24"  Cylinders. 

17"  X  24" 

Cylinders. 

Year. 

Weight— Lbs. 

Year. 

Weight— Lbs. 

1848* 

50  000* 

1850* 

57,000* 

i857' 

SS.ooof 

1857 

67,700 

1859" 

52.ooof 

1S65 

67.000 

iS6o' 

540oof 

18S2 

78,400 

i86i 

62.400 

1883 

80.000 

1880 

70,000 

1884 

90,000 

18S3 

82,000 

1885 

91,000 

1884 

83,000 

*  16"  X  20  '  cylinders. 

*  17"  X  20"  cy 

linders. 

t  16"  X  22" 

See  also  Tables  127-130. 

Most  of  the  striking  change  shown  in  this  table  is  accounted  for  by  the  gradual  in- 
crease in  boiler  pressure  carried.    See  par.  605. 

Strikingly.  After  allowing  its  full  weight  to  the  effect  of  the  increase  in  boiler 
pressure  carried,  it  is  clear  that  there  is  no  tendency  toward  using  larger  cylin- 
-ders  for  the  sake  of  being  able  to  cut  off  earlier. 

the  theoretical  gain  by  expansion. 

574i  Under  "  Mariotte's  Law"  (given  in  any  text-book  on  physics)  the  vol- 
time  of  a  gas  is  inversely  as  the  pressure,  so  that  if 
the  gas  has  expanded  into  twice  the  volume  it  exerts 
lialf  the  pressure,  etc. 

In  **  cutting  off  "  steam  at  some  point  in  the  stroke, 
say  half-  or  quarter  stroke,  the  steam  in  the  cylinder 
expands  according  to  this  law  (theoretically),  and 
thus  continues  to  push  the  piston  before  it  with  a 
■gradually  decreasing  pressure  as  the  interior  volume 
increases,  until  at  the  end  of  the  stroke  the  pressure 
is  (or  ought  to  be,  with  a  perfect  gas)  just  half  or  a 
•quarter  of  the  initial  boiler  pressure.  A  perfect 
indicator-diagram  of  such  a  stroke  would  have  the 
form  of  Figs.  124,  125,  the  bounding  curve  being  a 
iiyperbola,  as  in  Fig.  97.  The  shaded  portion  in 
these  cuts  represents  what  is  gained  by  expansion, 
or  oujjht  to  be. 

675i  But  steam  is  not  affected   in   precisely  the 


Fig.  124. 


Fig.  125. — The  Ratio  of  thr 
Shaded  Portion  to  the 
Unshaded  Rectangle  im- 
dicates  the  theoretical 
Gain  by  Expansion. 


isame  way  as  a  perfect  gas  by  changes  of  pressure  and  volume;  and,  moreover, 


4^8  CHAP.  XI.^LOCOMOTIVE— CYLINDER  POWER. 


Table  149. 

Theoretical  Efficiency  of  Steam,  Expanded  in  Non  conducting 
Cylinders,  involving  no  Waste  of  Heat. 

[Rearranged  from  "  Steam  Using,  or  Steara-Engine  Practice,"  by  Prof.  Chas.  A.  Smith.] 
Boiler  pressure  assumed  at  120  lbs.  per  sq.  in.  above  atmosphere. 


Cirr-OFF. 


Full  Stroke 

\ 

\ 
\ 

i 
i 


<< 
•  < 
(I 
<< 
<« 
<i 
<< 
<t 


Theoret  Pounds 

Steam  Per 

Horse-power 

Per  Hour  (120  lbs. 

over  Atmos.) 


31.3 
23.8 
21  4 
18.8 
16.4 

15-4 

II. o 

10.3 

8.8 
8.2 


Theoret.  Gain 

by  Expansion. 

Full  Stroke 

=  1. 00 

(absolute  press.) 


1. 000 
1.285 

1.459 
1.666 

1.905 

2.278 

2.854 

3-034 
3-547 
3.835 


Mban  Effectivk 

Pressukb  phr  Sq.  In. 

Gain  Per 

Cent  by 

Non-con- 
densing. 

Condens- 
ing. 

Condensing'.. 

119 

131 

10. 1 

115 

127 

10.4 

107 

119 

II. 2 

96 

108 

12.5 

81 

93 

14.8 

60.7 

72.7 

19.8 

32.1 

44.1 

37.4 

25.0 

37.0 

48.0 

7-9 

19.9 

151. 8 

1.3 

13-3 

923 

The  mean  effective  pressure  ,s  computed  by  assuming  a  minimum  back  pressure  of 
1.3  lbs.  per  sqm  above  the  atmosphere  in  non-condensing  engines,  and  a  minimum. 
back  pressure  of  4  lbs.  (or  12  lbs.  gain  by  condensing)  in  condensing  engines. 

Table  150. 

Theoretical  Economy  of  Steam  from  carrying  higher  Boiler 

Pressures. 

[Abstracted  from  "  Steam  Using,  or  Steam-Engine  Practice."  by  the  late  Prof.  Chas.  A.  Smith.J 


Pressure 
ABOVE  Atmos- 

FHKKK,  PoU.NDS 

Per  Sy.  In. 


O 

20 

60 

100 

140 

180 

220 

Per  cent  of 
Economy  be- 
tween 20  and 
220  lbs.  Press.  I 


Pounds  of  Dry  Steam,  if  Worked  in  a  Perfectly  Non-conductinc  Cv.iv 
DER  Per  Total  Hokse-power  Per  Hour,  with  Cut-off  at- 


Full  Stroke. 


35.7 
33-7 
32.5 
31.7 
30.9 

30.5 
30.2 


%  Stroke. 


^  Stroke. 


II. 6  p.  c. 


24.9 
23.6 
22.7 
22.2 
21.6 
21.4 
21. 1 


II -7  p.  c. 


21.4 
20.3 

195 
19.0 

18.5 

18.3 

18. 1 


M  Stroke. 


iVf  Stroke. 


12.2  p.  C. 


15-7 

II. 7 

14.9 

II. I 

14-3 

10.7 

13-9 

10.4 

136 

10.2 

13.4 

10. 1 

13-3 

10. 0 

12.0  p.  c. 


ii.o  p.  c. 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER, 


469 


2.278 


2.854 


its  expansion  in  the  cylinder  means  the  doing  of  work, — which  means  loss  of 
heat, — which  means  loss  of  pressure, — which  means  a  reduction  in  the  work 
done;  so  that  the  true  curve  which  should  bound  a  theoretical  diagram  (which 
was  called  by  Prof.  Rankine  an  '"adiabatic"  curve)  and  the  precise  theoretical 
gain  which  should  result  from  expansion  is  all  but  incapable  of  rigorous  an- 
alysis.    It  has  been  shown  that  there  is  little  error  of  practical  moment  in  as- 
suming that  the  steam  expands  in  accordance  with  Mariotte's  law,  and  it  is  laid 
down  that  it  does  so,  without  qualification,  in  some  popular  text-books;  but  we 
may  as  well  use  the  correct  theoretical  quantities,  as  given  in  Prof.  Chas.  A. 
Smith's  "Steam  Using,  or  Steam  Engine  Practice,"  by  whom  they  were  care- 
fully determined  from  a  large  diagram.     According  to  these  figures,  if  we  can 
conceive  of  a  non-conducting  cylinder  we  obtain  the  following  figures,  abbrevi- 
ated from  Table  149.     The  boiler  pressure  assumed  is  120  lbs.  per  square  inch 
above  the  atmosphere,  but  the  results  are  but  little  affected  by  the  initial  boiler 
pressure,  as  will  be  evident  from  Table  150: 

576t  If  steam  be  cut  off  at 

Full  stroke,     f  f  -J  f 

The  theoretical  gain  by  expansion  (Table  149)  is  as 

1. 000         1.285         1-459         1.666         1.905 
Whereas  by  Mariotte's  law  it  is  somewhat  less,  viz. : 
I. 000        I. 261         1.425         I. 616         1.837 
The  theoretical  pounds  of  steam  required,  per  horse-power  per  hour,  are 

31.3  23.8  21.4  18.8  16.4  15.4  II.O 

And  the  mean  effective  pressure  in  pounds  per  square  inch,  allowing  a  certain 
minimum  of  i  (1.3)  lb.  per  square  inch  for  unavoidable  back  pressure,  should  be 
119-  115-  107.  96.  91.  60.7  32.1 

In  a  condensing  engine  the  mean  effective  pressure  should  be  some  12  lbs. 
more  than  this  in  each  case,  representing  the  gain  by  the  additional  complication 
of  the  condensing  apparatus. 

677.  The  locomotive  engine  is  run,  as  an  average,  cutting  off  at  half-stroke; 
it  is  rarely  possible  to  cutoff  at  less  than  quarter  stroke (6  inches,  with  a  24.inch 
cylinder)  or  at  more  than  seven-eighths  stroke.  The  maximum  gain,  therefore, 
which  it  ought  in  theory  to  result  from  expansion  is  only  some  67  percent,  and 
if  we  had  an  engine  so  perfect  that  it  could  utilize  without  loss  of  heat  the  entire 
expansive  energy  of  the  steam,  so  as  to  discharge  it  into  the  air  at  atmospheric 
pressure,  it  will  be  seen  (Table  149)  that  the  utmost  possible  economy  would  be 
about  four  times  that  of  using  steam  at  full  stroke;  so  that  at  best  only  some  82 
X4=  328  heat-units  out  of  1159.  or  28. 3  per  cent,  could  be  utilized.  The  utmost 
that  is  actually  realized  in  the  very  finest  marine  engines  burning  1.3  to  1.5 
lbs.  of  coal  per  horse-power  per  hour  is  some  16  or  18  per  cent  of  the  heat  put 
into  the  steam,  which  is  perhaps  three  fourths  of  that  which  comes  out  of  the 
coal. 


2.139        2.511 


470  CriAP.  XL^LOCOMOTIVE-CYLINDER  POWER. 

valve  IS  therefore  given  a  lead  so  that  the  s.eam  is  admitted  nfronoHh,  I 

.,.£.  .r.:r;  i::r  -  ;r;:i^\::/r  rrrzrt: 

oression   «f  th.       ^     Tu  ^     "**'  '^5.  but  much  rounded   by  com^ 

pression   at  the  end  of  the  stroL'#»       Mr.f  oii     ^  .t.- 

tr„«   .•         •  siroke.     Not  all  of  this  compression  is  lost    it  i«i 

™n™"  b^r  ^^^^^f  ■"="-■=  "--"  Sivin.  motion  to  thi      ;<;:! 
eating  parts  ,  but  l,o>v  much  the  theoretical  loss  amounts  to  it  is  needless  to  in 

soTr«s  IfTosr"  r"  ^T""l'"  "■'  ^"'°"^  ""'"  -"  '"  n,o:e  impolnt' 
roTnts  to         •    "'  "^  "'  '"'  '""'"^   °^  '''P"-"  "'-  '"eir  agg'regate 

579.  The  chief  sources  of  loss  of  cylinder  efficiency  in  the  locomotive 
engine  are  those  numbered  i  to  8  below :  '  "i^oniotive 

1.  The  steam  is  ■wire-drawn.  &o  that   its  pressure  in  the  cylinder  is 
neyer  equal  to  that  of  the  boiler,  and  often  ,o  and  even  .o  lbs  below  U 

2.  The  steam-porls  are  not  large  e,w,<gh  to  admit  steam  as  fast  as  the 
P^ton  moves,  especially  if  it  be  moving  fast.  Both  of  these  sources  of 
loss  are,  owing  to  the  peculiarities  of  the  link-motion,  more  serious  at 
hgh  speed  and  with  early  cut-offs,  and  the  last  one  hardly  occurs  at  a" 
under  other  circumstances. 

These  two  causes  together  have  so  important  an  eflfect  on  the  tractive 
power  of  enomes   that  they  are  separately  discussed   below  (par.  587) 

LfcrfolTow;'  "'"'''  ""^'"^"^  ^"  "^^^^^  ^"  ^^^  indicato^diagL. 
580.  3.  All  entrained  water  in  the  steam  has  to  be  evaporated  •  a  loss 
however,  ".ore  properly  chargeable  to  defects  of  the  boiler  tha'n  to  the 
cylinder.  M.  Marie  found  in  his  carefully  conducted  experiments  that 
somethmg  over  10  per  cent  of  the  apparent  evaporations  was  real  J  only 
vapor  earned  along  mechanically  with  the  steam  at  the  same  sen  s^  be 
temperature,  350°,  but  unevaporated.  Other  tests  show  3  and  /per 
cent,  and  some  none,  but  it  is  probably  rarely  less  than  5  per  cent.     Thb 


CHAP.  XL— LOCOMOTIVE— CYLINDER  POWER. 


471 


means  that  with  the  half-pound  or  more  of  steam  which  enters  the 
cylinder  at  each  stroke,  from  half  an  ounce  to  an  ounce  of  hot  water  is 
injected  with  it.  The  loss  involved  is  not  simply  the  300°  of  heat  which 
have  been  given  to  the  water,  but  as  soon  as  the  pressure  and  tempera- 
ture fall  during  expansion  and  exhaust  this  hot  water  flashes  into  steam, 
absorbing  the  necessary  heat  for  that  purpose  from  the  hotter  walls  of 
the  cylinders,  and  having  all  the  practical  effect  upon  the  temperature  of 
the  walls  of  the  cylinder  of  a  spray  of  cold  water  at  every  stroke. 

581.  4.  A  constant  radiation  of  heat  from  the  metallic  cylinder  (only  a 
part  of  which  is  lagged)  and  its  connected  parts  into  the  surrounding  air, 
so  that  a  certain  small  fraction  of  the  steam  must  be  condensed  at  each 
stroke  to  supply  this  loss. 

Perhaps  Figs.  126  to  130  are  as  good  direct  evidence  as  any  of  the  very  great 
loss  which  results  from  this  cause.  It  will  be  seen  from  them  that  the  mere 
effect  of  leaving  off  the  cover  from  one  end  of  the  cylinder  was  to  make  a  very 
noticeable  reduction  in  the  effective  average  pressure.  It  is  to  be  remembered 
in  comparing  these  two  diagrams  that  this  "cover,"  the  removal  of  which 
caused  so  great  a  difference,  is  nothing  but  a  thin  plate  of  metal,  in  direct  metallic 
contact  with  the  cylinder  at  many  points,  and  including  only  a  thin  space  of  dead 
air  between  them.  We  are  not,  therefore,  comparing  a  well-protected  with  a 
badly-protected  cylinder,  but  a  badly-protected  with  a  worse-protected  one. 

It  is  not  probable  that  the  absolute  loss  of  heat,  measured  merely  by  heat- 
units,  is  anything  like  as  great  from  the  cylinders  and  connected  parts  as  from 
the  boiler;  but  each  unit  of  heat  subtracted  from  the  boiler  can  be  replaced  by 
another  without  any  indirect  loss,  whereas  after  the  steam  has  once  entered  the 
steam-chest  and  cylinder  the  loss  of  a  few  units  of  heat,  by  reducing  the  pressure, 
means  the  loss  of  much  of  the  efficiency  of  what  heat  is  left. 

682.  5.  Still  more  important  than  direct  external  radiation  is  the  phe- 
nomenon known  as  internal  radiation  into  the  exhaust  steam.  The  steam 
enters  at  120  to  140  lbs.  pressure,  corresponding  to  350"  to  360°  Fahr. 
It  leaves  the  cylinder  at  4  to  7  lbs.  pressure  and  225°  to  230°  Fahr.  In 
entering  it  heats  the  interior  walls  of  the  cylinder,  which  it  finds  at  per- 
haps 250°  Fahr.,  to  nearly  its  own  temperature,  and  some  steam  is  con- 
densed thereby,  reducing  by  so  much  the  pressure  and  the  work  done. 
When  the  exhaust  opens  and  the  temperature  of  the  steam  falls  these 
hot  walls  radiate  their  heat  back  again  into  the  steam,  wasting  it  by  re- 
evaporating  the  vapor  carried  out  in  the  exhaust.  Thus  a  certain  large 
fraction  of  the  heat  passes  throtis^h  the  cylinder,  by  a  kind  of  side-path, 
without  really  taking  any  part  in  the  work  done  in  the  cylinder,  as  a 
leaky  flume  might  let  a  portion  of  the  water  past  a  water-wheel  without 
its  doing  any  work  on  it. 


4/2  CHAP.  XI.—LOCOMOTIVE^CYLINDER  POWER. 


583.  The  loss  from  this  source  may  amount,  it  is  alleged  by  D.  K.  Clark,* 
to  anywhere  from  ii  to  42  per  cent,  the  latter  only  with  very  short  cut-offs.  As 
its  amount  increases  (i)  with  the  range  of  temperature  and  (2)  with  the  time  of 
€xposure,  it  is  less  at  high  speeds  or  with  late  cut-offs.     Mr.  Clark  adds: 

"  These  results  sufficiently  explain  how  it  happens  that  expansive  working 
in  locomotives,  especially  in  outside  cylinder  engines,  is  in  practice  carried  out 
to  such  a  limited  extent.  We  have  rarely  found  (1850)  on  the  Caledonian  Rail- 
way—a line  Slocked  with  outside-cylinder  locomotives— that  a  cui-off  materially 
less  than  30  per  cent  is  voluntarily  adopted  by  the  engine  drivers.  In  their  own 
words,  they  •  lose  as  much  as  they  gain'  if  they  endeavor  to  work  with  a  sup- 
pression much  less  than  30  per  cent." 

This  still  (1886)  remains  as  true  for  American  practice  as  when  Mr.  Clark 
first  wrote  it.  except  that  for  30  per  cent  we  should  read  37^  or  perhaps  40  per 
cent.  But  little  gain  results  in  practice  from  cutting  off  shorter,  if  any;  and 
accordingly  the  all  but  universal  rule,  where  parts  of  the  road  are  struck  which 
require  only  a  light  power,  is  to  .throttle  the  steam,  and  reduce  its  initial  pres- 
sure even  so  much  as  one  half  rather  than  attempt  to  cut  off  earlier.  While 
this  practice  is  often  pushed  too  far,  it  is  better  than  attempting  to  cut  off  at 
less  than  three-eighths  stroke  or  more,  except  at  very  high  speeds. 

584.  Prof.  Charles  A.  Smith,  who  studied  this  question  with  gieat  care  as 
respects  stationary  engines,  lays  down  the  approximate  rule,  as  the  average  re- 
sult of  some  49  tests,  that  the  average  loss  may  be  estimated  at  3.6  lbs.  of  ex- 
cess  water  (i.e.,  %K^-^nC)  per  hour,  per  foot  of  piston  diameter  per  deg.  Fahr. 
difference  of  initial  and  final  temperature.  This  is  on  the  assumption  that  time 
is  so  important  an  element  in  the  amount  of  this  loss  that  the  number  of  strokes 
per  hour  is  unimportant,  which  is  far  from  literally  true.  At  this  rate,  assuming 
an  average  range  of  temperature  of  100°  Fahr.  in  the  cylinder,  there  would  be 
some  500  lbs.  of  steam  per  hour  condensed  internally  in  a  17-in.  cylinder,  and 
some  600  lbs.  in  a  20-in.  cylinder. 

585.  6.  The  back  pressure,  amounting  to  anywhere  from  4  to  7,  or 
even  (in  bad  practice)  10  or  12  lbs.  per  sq.  in.,  or  to  from  2  to  20  per  cent 
of  the  total  power  developed.  It  is  caused  chiefly  (until  compression 
begins  at  the  end  of  the  stroke)  by  the  contraction  of  the  exhaust-nozzles 
to  produce  the  draft  which  keeps  up  the  fires,  but  in  part  by  the  impossi- 
bility of  the  steam  escaping  quickly  enough  without  a  considerable  pres- 
sure to  drive  it  out. 

7.  The  clearance  spaces,  already  alluded  to,  waste  a  considerable 
amount  of  steam,  from  7  to  9  per  cent  when  cutting  ofT  at  full  stroke, 
but  less  when  cutting  off  short,  since  the  steam  in  the  clearance  spaces 
expands  with  the  rest  and  does  a  certain  amount  of  work  in  that  way. 


♦  ••  Manual  for  Mechanical  Engineers."  p.  880. 


CHAP.  XL— LOCOMOTIVE— CYLINDER  POWER.  473 


586.  8.  The  energy  communicated  to  the  piston  and  connected  parts 
•during  the  first  half  of  the  stroke,  in  order  to  give  it  a  velocity  of  from 
X.       JL  /  stroke         \  ^ 

*  *  \diam.  of  dTh^j  °^  ^^^  ^'■^'"'  ^"^  ^^^"  surrendered  again  during 
the  last  part  of  the  stroke,  is  in  great  part  lost,  so  far  as  useful  work  is 
concerned.  It  is  expended  on  that  portion  of  the  exhaust  which  is  shut 
up  in  the  cylinder  by  the  preclosure  of  the  valve  and  practically  recon- 
verted into  heat,  by  raising  the  steam  so  shut  up  from  a  pressure  of  per- 
haps 4  lbs.  and  temperature  of  225°  to  perhaps  120  lbs.  and  35o^ 

587.  The  aggregate  effect  of  these  differences  is  to  very  greatly  de- 
crease the  TRACTIVE  FORCE  which  it  is  mechanically  possible  for  the 
locomotive  to  exert  at  the  higher  working  speeds,  but  not  therefore  the 
HORSE-POWER  which  theengine  is  capable  of  exerting,  nor  (within  reason- 
able limits)  the  economy  with  which  that  power  is  obtained  This  is 
especially  true  of  the  first  two  causes  (par.  579),  which  we  may  now  con- 
sider, m  connection  with  diagrams  which  will  show  more  clearly  the  ex- 
act limits  of  the  effect. 

588.  Under  the  most  favorable  circumstances,  with  the  throttle  wide  open 
and  speed  slow,  the  pressure  in  the  steam-chest  hardly  ever  rises  within  5  lbs. 
•of  the  boiler  pressure,  and  this  is  still  further  reduced  when  the  steam  enters 
the  cylinders,  so  that  the  initial  pressure,  with  all  the  assistance  of  compression, 
is  rarely  within  10  lbs.  of  the  boiler  pressure.  When  the  throttle  is  only  partially 
open  (Figs.  127,  128)  or  the  speed  is  very  high,  or  especially  with  both  together, 
there  is  a  still  further  and  great  loss  of  pressure,  often  more  than  one  half.* 
Throttling  is  also  a  very  common  resort  in  preference  to  using  an  earlier  cut-off, 
as  the  engine  runs  more  smoothly  and,  practical  experience  shows,  with  but 
little  more  waste  of  steam. 

589.  In  all  such  reductions  of  initial  pressure  as  those  alluded  to  there  is  a 
•certain  theoretical  loss,  but  only  a  small  one.  It  is  greatly  exaggerated  in 
popular  belief  (as  well  as  in  certain  text-books  of  excellent  standing)  by  con- 
fusing a  loss  of  mtx^  pressure,  or  pounds  of  traction,  with  a  loss  of  energy.  The 
tractive  force  in  pounds  is  undoubtedly  reduced  in  rather  more  than  constant 
ratio  with  the  reduction  of  initial  pressure;  but  then,  if  this  occurs  only  when  a 
larger  tractive  force  is  not  required  or  cannot  be  sustained  by  the  boiler,  this  is 
in  itself  of  no  importance,  and  as  respects  the  amount  of  work  which  can  be 
done  with  the  same  quantity  of  steam,  it  is  but  very  little  affected  by  the  reduc- 
tion of  pressure,  either  theoretically  or  practically.     Theoretically,  the  amount 

*  On  some  diag^rams  taken  on  an  express  passenger  engine  on  the  Philadelphia  & 
Reading  Railroad,  taken  at  65  miles  per  hour,  it  was  found  that  the  average  effective 
pressure  was  actually  less  when  cutting  off  at  10  in.  than  when  cutting  off  at  5  in., 
although  the  amount  of  steam  used  was  far  greater. 


474  CHAP.  XI.-LOCOMOTIVE-CYLINDER  POWER. 

Loss  p.  c.  .^.  .„.  o, /or:- ; ;  ^^■L.fLrLrLrLr-^.  3r' 

-ate  years,  a„d  especially  In  a  re'.arkable teVes  o7e ^eHZ.X  mT  De.f 
ford,  =ngmeer.m-chief  of  the  mines  at  Creuso.,  France  'alT-Zjint/ 
economy  between  steam  of  i,o  lbs.  and  steam  o(  64  lbs'  is  very    m^   a„H     t '" 
we  take  the  generation  of  steam  into  consideration,  as  well  Is^ts  us     1  lo 
pressure  is  the  more  economical  "  "'  ""*  '°"'*'' 

of  thrilT"'''  '''.°-  "•  '''""•^  "''°  '^  """'"'y  °"«  °'  '"e  most  careful  students 
of  the  theory  and  practice  of  the  locomotive,  concludes  that  "as  thl  oT, 
wre-drawing  is  of  little  or  no  moment,  and  as  wireiawing  Z  to    ot^eT' 

oTer„r;'"  "■ '°  ^" '"'-  -'■""■  ^  --'« -  p^-  ad™er  r^t 

of  e°n^;e*'s"'  Wh.nT'"*'  ""^  '?^  ^^"""^'^  ■■^•^""  "'^  '"«-«  power 
al:rdtar7w    .;/;;"edsTa'^?r:^  ^T  ^""^'^'-"'^ 

or  50  mi,es  peT  Hour  ^^^:^^:::^:^zz^:'^::!i:-: 

tram  l.ght,  and  much  tractive  power  is  not  required  ;  but  when  it  occu^ 
to  any  mater.al  extent  with  late  cut-offs  at  ordinary  working  s^eds  of  ,r 
to  1 5  mdes  per  hour,  it  is  more  objectionable 

th,f  >  •  ^"/°"""«^ly-  experiment  seems  to  indicate  quite  uniformly 
conVd  ""■^^;"^™'«  '"-  the  exception  for  freight  engines  to  show  I 
consKJerable  reducfon  in  cylinder  efficiency  even  a?  their  lower  workb^ 

rTn  h  '°  T  'T"'  "^  '°"  '^  "  '^  ^«f«  »°  "-  -'thout  danger  of    hf 
tram  bemg  brought  to  a  stop  by  slight  additional  resistance  fror^  curves 
grades  head  w.nds,  or  bad  track,  do  cause  a  very  material  decreieo^ 

uln  f  UsTvXTe  ult^^ T''""  '■■  ^"'  "^"'^^ '^^  ^"«'"'=  cannot "o'tb? 
uLiiize  us  available  ultimate   tract  ve  nower— i  ^     xr^^r  „^    i       i-      . 

wheels-at  any  practicable  wor.in,  s,lZL::::7^^'^^^^^^ 

d.fference  .  small  compared  with  the  effect  of  further  inc;ease  of fpel^ 

the  lit  J„Tdi;T.:^(tgr";rtt^r:  r  r".'""^^'^  ^^  ^"  ^-^  ^'^-  -^^  '•« 

^       ^  ^^'^^-  '3^  '°  '39)  of  the  engine  whose  performance  is 


*  Annales  Industrie^  Feb.,  1885 

t  "  Manual  for  Mechanical  Engineers,"  p.  879. 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER.  475; 

recorded  in  Table  146  and  Fig.  123  (par.  571).     The  same  thing  appears  in  the 
diagrams  accompanying  Mr.  Stroudley's  paper  (par.  570  and  Fig.  122).  where, 

With  a  cut-off  of , 

At  a  speed  in  miles  per  hour  of *     -  12  m  30  m 

And  steant-chest  pressure  of .'.*.'     140  lbs.      130  lbs. 

The  average  pressure  was ^^g  lbs.     57-2  lbs. 

The  horse-power  bemg 262  502 

At  12  miles  per  hour,  with  60  per  cent  cut-off  and  125  lbs.  steam-chest  ores- 
sure  (bmler  pressure  full  5  lbs.  more),  the  average  cylinder  pressure  was  95.4 
lbs.,  whereas  at  4  miles  per  hour  an  average  of  about  85  per  cent  of  the  boiler 
pressure  was  obtained  in  the  cylinder- about  the  best  which  is  ever  possible. 

593.  That  this  should  occur  at  high  speeds  is  practically  unavoidable 
but  tiiat  It  should  occur  at  slow  speeds  of  less  than  15  miles  per  hour  is 
in  no  respect  a  mechanical  necessity,  nor  does  it  require  any  radical 
modification  of  existing  engines  to  cure  it.  whenever  it  appears  desirable 
but  merely  some  slight  modification  of  the  valves.  Some  engines  do  not 
show  It,  but  more  do.  The  chief  reason  why  it  is  not  done  is  that  no 
particularly  useful  end  would  be  served  thereby,  since  the  imperfections, 
of  the  gradients  and  of  the  locomotive  serve  to  justify  each  other  bv  de- 
stroying to  a  very  large  extent  the  advantage  of  remedying  one  without 
the  other.  It  is  important  that  the  true  nature  of  the  difficulty  should  be 
clearly  understood.  \ 

594.  The  largest  tractive  pulls,  by  far.  on  nearly  all  railways,  are  ex^ 
erted  in  getting  trains  under  way  from  stopping-places  on  unfavorable 
grades  or  curves.  There  are  few  roads  indeed,  and  those  onlv  havings 
very  heavy  grades,  on  which  the  traction  between  stations  is  the  heaviest 
So  long  as  this  is  so.  the  need  is  not  felt  that  an  engine  should  be  able  to 
exert  sometiimg  like  its  maximum  pull  between  stations  at  fair  workin<r 
speeds,  and  as  a  very  natural  consequence  their  valves  are  not  arranged 
so  that  they  can  do  so.  *i"gea 

Now.  as  a  rule,  a  large  part  of  the  additional  tractive  force  demanded 
at  stations  may  be  saved  by  more  careful  study  of  the  grades  at  stations  • 
but  If  this  be  done,  and  ,t  be  attempted  to  increase  the  trains  correspond- 
ingly the  only  effect  with  very  many  engines  will  be  that  they  will  either 
"  stick  on  the  grades"  or  lose  so  much  time  that  to  utilize  the  improvement 
at  stations  will  be  impracticable.  For  the  same  reason,  if  it  be  endeavored 
to  find  out  where  the  engines  are  really  most  taxed  it  will  often  be  diffi- 
cult  to  do  so.  They  slip  their  wheels  most  at  stations,  but  "  thev  have 
all  they  can  do  to  make  time  on  the  grades ;  so  that  from  the  bare  face 
of  the  statements  there  will  be  little  to  show  where  the  weakest  point  is, 

{see  fiage  ^^Z)> 


; 


1 


rf 


It;). 


l| 


476  ClfAP.  XI.-LOCOMOTIFE^CYLmDEJ^ 


POWER. 


fflUHc^<^^ 


CHAP.  XI.-^LOCOMOTIVE— CYLINDER  POWER.  ^'JJ 


Figs.  126  to  133  were  taken  in  some  tests  on  the  Cincinnati,  New  Orleans  &  Texas 
Pacific  (Cincinnati  Southern)  Railway,  from  a  fine  Baldwin  passenger  engine  of  the  follow- 
ing dimensions  : 


Cylmders ... 

Drivers     

Weight  Jondnvers 

Tractive  force  per  pound  of  av. 
press,  in  cylinder  (Table  151)... 
ValvM    J  Allen-Richardson: 
vaives,  ^  Lap,  %  in. ;  lead,  ^  in. 


z8  X  24  in. 

68  in. 
60,000  lbs. 
90,000  lbs. 

zi4.4lbs. 


Ports,  -I  steam 

'lexhaust 

Exhaust  nozzle 

(  ^"^^ ;;.;  1,325  sq.  ft 

J  fire-box 133  sq.  ft, 


t6  X  \\  in. 

16  X  2i  in. 
si  in. 


Heating 
surface, 


] 


Grate  area 


The  train  hauled  consisted  of  8  cars,  weighing  480,000  lbs. 


Total 1,458  sq.fu 

17  sq.  f  t.. 


Fig.  lag. 


Fig.  130. 


Fig.  129. 


Boiler  pressure 

Cutoff 

Throttle  open 

Speed 

Av.  cylinder  pressure.. 
Indicated  horse-power.. 
Loss  initial  pressure 


145  lbs. 
8  in. 

\ 
53.4  m- 
37-2  lbs. 

583 
32  lbs. 


145  lbs. 
Sin. 

\ 
45 -o  m- 
44-3  lbs. 

608 
22  lbs. 


Fig.  130. 


140  lbs. 
6  in. 

54-6m. 

32.5  lbs. 

541 
24  lbs. 


135  lbs. 
4  in. 

i 
55-9m. 
28.0  lbs. 

477 
26  lbs. 


Figs.  129,  130  show  the  same  effect  of  speed  as  Figs.  126-128  very  forcibly,  both  bv 
comparison  of  the  full  and  dotted  diagrams  and  (still  more  forcibly)  by  comparing  the 
solid  diagrams  in  Figs.  120  and  121,  which  may  be  said  to  be  taken  under  precisely 
similar  circumstances  (balancing  difference  in  throttle  against  difference  in  boiler  pressure): 
except  that 

Speed  was ^'I.^f-       '^\--^' 

Reducing  average  pressure  from 61  8    to       -xn  2. 

Yet  that  this  does  no  real  harm  to  hauling  capacity  is*  * 
evident  from  the  fact  that  the  horse-power  at  which 

the  engine  was  working  increased  from    • 549       to     ^g^ 

Comparing  the  dotted  Fig.  131  with  the  solid  Fig.  132  we  see  that  the  combined 
effect  of  5  lbs.  liigher  boiler  pressure,  4  ins.  longer  cut-off,  and  a  throttle  %  instead  of 
\^  open,  gave  only  a  slightly  higher  average  pressure  (6.8  lbs.),  indicating  that  the  slight 
difference  of  0.8  mile  per  hour  in  speed  very  largely  counterbalanced  all  these  advantages 
Fig.  132,  contrasted  with  the  dotted  Fig.  129,  illustrates  a  truth  which  might  be  proved 
m  many  other  ways,  that  after  the  speed  gets  fairly  high  it  does  little  or  no  good  to 


478  CHAP,  XL^LOCOMOTIVE-CYLINDER  POWER. 

admit  more  steam  to  the  cvlindpr«s       tk«  o,«.,* 

.aine.  is  use.  „p  .  Uc.  p^Lr.^,  ^^1^.  7:iL^^^-:33r;:  --'O  ^ 


Boiler  pressure 

Cut-oflf 

Throttle  open , 

Speed 

Av.  cylinder  pressure. 
Indicated  horsepower 
Loss  initial  pressure, 


145  lbs. 
14  in. 
f 
26.3111. 

83.3  lbs 

668 
24  lbs. 


142  lbs. 
14  in. 

24.3  ni. 
81.3  lbs. 

603 
20  lbs. 


141  lbs. 
II  in. 

46.9  m. 
37.9  lbs. 

542 
50  lbs. 


nor  to  indicate  that  the  one  arises  from  excessive  demand  on  the 
tract^e^power.  which  is  remediable  only  by  changing  theTades  while 
r  "  1 148  the  other  fs  caused  by  deficiency  of  cylin- 

der power  only,  which  is  remediable  for 
the  most  part  by  trivial  changes  in  the 
valves. 

696.  By  the  use  of  smaller  drivers, 
both  the  cylinder  and  boiler  power  are  in 
effect  increased  proportionately,  so  far  as 
tractive  power  in  pounds  is  concerned, 
at  the  expense  of  speed  ;  so  we  may  con-' 
elude,  as  we  began  (par.  483),  bv  saying 


Fig.  133 


Boiler  pressure, 
■Cut-off,  .  .  . 
Throttle  open,  . 
Speed,  .  .  . 
Av,  cyl,  press., 
Ind.  H.  P.,  .  . 
Grade,  .  .  . 
I<oss  init.  press., 


X48  lbs.  that  w.thin  the  limits  of  necessary  freight 

48 1  m     ^^?^^^    ^"5^  x.r^cx:xv^    power  is    feasible 

?.4  ibi.  which  the  adhesion  between  the  drivers 


39-.  ,_ ,^^^ 

level.      a"d  rails  is  capable  of  transmitting.     At 
5Q6    p  ,  ,       ^  '^''  Passenger  speeds  it  is  quite  otherwise. 

„h-^  ; '  f '*'''"^'''  ""«^'"^^'  '"""'"g  ^t  speed,  almost  never  need  to  have  their 
ultimate  tractive  power  in  pounds  available,  and  accordingly  we  find  that  they 


CHAP.   XL— LOCOMOTIVE— CYLINDER  POWER.  479 


•often  fall  m  practice  very  far  below  it;  nor  can  this  be  considered  an  evil  As 
a  small  reduction  of  speed  means  a  considerable  increase  of  tractive  power  we 
see  another  reason  beside  the  great  aid  given  by  momentum  (par.  397)  why  the 
practical  limit  to  the  power  of  passenger  engines  is  but  little  aff<.cied  by  the 
grades,  w.thm  moderate  limits,  provided  the  average  speed  is  not  brought  too 
low  by  the  necessary  reduction  at  a  few  points. 

697.  Tables  151  and  152  and  Figs.  140  to  148  not  unfairly  represent  the 
average  conditions  of  American  freight  practice.     The  full-line  diagram  in  Fig 
132  shows  about  the  highest  average  cylinder  which  is  ever  practically  realized 
ixcept  in  starting,  and  comes  very  near  to  the  latter  in  the  form  of  the  diagram 


Table  I6I, 

Cylinder  Tractive  Power  of  Various  Engines  for  an  Average 

Effective  Pressure  of  100  Lbs.  Per  Square  Inch. 

diam.a  cylinders  X  stroke 


Formula :  T  = 


diam.  drivers. 


SiZB 

OP  Dkivers. 
Inches. 


48. 
50. 
52. 
54. 
56. 
58. 
60. 
62. 

^4. 

66. 

68 

70. 

72. 


Size  of  Cylinders. 


16  X 


24 


17  X  24 


' 


12,800 
12.288 
II. 815 
11.378 
10.971 

10  593 
10. 240 

9910 
9.600 
9309 
9035 
8.778 

8,533 


14.450 
13  872 

13.339 
12.844 

12.386 
12.237 
11.560 
11.187 
10,838 
10.509 
10.200 
9.909 
9.633 


18  X  24 


16.200 

15.553 

14-954 
14  400 

13  886 

13.407 
12,960 
12,542 
12,150 

11.782 

11.435 
11,109 

10,800 


19  X  24 


18,050 
17.328 
16  662 
16.044 

15.474 
I4.93« 
14,440 
13974 
13.538 
13.128 
12.749 

12.377 
12,033 


20  X  24 


20.000 
19  200 

18.468 

17.778 

17.143 
16.552 

16.000 

15  484 

15.000 

14  546 
14.118 

13.714 
13333 


FOR  A  DIFFERENT  STROKE.-For  a  Stroke  o{%.  instead  of  .4  in.,  diminish  the  tabu- 
lar tractive  force  for  given  diameter  of  cylinder  and  drivers  by  A,  or  multiply  by  U  (l|). 
For  a  26  in.  stroke,  increase  the  tabular  quantity  bv  ,'. 

*•  28 "    «       ..     ..     ..       u      .:  "• 

"     30  ••        ••  •«         "        "  ..  ..  J'^t^ 

FOR  A  DIFFERENT  SIZE  OF  DRIVERS.-The  tractive  force  is  inversely  as  the  diameter 
of  the  drivers,  whence  it  may  usually  be  determined  from  the  above  table  by  a  simple  pr^ 
portion,  or  computed  directly,  as  also  for  a  different  diameter  of  cylinder 

One  hundred  pounds  average  pressure  is  as  high  as  can  be  counted  on,  even  in  starting 
from  130  to  140  lbs.  boiler  pressure.  '  starting 


H^ 


480 


CffAP.  XI.-LOCOMOTiyE-CYLINDER  POWER. 


Lbs.  per 
sq.  in. 
Boiler  Pr.  129. 
Initial   "    112,5 
Back     "       2.0 
Mean    "     55.4 


Lbs.  per 

sq.  in. 
Boiler  Pr.  135. 
Initial   "    122.0 
Back     "       9.6 
Mean    "     48.9 


Lbs.  per 

sq.  in. 
Boiler  Pr.  98. 
Initial   **    78.6 
Back      '•      a.8 
Mean    "   33.2 


Speed                                     ^'°8m''  ^'''- ''''  ^'"- '36. 

Theoretical  mean  pressure  93.'66  li;s.  os' ff  lb,  '^'^  ,w ' 

Actual              "           "         „  9801  lbs.  71. IS  lbs. 

^^■^  J8.9  33^ 
Loss  of  pressure 


38.3 


39-1 


38.0 


.0  cyn^ae.  v::^::  a.^  :■"::■;  'corf.  T't  """  -^^  "-'"^  ""' 


CHAP.  XI.—LOCOMOTIVE— CYLINDER  POWER.  481 


Lbs.  per 

sq.  in. 

Boiler  Pr.  140. 
Initial   "    135.8 
Back     "       i.o 
Mean    "   111.7 


Lbs.  per 

sq.  in. 

Boiler  Pr.  130. 
Initial   "    123.8 
Back     "       2.1 
Mean    "     90.6 


Lbs.  per 
sq.  in. 

Boiler  Pr.  132. 

Initial   "    115. 

Back     "       1.9 

Mean    "     72.2 


FifiTs.  134  to  139,  diagrams  of  16x24  American  Engine,  61-in.  drivers,  taken  on  the  test  trip 
of  which  details  are  given  in  Table  146-7. 


be  seen  that  only  71  per  cent  of  the  boiler  pressure  is  realized  in  the  cylinders, 
aiid  that  even  then  it  is  developing  a  fairly  high  average  horse-power.  Both 
Figs.  140  and  141  develop  the  effect  of  higher  speed  to  reduce  tractive  force 
very  clearly,  and  also  show,  by  the  comparative  indicated  horse-power,  that  it 
31 


.jmmi 


482 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER. 


CHAP.  XI.— LOCOMOTIVE— CYLINDER  POWER. 


483 


Table  152. 

Indicator  Tests  of  Mogul  Engine,  18  x  24,  Cincinnati,  New  Orleans 
&  Texas  Pacific  Railway,  hauling  Train  of  ii  Loaded  and  23  Empty 
Cars,  836.000  Lbs. 


Boiler  pressure 

Cut-off 

Throttle  open.. 
Speed  per  hour 
Av.  cyl.  pres. . 

Ind.  H.  P 

Loss  init.  pres. 


29.3  m. 

48.8  lbs. 

680 

34  lbs. 


Boiler  pressure 

Cut-off 

Throttle  open.. 
Speed  per  hour 
Av.  cvl.  pres  . 

Ind.  H.  P 

Loss  init.  pres 


140  lbs. 
7  in. 

i 
12.5  m. 

47.0  lbs. 

279 
17  lbs. 


*^^= — ^^ 

C_.   - 

— ^=^ 

49. 

Fig. 

143- 

132  lbs. 

135  lbs. 

127  lbs. 

7  in. 

7  in. 
Full. 

7  in. 
i 

27.3  m. 
37.7  lbs. 

35  9  m. 
32 . 7  lbs. 

31.2  m. 
30.6  lbs. 

491 
20  lbs. 

558 
9  lbs. 

455 
12  lbs. 

Table  153. 

Indicator  Tests  of  Mogul  Engine,  19  X  24,  Cincinnati,  New  Orleans 
&  Texas  Pacific  Railway,  hauling  a  Heavy  Freight  Train,  28  Cars, 

WEIGHING,  with    LoAD,  969,000  LbS.      AVERAGE  SPEED   OF  ALL  TESTS,  26.4 

Miles  Per  Hour.     Average  I.  H.  P.  426. 


Fig.  X44. 


Fig.  145. 


Boiler  pressure 

"Cut-off 

Throttle  open.. 
Spee«l  per  hour 
Av.  cvl.  pres. . 

Ind.  H.  P 

i^oss  init.  pres. 


120  lbs. 
12^  in. 

f 
20.9  m. 

47.9  lbs. 

440 

29  lbs. 


125  lbs. 
7  in. 

i 
29.4  m. 
30.6  lbs. 

396 
9  lbs. 


132  lbs. 
7  in. 

f 

27.5  m. 
29.0  lbs. 

351 
20  lbs. 


Fig.  146. 


Boiler  pressure 

Cut-off 

Throttle  open.. 
Speed  per  hour 
Av.  cvl.  pres. . 

Ind.  H.  P 

Loss  init.  pres. 


130  lbs. 

130  lbs. 

120  lbs. 

130  lbs. 

7  in. 

7  in. 

\i\  in. 

12^  in. 

i 

i 

i 

i 

32.2  m. 

30  6  m. 

21.9  m. 

30.6  m. 

31.8  lbs. 

32.1  lbs. 

43 . 8  lbs. 

33.9  lbs. 

450 

432 

422 

456 

8  lbs. 

10  lbs. 

33  lbs. 

14  lbs. 

Hi 


484  CHAP.  XI.—LOCOMOTIVE-^CYLINDER  POWER, 


CHAP.    XII.— ROLLING-STOCK. 


485 


can  do  no  possible  harm,  so  far  as  the  load  hauled  is  concerned.  Figs.  142: 
and  143  develop  the  same  facts  still  more  forcibly.  Seven  of  the  eight  dia- 
grams  of  Table  152,  it  will  be  seen,  develop  nearly  the  same  horse-power,  600. 
being  about  the  maximum  for  this  type  of  engine,  and  amounting  to  35  horse- 
power per  square  foot  of  grate  per  hour— which  is  more  than  can  be  averaged, 
but  is  often  reached  for  the  moment  (see  par.  550). 

598.  Table  153  shows  the  performance  of  a  somewhat  heavier  en- 
gine hauling  a  heavier  train,  but  doing  less  work.  Very  naturally,  the 
effect  of  speed  to  modify  the  average  cylinder  pressure  is  less  conspicuous. 
In  the  two  diagrams  given  in  Fig.  147  we  see  the  effect  of  speed  to  re- 
duce the  effective  pressure  very  clearly,  for  Fig.  146  and  others  show 
that  throttling  alone  accounts  for  but  a  small  part  of  the  difference. 

599,  Fig.  148  shows  a  couple  of  diagrams  taken  from  a  test  of  a  Con- 
solidation engine  on  the  same  road  when  doing  fairly  heavy  work,  about 
20  H.  P.  per  square  foot  of  grate  per  hour,  or  about  80  per  cent  of  an 
everyday  maximum.  The  way  in  which  the  same  horse-power  is  pro- 
duced and  used  up  in  a  very  different  way  is  very  clearly  brought  out. 


FiG.  148. 


Boil. 
Pres- 
sure. 
Lbs. 

Cut- 
off. 
Ids. 

Throt- 
tle. 

Speed. 

Miles 

per 

Hour. 

Av. 

Pres- 
sure. 
Lbs. 

Indi- 
cated 
H.P. 

Loss 
with- 
out 
Pres. 
Lbs. 

»5- 
«3. 

% 

H 

• 

ia.4 

SQ.I 

93-3 
40.5 

605 
616 

IX. 

35. 

X40. 
»35- 

CHAPTER  XII. 

ROLLING-STOCK. 

600.  One  of  the  greatest  changes  in  the  recent  history  of  American 
railways,  and  one  which  has  contributed  as  powerfully  as  any  to  the  great 
reduction  in  cost  of  transportation  which  has  taken  place,  is  the  marked 
increase  in  the  average  capacity  of  freight  cars — an  increase  which  has 
been  accompanied  by  a  very  slight  increase  in  the  dead  weight  of  the 
•cars.  In  Table  154  are  given  the  leading  dimensions  of  both  the  new 
and  old  standard  freight  cars  of  the  Pennsylvania  Railroad,  which  may 
be  accepted  as  in  a  measure  typical  of  all  American  rolling-stock,  and 
the  contrast  is  at  once  evident. 

This  change  has  taken  place  almost  entirely  since  the  first  edition  of 
this  treatise  was  prepared,  in  1876,  and  is  in  good  part  the  result  (and  the 
most  useful  result)  of  the  narrow-gauge  movement,  which  concentrated 
attention  upon  admitted  extravagances  of  past  administration.  In  part 
it  is  an  indirect  effect  of  the  introduction  of  steel  rails.  A  still  more  po- 
tent cause,  however,  has  probably  been  the  enormous  increase  in  volume 
of  traffic,  especially  in  bulky  freight  to  be  transmitted  great  distances  at 
low  rates,  which  made  the  last  degree  of  economy  indispensable. 

601.  Ten  or  twelve  years  ago,  ten  tons  (20,000  lbs.)  was  the  ordinary 
maximum  load  for  freight  cars,  24,000  lbs.  only  occasional,  and  30,000 
lbs.  almost  unheard  of;  but  of  the  capacities  now  specified  (1885),  40,000 
lbs.  is  more  common  than  any  other,  anything  less  than  28,000  or  30,000 
quite  exceptional,  and  50,000  lbs.  no  longer 'rare.  There  were  in  1885, 
180  fiat  cars  and  10  box  cars  of  60,000  lbs.  capacity  on  the  Northern  Pa- 
cific, and  from  2  to  10  of  the  same  capacity  on  a  number  of  other  roads. 
Of  50,000-lb.  or  25-ton  cars  there  are  far  more,  numbering  several 
thousands  on  many  roads,  and  this  bids  fair  to  become  the  standard  coal 
car;  while  there  are  not  a  few  box  cars  in  use  of  that  capacity.  As  fair 
evidence  as  any,  perhaps,  of  the  gieat  increase  in  the  average  car-load  in 
recent  years  is  the  classification  list  of  the  Pennsylvania  Company,  given 
in  Table  155,  which  includes  all  the  freight  rolling-stock  of  that  com- 
pany's system,  existing  in  sufficient  numbers  to  form  a  class,  in  1885. 


486 


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Ciy^/>.    XII.— ROLLING-STOCK, 


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CLfAI".   XIL— ROLLING-STOCK. 


487 


Table  155  is  interesting,  not  only  as  giving  the  average  capacity,  but 
for  the  variety  of  dimensions  appearing  among  the  standard  types  of  a 
single  line.  It  will  be  seen  that  in  these  13  classes  there  are  10  different 
lengths  (not  counting  differences  of  less  than  an  inch),  and  9  different 
widths,  ranging  by  jumps  of  a  few  inches  each  from  7  ft.  5  in.  to  8  ft.  1 1 
in.;  all  in  freight  service  only.  This  diversity  is  in  part  because  the  cars 
must  be  adapted  to  many  different  uses,  but  in  the  main  it  is  evidence  of 
the  fact  that  a  process  of  evolution  is  still  going  on,  so  that  the  rolling- 
stock  of  the  country  is  for  the  present  in  a  transition  state.  The  general 
tendency  of  this  process  can  alone  be  stated  :  to  increase  the  capacity  of 
freight  cars  up  to  25  or  even  30  tons  of  paying  load,  and  perfect  their  con- 
struction so  that  such  loads  may  be  handled  with  safety,  at  fairly  high 
speeds. 

602.  Two  changes  which  may  reasonably  be  expected  to  come 
about  in  the  next  few  years  will  greatly  strengthen  this  tendency,  and 
probably  materially  modify  the  handling  of  freight  trains  as  well — the 

Table  155, 

Classification   List  of   Freight  Cars  of  the  Pennsylvania  Company, 

1885. 


Kind  of  Car. 


Long  box*... 

Box* 

Refrigerator, 


Provision 

Stock  (standard) 


Gondola  (standard) 

"        (widened) 

"  (standard,  long)  . . 
Drop  bottom  (standard)*. . . 
Hopper  bottom  (standard)*. 
Stone  flat  (sundard) 


Class. 


Q. 

M. 

R. 
M.  &0. 
M.  &0. 

O. 
P.  B. 
P.  D. 
P.  E. 

E. 

D. 

C. 

S. 


Inside  Dimensions. 


Length. 


ft.  in. 

33  ioJ4 

21  5 

23  I 

33  10 

29  A% 

29  8% 

29  m. 

33  o 

33  o 

23  5 

35  7 


Width. 


ft.  in. 
8    4^ 
7  wYi, 

7  ^o^ 
7  10 
7  10 
5 


8 
8 
8 
8 

7 

7 
7 


3 
o 

4 
5 
S 
7 


8  II 


Height. 


ft.  in. 
7    4 

5  10^ 
5    81^ 
5  10 
5  »o 
7    2 


6 

2 
3 
2 
3 


3  " 


Standard 
Capacity. 


lbs. 
40,000,  50,000 

26,  30,  40,000 

40,000 

40,000 

40,ocx> 

40,000 
26,  28,  30,000 
26,  30,  40,000 
50,000,  60,000 

40,000 

40,000 

50,000 

50,000 


Standard  height  of  floor  from  rail,  all  cars,  4.0^4.  P.  D.  gondolas,  built  before  present 
standards  were  adopted,  have  sides  only  20  in.  and  2  ft.  high. 

The  weights  of  these  cars  are  substantially  the  same  as  those  for  the  Pennsylvania 
Railroad,  given  in  the  preceding  table,  those  marked  *  being  substantially,  if  not  exactly, 
the  same  cars. 


0mm 


:i 


488 


CHAP.   XII.— ROLLING-STOCK. 


adoption  of  some  form  of  automatic  coupler,  and  the  adoption  of  a 
freight-train  brake.  The  effect  of  all  these  causes  combined  will  prob- 
ably be  to  assimilate  the  handling  of  freight  trains  more  and  more  to  the 
handling  of  passenger  trains,  except  that  the  speed  will  be  much  more 
variable  :  as  low  as  now  on  heavy  grades,  but  very  much  higher  on  the 
easier  sections  of  the  line,  where  great  tractive  force  is  not  demanded 
and  where,  consequently,  higher  speed  is  entirely  feasible.  As  the  ordi- 
nary passenger  piston  speed  is  not  found  to  be  injurious,  we  may  expect 
with  some  confidence  that  at  no  distant  day  maximum  freight  speeds  of 
28  to  30  miles  per  hour,  which  would  give  about  the  same  piston  speed 
will  be  established  in  general  practice. 

The  effect  of  this  change  will  be  to  greatly  facilitate  the  haulin^r  of 
heavy  trains,  even  without  considerable  modification  of  gradients  for 
reasons  discussed  in  Chapter  IX..  and  elsewhere.  With  the  more  per- 
feet  road-beds  and  track  which  become  every  year  more  general  there  is 
no  reason  to  believe  that  wear  and  tear  will  be  materially  increased 
while  the  cost  of  power  per  ton-mile  will  certainly  be  rather  less  th  in 
more,  not  only  because  of  the  less  time  afforded  for  radiation  of  heat 
from  the  exterior  of  the  locomotive  and  journal-boxes  and  interior  of  the 
cylinders,  but  from  less  destruction  of  energy  by  brakes,  since  it  can  be 
stored  in  the  train  in  the  form  of  velocity,  and  afterwards  used,  to  a 
much  greater  extent. 

603.  The  primary  requirement  for  the  attainment  of  this  desirable  end 
is  the  adoption  of  a  freight-train  brake,  and  fortunately  there  now  appears 
every  prospect  that  some  approved  form  of  freight-train  brake  will  come  into 
general  use  within  a  few  years,  and  thus  greatly  simplify  the  problem  of  ob- 
taming  the  most  favorable  virtual  gradients  cheaply,  in  addition  to  the  direct 
advantages.  The  latter  alone  are  much  considered  bv  the  public,  but  on  cer- 
tain lines  at  least  their  effect  on  the  virtual  gradients  will  almost  certainly  be  of 
more  financial  importance,  and  make  the  expenditure  for  train-brakes  a  most 
profitable  one.  independently  of  the  greater  safety  and  convenience. 

604.  The  ultimate  solution  of  the  problem  of  automatic  couplers  is  a  more 
doubtful  matter,  and  it  may  be  well  on  toward  the  close  of  this  century  before 
automatic  couplers  come  into  use.  To  the  highest  efficiency  of  train-brakes 
they  are  almost  essential,  and  the  breaking  in  two  of  trains  is  another  evil 
lending  to  discourage  the  hauling  of  heavy  trains,  which  they  will  very  largely 
remedy.  The  chief  obstacle  to  their  introduction  is  and  has  always  been  not 
the  mechanical  difficulty  of  the  problem,  but  the  fact  that,  owing  to  the  contin- 
uous interchange  of  cars,  no  real  benefit  would  be  derived  from  such  a  coupler 
until  It  had  come  into  almost  universal  use.  whereas  a  passenger-coupler  was 
as  useful  to  the  road  applying  It  as  it  ever  could  be.  as  soon  as  it  was  applied 


CHAP.   XII.— ROLLING-STOCK. 


489 


to  their  own  cars,  or  even  to  a  few  trains.  The  consequence  of  this  difference 
is  that  the  usual  cut-and-try  process  of  development  and  survival  of  the  fittest 
was  impossible  wii«h  freight  couplers,  whereas  the  first  practicable  passenger- 
coupler  was  adopted  by  a  few  roads  almost  immediately,  from  which  the  conta- 
gion of  example  sped,  each  gaining  the  full  benefit  of  their  own  expenditure  as 
soon  as  made,  and  losing  nothing  by  the  backwardness  of  others. 

The  greatest  immediate  obstacle  to  a  general  agreement  on  some  one 
•freight-coupler,  or  on  two  or  more  couplers  working  well  together,  is  the  exist- 
ence of  two  distinct  types  of  such  couplers,  which  have  become  known  as  the 
"link"  and  (by  a  somewhat  awkward  and  inappropriate  term)  "vertical-plane" 
or  lateral-hook  couplers.  The  link  type  resembles  more  or  less  closely  the 
ordinary  form  of  coupler,  but 
arranged  to  work  automatical- 
ly, and,  in  the  best  types,  dis- 
pensing with  loose  links  and 
pins.  The  hook  type  is  model- 
led after  the  couplers  which 
have  been  so  successful  in  pas- 
senger service.  Fig.  149  shows 

,    ^,  ^  J  Fig.  140. — Ames  (Link)  Car-couplkr. 

'One    of    the    most    approved  ^^ 

forms  of  link-couplers— the  Ames,  and  Figs.  150.  151  one  of  the  most  approved 
iorms  of  hook-couplers— the  Janney.     Neither  of  these  couplers  has  been  se- 


FlG.  150. 


Fig.  151. 


Janney  (Hook)  Car-coupler. 


.lected  for  illustration  as  the  best  of  its  type,  but  merely  as  fairly  representative 
and  among  the  best  and  most  approved. 

605.  Each  of  these  types  has  strong  advocates,  but  it  may  be  expected  with 
some  confidence  that  the  hook  type  will  ultimately,  and  perhaps  very  speedily, 
prevail,  for  the  reason  that  it  insures  a  steadier  and  smoother  motion  of  the 
train  by  doing  away  with  loose  slack,  which  is  the  chief  provocative  of  breaking 
in  two.  of  trains  and  of  broken  draw-bars  and  other  damage,  while  it  has  been 
proved  not  to  be  of  appreciable  advantage  in  starting  heavy  trains.     There  is 


wmimm 


490 


CHAP.   XII.—KOLLING-STOCK. 


a  general  impression  to  the  contrary,  and  not  a  little  floating  evidence-  but  in 
careful  tests  at  Burlington,  la.,  .886,  it  was  found  that  there  was  nnth' 
gained  by  loose  slack  n.ore  than  could  be  secured  by  first  bac^Th  locoZ 
t.ve  against  brakes  set  at  the  rear  of  the  train,  and  so  compressing  the  sprir. 
hroughout  the  train.  On  the  locomotive  starting  forward  the  com  Pre  sed 
spnngs  g,ve  a  push  to  each  car.  and  this  push  seems  to  be  more  effecUve  tha^ 
when  the  same  thing  is  done  with  a  train  having  slack 

As  several  good  couplers  of  each  type  now  exist  which  will  work  ouiti^ 
well  together,  nothing  now  impedes  a  decision  of  the  coupler  questTon  except 
the   existence   of  these    two   types,    each   of  which    has    certain  Idvantages 
The  advocates,  of  each  are  indisposed  to  proceed  very  actively  with  the  equtpi 
ment  of  the.r  cars  until  the  vexed  question  of  a  choice  is  settled  ^    ^ 

h,»:     ;■  '"Z^'"'''  '56  are  given  various  details  as  to  certain  very   large  or 
heavy  freight  cars,  and  in  Table  157  the  leadmg  dimensions  of  the  mot  usua^ 
passenger  cars.    In  respect  .0  the  latter,  the  tendency  is  more  and  more  towa^i 
the  use  of  the  heavy  sleeping  and  drawing-room  cars  for  a  large  percentage  0I 

Table  156, 
Dimensions  of  Certain  Very  Large  and  Heavy  Freight-Cars. 


Furniture 

Car 
Chicagfo  & 

N.  W. 
Railway. 


Length  over  sills. 
Width  over  sills. . 
Length  over  roof. 
Width  over  roof. 


Inside  length 37 


width 
"       height... 
Extreme  height  . 
"         length. 
Total  wheel-base 

Weight 

Capacity 


ft. 
38 

8 
38 

9 


M.  C.  B. 

Standard 
60.000-lb. 
Box  Car. 


8 
8 
13 


in. 
O 

6 

li 

6i 
oi 
5f 

8i 


Pile-driver 

Car 

Ga.  Central 

Railroad. t 


Philadelphia 

&  Reading 

Standard 

Coal  Car. 


40  Hi 
31   lOf 


40,000  lbs. 


60,000  lbs. 


32,000  lbs. 
+39.000    •* 


\  18,480  lbs. 
56,000    ** 


*  To  top  of  brake-shaft,  la  ft.  lo  in.  ~ 

t  Leaders  to  hammer,  40  ft.  high,  taking  a  pile  18  in   X  w  ft  •  c«  ,vv.  m. 
moved  back  to  let  the  front  of  the  car  profect      Four  t^u^ks  in  ^if  'rami  "^  ^'^"''" 
piles  to  ,8  ft.  below  the  rails.  irucics  in  all.     Hammer,  8000  lbs.;  drives 

The  Baltimore  &>  Ohio  Railroad  have  a  large  and  increasing  numh..  nf .     / 
in  use  carrying  so^ooo  lbs.,  and  weighing  loaded  3614 /^Z  f  "'"''" 

lbs.  in  all  on  ^r//.  out  to  out  0/ bu/ers    :!Tto\...l     1'  .>*^^;«««'«^  >''''•  76,000 
Consolidation  locomotives.  ^         ^  ^"''  ''''  '""^  '"^  ""''^'*'  P'''  >-'  e^ 


CHAP.    XII.— ROLLING-STOCK. 


491 


the  travel,  and  many  through-trains  consist  of  them  almost  exclusively — a  fact 
which  tends  to  make  the  rate  of  long  grades  and  of  grades  at  stations  of  almost 
as  much  importance  to  them  as  to  freight  trains,  but  owing  to  the  fact  that,  by 
varying  high  velocities  slightly,  a  great  difference  in  tractive  power  on  up 
grades  results,  and  all  but  quite  long  grades  may  be  operated  almost  as  virtual 
levels  (par.  397),  the  disadvantage  of  dead  weight  is  very  much  less  in  passen- 
ger service  than  is  sometimes  assumed,  and  the  tendency  toward  luxury  in  that 
respect  may  be  expected  to  continue. 

Drawings  and  dimensions  of  a  great  variety  of  cars,  and  of  all  car  details, 
will  be  found  in  the  Car-Builders'  Dictionary,  as  revised   by  the  writer. 

Table  157, 
Leading  Dimensions  and  Weight  of  Sundry  Passenger  Cars. 


Penna.  Railroad. 
Standauds. 


Passenger* 

Baggage 

Postal 

Sleeper  (old  style). 


Dining KC  B.  &Q.).. 

Monarch  sleeping-cars.. 

Mann  sleeping-cars... 

Parlor  Car  (B.&O.R.R.) 

Woodruff  sleeper 

Harl.  &  H.  Co.,  ist-class 
passenger 


Length. 

Width. 

Height. 

Weight 

Capacity. 

Body. 

Out  to 
Out. 

Body. 

Max. 

ft.  in. 

ft.  in. 

ft.  in. 

ft.  in. 

ft.  in. 

lbs. 

Pass. 

t46    6 

52    9 

9  10 

10     1% 

14    1% 

*44,989 

51 

40    0 

46    0 

9  »oM 

10     \% 

14    1% 

32,000 

.... 

t6o    <M 

66  ii94 

9  loH 

10     \% 

14    t^ 

58,000 

20,000  lbs. 

§58    0 

64    8 

10    0 

10     I 

13  10 



... 

64    0 

.... 

10    4 

10    6 

14    2 

82,500 

10  sec. 

75     0 

.... 

.... 



75.000 

.... 

•  •  • 

.... 

•  •  •  • 

•  •  •  • 

•  «  •  • 

71,000 

.... 

58    0 

65     0 

9    6 

10    0 

14    0 

70,000 

28 

•  •  •  • 

71     0 

•  •  •  • 

10    3 

15    5 

60,000 



49     6 

57     8 

9    6 

.... 

13    6 

58 

Weight 

One 
Truck. 


lbs. 
7,200- 


\  iS.Soa 


16,200- 


*  The  Lehigh  Valley  standard  passenger  car,  of  the  same  general  dimensions  as  this,  weighs- 
45,136  lbs.;  one  truck,  8624  lbs. 

t  Centre  to  centre  of  truck,  33  ft.;  7  ft.  wheel-base. 

\  Centre  to  centre  of  truck,  46  ft.  2^^  in  ;  10  ft.  wheel-base. 

§  Centre  to  centre  of  truck,  44  ft.;  14  ft.  wheel-base. 

\  Six-wheel,  10  ft.  6  in.  wheel-base. 

Sleeping:-cars  have  usually  12  sections  and  a  state-room  and  smoking-room  ;  sometimes 
only  10,  rarely  14;  and  a  few  cars  have  16  sections,  but  without  state-room  or  smoking- 
room.  Many  sleepers  and  parlor  cars  weigh  75,000  to  78,000  lbs.  Pullman  sleeping-cars 
built  for  English  service  are  much  narrower  than  in  American  practice,  and  weigh  only 
some  48,000  lbs. 


492 


CHAP.    Xni.^TKAJN  RESISTANCE. 


CHAPTER  XIII. 

TRAIN     RESISTANCE. 

607.  Although  over  fifty  years  have  passed  since  experimental  inves- 
tigations in  respect  to  it  began,  tliere  is  no  single  element  of  train  re- 
sistance  whose  laws  can  be  said  to  be  definitely  known.  Within  the 
years  1875-1885,  however,  much  progress  has  been  made,  and  although 
our  knowledge  is  still  defective,  yet  the  limits  of  error  are  now  quite 
narrow.  ^ 

608.  Train  resistance,  properly  so  called,  may  be  defined  as  the  sum 
of  all  the  resistances  which  constitute  a  tax  upon  the  adhesion 
of  the   locomotive;    thus   excluding   all   those    resistances   which    are 
internal  to  the  locomotive  itself,  and  hence  are  a  tax  upon  the  cylinder 
power  only,  which  is  a  much  less  serious  matter.     These  latter  resist- 
ances are  (i)  all  the  friction  of  the  valve-gear,  piston,  and  connecting, 
rods,  and  (2)  aliy^«r;w/-friction  of  the  driving-wheels.     The  resistances 
which  do  tax  the  adhesion  are  (i)  the  r^///«^-friction  proper  (between 
wheel  and  rail.  Fig.  152)  of  the  drivers,  with  (2)  both  the  rolling  and  the 
journal  friction  of  the  truck-wheels,  or  of  any  other  wheels  not  drivers- 
(3)  all  head  and  other  atmospheric  and  oscillatory  resistance  of  the  loco- 
motive ;  (4)  all  grade  resistance  of  the  locomotive  and  (5)  all  resistances 
of  every  kind,  of  the  train  behind  the  locomotive.  * 

609.  Simple  as  would  seem  the  problem  of  determining  what  is  and 
what  IS  not  a  tax  upon  the  adhesion,  frequent  errors  have  arisen  in  de- 
termining  it,  both  by  including  among  the  resistances  which  tax  the  ad- 
hesion the  journal-friction  of  the  drivers  and  even  the  friction  of  the 
machinery,  and  by  excluding  from  it  the  atmospheric,  oscillatory,  and 
even  grade  resistance  of  the  locomotive. 

610.  It  seems  especially  plausible  to  assume  that  all  resistances  which  would 
-still  exist  if  the  engine  were  a  dead  engine,  with  disconnected  side  rods,  hauled 
.by  another  engine  in  front  of  it.  are  a  tax  upon  the  adhesion  when  the  engine 
IS  under  steam.  This  is  not  correct,  for  it  includes  as  a  tax  on  the  adhesion 
ihe  considerable  item  of  the  journal  friction  of  the  locomotive. 

The  true  lest  for  what  is  and  is  not  a  tax  upon  the  adhesion,  is  to  conceive 


CHAP.    XIII  — TRAIN  RESISTANCE. 


495 


the  locomotive  to  be  stationary  and  lifted  from  the  rails  with  belts  on  the 
drivers.  Whatever  power  would  then  be  lost  by  friction  within  the  locomotive 
itself,  before  it  reached  the  belts,  is  similarly  consumed  in  the  locomotive  with- 
out taxing  the  adhesion.  All  the  remainder  of  the  power,  including  any  loss 
by  the  friction  or  wear  of  belt  or  driver,  would  be  transmissible  only  by  the  ad- 
hesion of  the  belt  to  the  driver,  and  the  measure  of  that  adhesion  would  be  the 
measure  of  the  net  power  of  the  engine  aside  from  its  own  internal  friction. 

The  locomotive  engine,  in  fact,  is  to  all  intents  and  purposes  a  mechanical 
equivalent  for  a  stationary  engine  with  fly-wheel  and  belt,  the  rail  being  the 
belt.  Only,  instead  of  the  engine  being  stationary  and  the  belt  moving,  the 
belt  is  stationary  and  the  engine  moves  along  it.  The  locomotive,  it  is  true, 
uses  a  large  part  of  its  power  in  raising  and  lowering  itself  on  grades,  but  a 
stationary  engine  might  easily  be  made  to  do  the  same  without  altering  any  of 
its  essential  features. 

611.  Regarding  train  resistance,  therefore,  as  the  sum  of  all  those  re- 
sistances which  tax  the 

adhesion,   they   may   be  ^      ^-^ 

subdivided  as  follows : 

1.  The  journal-fric- 
tion, between  journal  and 
bearing.  Fig.  152. 

2.  The  rolling-friction  proper,  between  wheel  and  rail,  from  the  caus& 
outlined  in  Fig.  152. 

Both  these  together  are  commonly  included,  both  in  this  volume  and 
elsewhere,  under  the  general  name  of  rolling-friction,  and  their  acr- 
gregate  only  has  been  determined  with  approximate  exactness.  Experi- 
ment indicates  that  their  aggregate  varies  somewhat,  but  not  materially, 
with  the  velocity. 

612.  The  three  following  are  known  collectively  as  the  "  velocity  re- 
sistances ; "  and  experiment,  so  far  as  it  goes  (which  is  not  far),  seems  to 
agree  with  the  requirements  of  theory,  that  they  should  vary  as  the- 
square  of  the  velocity  : 

3.  Atmospheric  head  and  tail  resistance,  including  the  head  resistance 
of  the  locomotive  and  of  the  front  car  above  the  tender,  and  that  result- 
ing from  the  suction  of  the  last  car. 

4.  Atmospheric  side  resistance,  including  that  between  the  successive 
cars. 

5.  Additional  rolling  and  journal  friction  resulting  from  oscillation 
and  concussion. 

As  with  the  rolling-friction,  the  aggregate  of  these  three  items,  and 
especially  of  the  last  two,  is  far  better  known  than  the  separate  impor- 


It 


I 


4CU 


[V 


CHAP,   XIIL-TRAm  JiESISTAlSTCE. 


i"  Tabie  ,66)  assume  the  vlToc  ty^e^s  a„ce%o  T  n  '  "'"'  ""^  ^""'°--^ 
others  assume  it  to  be  all  oscillatory  atmospheric,  while 

a.-,  altho^h  an  esi.tiara„;LrLTer:rt\hl'rsl"^'^""  ^ 

whi!hf:rarfs::thrs;r:-:;  ^^^  ---  °^ -eUe  ad.itio„ 

par.  368  ./  seq.  P«™'^"«"'  '^am  resistance  has  been  considered  in 

resiS,;'!-"  ''"•  "  ""^  °"'^  '"•°-  -<^  invariable  element  of  train 

7-  C;ra</^  resistance,  which  is  sf»nc;h],r  *i, 
total  weight  of  the  train  as  th  ^ie^^''   ,'„Vj-="«  P-  -nt  of  the 
per  ton  of  2000  lbs.  for  each  .  per  cenfof  T\    ,       '  ^"'"^^ '  '•^-  ^°  ^^^ 

On  badly  located  lines  onl/t^rdli!  t ctsidfr^^- 

.d  onjTrr::;;o3e°rm^ -'■■'^r  "-  '"  '^--  '^  --'<^er. 
eliminate  it  altogether  Theretre^ffr"''  '"'""""  °^  ^^^'^'^  -  ^^all 
<loes  not  constitute  an  element  of  ^i  """.^^P'^-^  »"ch  a  line  it 
niovement  of  trains.  ^  "  resistance  which  affects  the 

..  .0  its  _.  s..n\-T;r  - 1::^  ■:  - 1- ::  ;f;; 

^     '*  element  of  train  resistance. 


Heeui\ 


'1'%^ 
^2^ 


properly  so  called.  The 
simplest  method  of  compu- 
ting the  efficiency  of  brakes 
is  given  beneath  Table  ii8, 
page  336,  and  Fig.  153 
outlines  the  principle  of 
the  method  there  given.   It 

need  only  be  added  that  the 
average  retarding  efficien- 

0886)  considered  as  from  10  to  14  percent^/M.  /.  f^  °f  ^'^^^^  ""^^  ^^  "°^ 
senger  service,  with  air-brakes,  and  frrm  //t '/r^^''  ^^^W.^  «,,.,/,  |„  p^. 
brakes  on  heavy  freight  trains.  The  sa"  pressure' ''"k'k'  '^"'  ^"^  ^"^^ 
much  over  two  thirds  of  the  load  on  Ihe  whids      -^H  '^^^-^^-"  -  "ot 

which  has  ever  been  realized  was  with  an  in  Jn  "maximum  retardation 

George  Westinghouse.  by  which  thetrel"^^^^^^^^  ^^  ^^- 

^ery  great  at  high  speeds  and 


STOP  ON  DESCENDING  GRADE 

Fio.  153. 


CHAP.   XIII.— TRAIN  RESISTANCE. 


495 


Table  158. 

Maximum  Efficiency  of  Power  Brakes  during  all  Parts  of  Stops  in 
Passenger  Service  or  with  Short  Freight  Trains. 

[Abstracted  from  computations  by  the  writer,  being  averages  of  a  large  number  of  stops.] 


PoRTioKS  OF  Stops. 


\jASX.  fraction  of  loo  ft 

Last  even  100  ft 

Preceding  100  ft 

it    it 


Average 

Speed, 

Miles 

Per  Hour. 


Ratios  of  Brake  Retarda- 
tion To  Load 
on  Braked  Wheels. 


Westinghouse 
Brake. 


(t  •( 

U  it 

«t  (( 

i(  t* 

it  (t 


Averages,  excluding  last 
fraction  of  100  ft 


8  to  10 
2o 
38 

35 

40 

44 

47. S 

50 
52 


Regular 
Stop. 


20  to  52 


20.9 

139 
147 

13 -75 

12.9 

14.2 

14.8 
14  75 
(4-5) 


Against 
Engine. 


1415 


193 
12.9 

14s 

-I    15-55 
\    136 

"•95 

[    13.85 
*    13-8 

13-3 
(11.6) 

(8-65) 
13-68 


Smith 

Vacuum 

Brake. 


Ratios  of  Bkakr 
Retardation  to 

Fkessurh  on 
Brake-blocks. 


Gallon.     Theoreti- 
cal (Table  112) 
Unilorm  Pressure. 


19-3 
11.6 
II. 6 

14-45  (. 
9-95) 

10.75 

8-35  1 
8.9    f 

8.4 
8.7 


After  TO 
Sectitms. 


10.00 


24.0 

13-3 
II. 9 

8-5 
7.7 
7-3 
7.0 

6-7 
6.4 


Initial. 


8.6 


25.0 
18.2 
17.1 

*S-3 
14-4 
13  8 

13-0 
12.0 

II. o 


14-35 


N  B.-The  -average  speed"  given  in  the  first  line  of  this  table  is  for  the  period  of  a 
*top  begrnntng^.^  15  to  20  miles  per  hour  and  ending  at  zero,  so  that  it  averages  8  to  10 
miles  per  hour.  ** 

For  the  original  records  of  these  stops,  with  very  valuable  further  data  on  brake 
effic^ncy  and  the  laws  of  brake  friction,  see  Dredge's  "  Pennsylvania  Railroad  "  (Wiley  & 

From  analysis  of  these  and  other  data  the  writer  concluded  that  the  following  ratios 
represent  X\.^  maximum  efficiency  of  brakes  in  ordinary  practice,  being  such  as  is  fairly 

t^thlh    vl?^  "  '"       I  ^"^^"^f  ""d^'-  favorable  conditions  with  aU  in  good  order  and 
with  the  best-known  appliances  : 

Retardation  of  Brakes  in  per  cent  of  Load  on  Braked  Wheels. 
With  special  apparatus  not  in  practical  use  : 

About  one  fifth,  or  20  per  cent  at  all  speeds. 
With  efficient  power  brakes  of  ordinary  type  : 

At  speeds  decreasing  from  15  to  20  miles  per  hour,  about  onefiftA  or  20  per  cent 
At  all  speeds  exceeding  15  to  20  miles  per  hour,  about  one  seventh,  or  ,4.14  per  cent 
For  entire  stops  of  long  trains  at  high  speeds,  including  lost  time  in  applying  fuU 
fcrake-power,  one  eighth  to  one  ninth.  ^ 


496 


CHAP.    XI II.- TRAIN  RESISTANCE, 


■I 


! 


was  reduced  automatically  as  the  soeed  fHI    cr.  ^7^^^  T  '  ' 

within  the  nearly  constant  force  necessal'    o  !Ld°  .h"' H   V""'""'"  '"'^ 
fourth  of  the  insistant  weight      Thlln^ri  '  "'""''•  "''"''=••  '»  °n« 

a  single  car,  and  thus  didfwav  I.th  anoT      '  "'°''°""'  ""^  "PP"'<^  ""'^  '^ 
of  brakes-that  it  talces  a  conirK,"/"'""" '"'''*<='«  •"  '"«  =«iciency 

.or  then,  to  even^tn  ra^X^rrhl'r  t;";.urs^c^r  ^ 

over  ten  seconds  is  lost  in  this  way  ^^  ^*^^'"^ 

cn.iripi^t.^'^rhirnTveTrf: '''.^''h"'=^°'.°"'  °'  -^^  ""'---i '- '"« 

not  being  the  end  aimed  at  ,n  '"'"""«<'  '"•°  «"'«■  «tren,e  efficiency 
of  action  Itls  po  "bfe  th«  .r  "%"■""""''  ^'"P'-'X.  -1  "ruinty 
.«e.nces  in  the  IT^^^^^^^:^  ^  ^^^^^  -J!^' 

alarge  fraction  of  such  e.^rin^e^tJi::,:::^ ^iTrZ^:.' :::: 
but  are  not-as  for  one  reason  or  another  worthless  as  pract^car^ides    ' 

''  '' witfCif^^her''":-  ^^^K,""  '"'"'  '^  -•'"Po^ant  compared 
resistance.  ^  ^      ''°'""'  '°'''^  °^^^  '^"^  P^'"'^  "f  "maximum 

2.  ^.  r«/.././«„,„^,^  ,^«,.«,.  to  which  the  possibility  of  high  speed  is 
the  more  important  consideration.  ^      '^ 

In  each  case  formulae  which  dpal  mJf  h  »i,« 

ing  the  head   and  roHing  rTsistancT  of  th.J  '"  °"'^'  ""«'^"- 

valup|pc:«      Who,         J     i'   "^^'^'ance  of  the  engine,  are  comparatively 

FREIGHT-TRAIN  RESISTANCE. 
617.  The  best  existing  evidence  known  to  the  writer  as  to  «,!,».  ;.  ,i, 
absolute  amount  of  the  train  resistanceof.«..>;We;n  fret" 

phw  S;;pt:  net^ii^prS^r^'rcn^en - 

xucy  were  made  by  the  "  gravity  method  "  de- 


CHAP.   XIII.— FREIGHT- TRAIN  RESISTANCE.  ^gj 


scribed  in  Appendix  A.  the  train  being  caused  to  approach  the  starting 
post  at  as  nearly  as  might  be  20  miles  per  hour,  when  steam  was  shut  off 
and  the  train  permitted  to  run  over  a  very  slight  down  grade  till  it  came 
to  a  stop.  It  was  then  caused  to  approach  a  succeeding  stop-post  at  a 
sharp  down  grade,  having  a  slightly  curved  alignment,  at  5  miles  per 
hour,  and  permitted  to  acquire  what  velocity  it  would  (about  35  miles 
per  hour)  for  a  certain  distance.  There  was  no  wind;  and  the  ther- 
mometer averaged  about  80°  Fahr.  The  results  of  the  tests  are  summa- 
rized in  Table  160  and  Fig.  154.  which  maybe  accepted  as  an  almost 
absolutely  accurate  record  of  actual  resistances  *  over  the  entire  range  of 


Fig.  154.-RESULTS  OF  THE  Burlington,  Ia.,  Tests  of  thf  Resistance  of  Entire  Trains. 

AS  Summarized  in  Table  i6o,Page  500  ikains, 

[Computed  by  the  method  shown  in  Table  ,59,  on  follo^ving  page,  and  in  Appendix  K? 
( 1  he  dotted  lines  eive  the  tests  made  on  curved  tr'^r\r  mr-n-r-t ^a  t * 

76finJXpIn^dV:^r  ''°^  -"^"^  ""•  ^^^^^^^^^^^S^^'il^^^^, 


*  As  the  writer  was  referee  of  these  tests  he  was  familiar  with  the  condition 
Of  the  cars  and  all  other  modifying  circumstances.     Therefore  be  can  vouca 
for  the  accuracy  of  the  results,  which  seem  somewhat  peculiar, 
32 


ij— I 


498 


CHAP.    XII I. ^TR  A  IN  RESISTANCE. 


Table  169. 
Manner  of  Computing  Gravitv  Tests  of  Train  Resistance  of  Entire 

Freight  Trains. 

Speed,  decreasing  from  «,  „i,es  per  hour-.;  mixed<ar  trains,  i.  loaded,  ,,  emptv  with 

dynamometer  car  and  way  car-American  rj  x  .4  in.  engine  '      "^  ^'      * 

[Competed  b.  the  writer  fro.  test  runs  down  a  sHgh.  grade  with  steam  .hut  of,  at  the 

Burlington,  la.,  freighttrain  brake  tests,  July,  ,886 ] 

ma*.?d'V;?::.r;ru3en^,;^g:„:"7"'^''°"  °'  "-«  '-  ">-'  resistances  mFlg.  .54. 


Station. 


Elev. 
Track  at 

^fif.  of 
Train. 


Speed. 

Miles 

Per  Hour. 


Vel.-Head 

(by  Table 

118). 


Virtual 
Elevation. 


Differ- 
ences in 
ditto. 


Pounds 

Per  Ton 

Resist- 


.1 


^^-^^-    XIII.-TRAIN  RESISTANCE.  499 

It  was  found  on  invest^aUoi  thai  thT  t     T".   ''''"  ""'^  '""  '"''""^^  ^"  *^^  ^-^— • 
had  been  reballi ted  l^e^^:^^^^^^  ^   ",^^^^  ^^  ^  ^^^  ^^^ow  of  a  ,rade) 

atnount  (probably  -ethl^^^leral^ot)^^^^^^^^^^^  ^f-- 

of  the  table  are  due  to  two  defects  of  ob  Nation  •  a)  Lack  of  In,  "'"^^^^"^'^^ 

track  elevations,  and  (3)  lack  of  exact  correctness'  in\he  spe^Ltato^  ^  h  ^'^ 

mometer  record,  which  was  on  a  scal^  of  >  i.  •,  ,  '^""^  *^^  ^y^^" 

run.    TO  attem;.  to  compr  U.:  SL  cl^Tpara^r  relctsuC  "•  °'  T^*^^  """^ 
crucial  test  of  the  accuracy  nf  th.  .^...v,  ^      ^^^^^'^^^  ^O'^  each  successive  1000  ft.  is  a  very 

point  Of  view.    The™:.:  it  Z^^^^",:  TllT'^''  °"^  '""^  ^  """'-' 
.hat  no  other  method  can  'approach  this  inTecitnTn'd  errtar'"^  ""''^-  '""^"^''"^ 
The  weights  of  the  trains  tested  were  a.  follows,  in  tons  of  ^  lb.  • 


25  box-cars,  empty  weight 

12  loads,  at  20  tons  each  ....'..*  .* 

Equalizing  load,  when  used 

Dynamometer  car.  with  15  persons.' 
Way  car,  with  10  persons.. . . 


Total  train 

Engine  on  drivers **, 

on  truck 

Tender  empty \ 


Total  engine  and  train, 
Of  which  there  was  braked 
Percent  braked 


639.48 

339  96 
5316 


639-71 

300.16 

46.90 


68r.6i 

382.16 

56.04 


Every  box-car  truck  but  one.  as  well  as  Hip  t^r.A^^      7       '.  " 

a  very  unusual  proportion  ^^^'  ^"^  ^°^'°^  ^"^^".  ^ad  brakes  on- 

field^^  tt^nrih-tt^^^^^^^^  ^^-^-^  -'-  «  X  7  in.),  except  the  Widdi- 

IN  .887  (see^«^«....^^^,,  May,  5...^:^z:::iL:;:?'' """  °^  ^^^^^ 


rrcste  had  not  been  made  when  the  first  edition  of  this 


treatise  was  issued.] 


5cx> 


CHAP.    XIJI.^FREIGHT-TRAIN  RESISTANCE. 


Table  160. 

Train  Resistance  of  Entire  Freight  Trains,  including  Engine. 

[Giving  the  mean  resistances  in  pounds  per  ton  (of  2000  lbs.)  computed  as  shown  in' 

Table  159,  with  the  corresponding  velocities  in  miles  per  hour.] 

(Each  of  the  resistances  on  tangent  is  the  average  on  a  run  of  5000  ft.     Each  of  the 
resistances  on  curves  the  average  on  a  run  of  2500  ft.) 


Resistances  on 
Tangent. 

Resistances  on  Curves. 

Tangent 

Vel. 

Resist. 

Vel. 

Resist. 

Curve. 

Resist.* 

Wcstinghouse  (C,  B.  1 
&  Q.  cars) » 

16.93 
16.06 

21.58 
24.78 
21.55 

3.80 
4.36 
4-56 
4.24 
4.44 

18.86 

33  90 
34.90 

•  •   •   • 

*  •   •   • 

4.56 
7.56 
6.41 

•  •   •   • 

•  •   •    • 

1.08° 
2.60° 
1.47" 

•  •   •   • 

•  •   •    • 

4.02 
6.26 
5-68 

•  •  •  • 

•  •  •   • 

Mean    

20.51 

4.32 

26.33 

6.07 

1.75° 

5-30 

Eames   (I.,   D.    &   S.  f 
cars)  and  Widdifield  -J 
&  Button  (L.V.cars)  ( 

8.42 
18.28 
19.70 

6.50 
6.76 
7.04 

14.03 

24-55 
30.10 

9.68 
9.20 
936 

1.08° 
2.60" 
1-47° 

9.14 
7.90 
8.63 

Mean 

16.82 

6.84 

21.70 

9.42 

I  75° 

e     rr 

1 •  /3                 "-33 

American  (St.  L.  &  S.  j 
F.  cars) 1 

9.62 
13-72 

•   •   •    • 

930 

7.88 

•   •   •   • 

13  03 
24-45 
30.75 

8.08 
10.40 

7.84 

1.08°         7-54 
2.60"        9.10 
1.47°         7-21 

Mean 

11.66 

8.50 

21.19 

8.94 

1.75° 

8.07 

*  Tangent  resistance  determined  by  subtracting  ^  lb.  per  degree  of  curve  from  the  total 
resistance.  Average  degree  of  curve  determined  by  determining  degrees  of  central  angle 
passed  over  by  head  and  rear  of  train  on  given  distance,  averaging  the  two,  and  dividing  by 
number  of  stations. 

Velocities  are  in  miles  per  hour ;  resistances  in  pounds  per  ton. 

practicable  freight  speeds.     The  track  was  in  fair  but  not  remarkably- 
good  condition. 

618.  The  conditions  of  the  trains  tested  (which  will  be  seen  to  have 
shown  quite  different  results)  were  as  follows  : 

I.  Westinghouse\  train. — Made  up  of  old  cars  in  excellent  running 
order,  with  well-worn  journals  and  wheel-treads.  The  performance  of 
this  train  should  fairly  represent  the  ordinary  conditions  of  practice. 

2.  Ainericatt  train. — Made  up  of  entirely  new  and  very  heavy  cars, 
which  had  only  run  some  300  to  500  miles  since  leaving  the  shop,  and 

f  The  trains  are  designated,  for  convenience,  by  the  names  of  the  brakes 
with  which  they  were  fitted,  although  these  brakes  had  nothing  to  do  with  the- 
tests. 


CHAP.    XIII.— PR  EIGHT- TR  A  nv  RESISTANCE. 


501 


•consequently  had  bearings  and  wheel-treads  still  comparatively  rough, 
and  not  fairly  representing  the  average  conditions  of  practice. 

3.  Eames  train.— Ma.dQ  up  of   fairly  old   but  poorly  built  cars,  and 
generally  in  rather  inferior  condition. 

619.  The  effect  of  these  differences  in  the  trains  is  clearly  visible  in 
Pig.  154,  where  the  Wcstinghouse  train  shows  rather  less  than  half  the 
rolling  resistance  of  the  other  two,  or  about  4  lbs.  per  ton  for  all  speeds 
up  to  25  miles  per  hour.  The  general  fact  that  speed  causes  very  little 
increase  in  train  resistance  up  to  speeds  of  30  miles  per  hour  is  clearly 
indicated  ;  and  this  many  other  indications  tend  to  confirm,  as  notably 
various  dynamometer  tests  made  by  the  Pennsylvania,  New  York,  Lake 
Erie  &  Western,  Chicago,  Burlington  &  Quincy,  and  other  roads,  where 
very  low  car  resistances,  running  down  to  from  2i  to  4  lbs.  per  ton,  have 
been  indicated,  with  little  variation  as  an  effect  of  speed. 

These  latter  tests  alone  would  leave  the  question  open  to  much  doubt, 
since  they  do  not  include  any  of  the  head  or  engine  resistances,  which 
at  high  speeds  become  more  important  than  any  other,  but  the  tests 
^iven  in  Fig.  154  include  ALL  resistances  and  lead  to  the  same  conclusion 
so  clearly  as  to  be  unmistakable. 

620.  The  peculiar  manner  in  which  the  Eames  and  American   resistance 
lines  on  curves  cross  each  other,  as  shown  by  the  fol- 
lowing sketch,  may  appear  to  indicate   that  there  is       ^  ' 
something  wrong  in  the  computed  results.   This  is  by 
no  means  so.     The  anomaly  may  be  thus  explained  : 

(a)  Each  train  was  made  up  of  25  cars  from  the  same  road  and  built  nearly  at 
the  same  time. 

(6)  All  freight  cars  are  roughly  built.  The  axles  are  not  likely  to  be  pre- 
4:isgly  parallel,  except  by  accident.  To  have  the  axles  enough  out  of  parallel  to 
precisely  fit  a  1°  curve  requires  that  the  wheel-base  shall  be  only  y-^  part  longer 
on  one  side  than  the  other,  or  ^V  i"-  A  lot  of  cars  built  at  one  time  are  very 
likely  to  have  the  error  all  on  one  side. 

ic)  Resistances  a  and  c  (see  sketch  above)  were  on  curves  turning  to  the  right; 
resistance  d  was  on  a  curve  turning  to  the  left. 

If,  therefore,  the  American  train  curved  most  easily  to  the  right,  resistances 
/land  c  would  be  abnormally  low,  or  very  near  the  tangent  rate,  and  resistance 
/J  abnormally  high:  while,  if  the  contrary  was  the  case,  with  the  Eames  train  re- 
sistance a  and  c  would  be  abnormally  high,  and  resistance  b  abnormally  low,  or 
well  down  toward  the  tangent  rate. 

Whether  this  or  other  cause  led  to  the  variation,  it  is  certain  that  it  was  an 
actual  one,  and  the  fairer  plan,  therefore,  seems  to  be  to  take  the  average  of  both 
•trains.     The  trottlc  of  each  engine  was  absolutely  tight. 


14 


502 


CHAP.    XIIl.—I'KEIGHT-TKAIN  RESISTANCE. 


621.  The  experiments  by  the  writer  recorded  in  Appendix  A  were 
made  by  the  same  general  method  as  those  just  described,  and  were  the 
first  in  which  the  very  low  train  resistances  for  trains  in  motion  which  are 
now  generally  admitted  were  observed.  They  indicated  that  the  normal 
magnitude  of  the  rolling- friction  at  speeds  of  lo  to  30  miles  per  hour  was  : 

For  passenger  and  loaded  freight  cars 4  ibs.  per  ton 

For  empty  freight  cars  and  other  light  loads,       ...  6    "  " 

For  street  cars  and  other  still  lighter  loads,    .....*     10    " 
For  freight  trucks  without  load, !     !     !     14    "  ^ 

The  starting-friction  is  very  much  higher,  rising  to  over  20  Ibs.  per 
ton  in  some  cases.     (See  Appendix  B.) 

622.  Some  experiments  on  train  resistance,  both  on  curves  and  tan- 
gents, made  in  1885  on  the  Breslau-Schmoltz  line  in  Germany,  apparently 
in  an  accurate  and  careful  manner,  but  covering  only  the  resistance  of 
cars  behind  the  tender  and  dynamometer  car,  gave  still  lower  results  than 
these,  as  shown  in  Table  161.  The  tests  covered  also  the  question  of 
remedies  for  oscillation  and  the  advantages  of  a  device  for  radiating  axles 
on  curves,  as  to  which  nothing  important  was  developed.  The  resist- 
ances are  noticeable  as  being  among  the  lowest  ever  reported  for  similar 
speeds.  Similar  tests  on  the  Freiburg-Sulzbrunn  line,  with  the  same 
apparatus  and  by  the  same  individuals,  gave  somewhat  higher  averaije. 

Modern  evidence  to  the  same  general  purport  as  that  which  precedes 
might  be  multiplied  almost  indefinitely,  but  it  appears  needless  to  do  so. 

623.  We  may  conclude,  therefore,  as  to  freight-train 
resistance 

I.  The  particular  velocity  adopted  is  wholly  unimportant, 
both  because  it  makes  absolutely  but  little  difTerence  in  the 
resistance,  and  because,  if  the  resistances  are  mounting  too  high 
for  the  power  of  the  engine,  the  speed  can  always  be  cut  down 
at  critical  points.     The  total  work  in  foot-pounds  done  to  move 


Table  161. 
Resistance  of  European  Cars  (16  to  23  ft.  rigid  wheel-base). 

[Reported  in  full  in  the  Railway  Engineer,  Dec.  1884  et  seg.     Resistance  in  Pounds  Per  Ton. 


Spekd. 

Radiating  Axlrs. 

Fixed  Axles. 

Miles  Per  Hour. 

Limits. 

Average. 

Limits. 

Averafje. 

12.4 
21.8 
28 

2.0     to  3.75 

3.97  to  4.19 

5 -07 

2.65 
4.08 
5-07 

2.42  to    3.75 

3.97  to   4.85 

6.17 

3.09 
4.19 
6.17 

CHAP.    XIII.— FREIGHT-TRAIN  RESISTANCE. 


503 


the  train  is  not  affected  enoueh  to  have  any  measurable  effect  on 
the  cost  of  power  (see  par.  664). 

2.  The  normal  tangent  treight-train  resistance  in  summer, 
ENGINE  AND  ALL  INCLUDED,  is  often,  and  perhaps  usually,  as  low 
as  4  lbs.  per  ton,  up  to  speeds  as  high  as  25  miles  per  iiour,  run- 
ning down  in  cases  to  3  lbs.  and  even  less;  and,  on  the  other 
hand,  rising  in  cases  as  high  as  6  or  8  lbs.  per  ton  when  the  cars 
are  in  bad  order,  or  against  a  head  or  side  wind,  or  (as  we  are 
about  to  see)  at  winter  temperatures;  these  latter  figures  being 
a  fair  working  maximum  for  freight  service. 

Four  pounds  per  ton  will  make  a  difference  of  some  2400  lbs.  in  tractive  re- 
sistance with  an  average  train  of  25  cars,  which  will  use  up  the  adhesion  of  4.8 
tons  of  weight  on  drivers,  or  12  to  20  per  cent  of  the  total  load. 

624.  It  is  entirely  uncertain  how  much  of  the  so-called  rolling  friction  is 
journal-friction,  and  how  much  rolling-friction  proper.  The  present  proba- 
bilities are  that  most  of  it  is  journal-friction.  Experimental  determination  of 
the  rolling  friction  proper,  apart  from  all  journal-friction,  is  a  matter  of  the 
greatest  difficulty,  and  has  never  been  attempted.  Journal-friction  has  been 
far  more  thoroughly  investigated  within  the  last  few  years,  but  until  then  the 
laws  of  it  also  had  been  but  little  investigated,  and  what  investigation  had  been 
made  was  largely  erroneous. 

625*  By  some  singular  chance, — probably  the  beautiful  simplicity  of  the  laws 
developed,  which  only  lacked  correctness  to  make  the  laws  of  friction  very 
easily  understood, — some  experiments  made  by  M.  Morin,*  a  French  officer  of 
artillery,  in  1831,  obtained  almost  universal  acceptation  as  a  final  determination 
of  the  laws  of  friction.  There  is  even  at  the  present  day  (1885)  hardly  a  single 
text-book  of  engineering,  at  least  in  English,  in  which  these  laws  are  not  laid 
down  as  facts,  yet  they  are  now  generally  admitted  to  be  entirely  incorrect. 
They  were  in  substance  that  the  coefficient  of  friction  was  independent  both  of 
the  pressure  and  of  the  velocity,  so  that,  once  determined,  it  was  universally 
applicable.  The  range  of  the  experiments  was  very  limited,  and  Morin  himself 
disclaimed  any  extension  of  them  beyond  the  range  of  his  experiments;  but  it  is 
clearly  proven  that  there  are  no  limits  nor  conditions  under  which  his  laws  are 
approximately  true,  since  the  coefficient  varies  materially  both  with  pressure 
and  velocity,  with  both  lubricated  and  unlubricated  surfaces,  and  with  tempera- 
ture and  other  conditions  as  well  ;  as  notably  with  the  character  of  the  surface, 
which  makes  any  general  coefficient  of  "  iron  on  iron,"  or  "  iron  on  brass,"  for 
example,  rather  worse  than  useless. 

*  "  Nouvelles  Experiences  sur  le  Frottement.  Faites  4  Metz  en  1831.'  Par 
Arthur  Morin,  Capitaine  d'Artllerie.  128  pp.,  4°,  plates.  Seconde  M6moire, 
1832,  103  pp.,  4',  plates.     Tro  si^me  Memoire,  1833.  142  pp.,  4°,  plates. 


504 


11 


II 


CHAP.    XIIL—FREFGHr-TKAIN  RESTSTAKCE. 


626.  Prof.  R.  H.  Thurston  was  among  the  first,  if  not  the  first,  to  discover 
and  announce  the  true  laws  of  friction,  in  1876-78.  having  made  a  large  number 
of  experiments  on  an  ingenious  machine  of  his  invention.     The  writer   in  the 
summer  of  1878,  made  a  series  of  tests  of  rolling-stock  resistances,  summarized 
in  Appendix  A,  by  dropping  cars  down  grades  and   registering  velocities  elec- 
trically, in  which  he  believes  he  was  the  first  to  discover  and  announce  the 
variation  in  coefficient  for  loaded  and  empty  cars  and  the  aggregates  of  4   6 
and  10  lbs.,  above  mentioned,  which  at  the  time  appeared  quite  without  prece- 
dent, as   Prof.  Thurston's  results  were  not  at  that  time  generally  known    and 
were  not  at  all  known  to  the  writer.     A  large  number  of  dynamometer  tests 
on  various  roads  were  made  shortly  after,  and  in   fact  were  then  in  progress 


COtFHCIE«IT  0»  FRiCTiON 

AT  VARIOUS  PWESSyRES. 

LUBRICANT  PARAFFINC  OH. 

VtLOCiT-/  300  FEET  PER  MINuV| 

C./  M    »OO0«U«T. 


a»  40  »  i4> 

Lh»  Per  Ton  TVain  Resistanct. 

(The  velocity  given  for  the  rubbinp-surfaces  of  300  ft.  per  minute  is  equivalent  to  a  train 

speed  01  some  34  miles  per  hour.) 

Fig.  155. 

Showing  the  same  low  rate  of  4  lbs.  per  ton  or  even  less  for  loaded-car  resist- 
ances, although  empty-car  resistances  were  less  carefully  determined.  Shortly 
thereafter  Mr.  C.  J.  H.  Woodbury  began  tests  of  great  interest  for  mill-work, 
which  give  strong  confirmatory  evidence  of  the  above  results  as  respects  the  gen- 
eral laws  of  friction,  although  not  directly  applicable  to  railroad  practice.  Finally, 
in  18S3-4  Mr.  Beauchamp  Tower  made  a  series  of  elaborate  and  remarkable 
tests  under  the  auspices  of  the  Institution  of  Mechanical  Engineers,  which 
appear  to  have  been  the  first  made  in  England  of  a  character  to  reveal  the 


CHAP.    XIII.—FREIGHT-TRAIN  RESISTANCE. 


505 


•errors  of  Morin's  results.     The  Germans  and   French  do  not  appear  to  have 
shown  their  usual  scientific  activity  in  this  matter. 

627.  All  these  modern  results  agree  in  essentials  with  each  other,  although 
some  have  covered  results  not  touched  by  the  others.  Their  general  results 
and  indications  are  summarized  in  Appendix  B.  Mr.  Woodbury's  results*  begin 
with  the  lowest  pressures,  and  are  shown  in  Table  162,  and  graphically  in  Fig. 
155.  For  the  very  reason  that  this  diagram  is  for  pressures  lower  than  ever 
occur  in  normal  railroad  practice,  it  is  particularly  interesting,  since  it  furnishes 
a  check  on  the  conclusions  which  have  been  reached  by  other  experimenters 
operating  within  the  limits  of  railroad  practice  only,  by  beginning  as  it  were  at 
the  foundation,  and  showing  the  law  of  change  in  journal-friction  from  i  lb.  per 
square  inch  of  journal  pressure  upwards.  There  has  been  added  below  the 
diagram  a  line  showing  the  equivalent  in  pounds  per  ton  of  train  resistance  to 
the  abstract  "coefficients  of  friction"  given,  as  being  a  unit  better  suited  for  our 
immediate  purpose. 


Table  162. 
Coefficients   of    Friction   with   Very    Low    Pressures,    and    Effect 

THEREON   of   TEMPERATURE. 
[Abstracted  from  records  of  tests  of  C.  J.  H.  Woodbury.] 


Pressure 

Coefficient  of  Friction. 

Total  Friction  at  Tempera- 
ture OF — 

Per  Cent  of 

Per  Sq.  In. 

40". 

IOO». 

40°. 

100°. 

100°  to  40*. 

I 

a 

3 
4 
5 

7 

8 

9 

ID 

.538 
.299 
.211 
.167 
.140 
.122 
.109 
.098 
.ogo 
.084 

.138 
.080 
.060 
.050 

.044 
.039 

.036 

.034 
.032 

.030 

lbs. 
.538 
.598 

.633 
.668 
.700 
.732 
•  763 

.784 
.810 
.840 

lbs. 

.138 
.160 
.180 
.200 
.220 

.234 
.252 

.272 

.288 
.300 

25.6 

26.8 
28.5 
30.0 

31.3 
32.0 
330 
34.7 

35.7 
35-8 

15 
20 

30 

35 
40 

.063 

.053 
.046 

.041 

.038 

.035 

.025 
.023 
.021 
.020 
.019 
.018 

.945 
1.060 

1. 150 
1.230 

I -330 
1.400 

.375 
.460 

.525 
.600 

.665 
.720 

39-7 
43-3 
45.7 
48.8 

51. 1 
51.5 

*  For  complete  paper,  which  is  full  of  interesting  information  on  friction, 
see  "Measurements  of  the  Friction  of  Lubricating  Oils,"  by  C.  J.  H.  Woodbury, 
Trans.  Am.  Soc.  M.  E.,  1S84-85. 


ii^i^ 


5o6 


CHAP.   Xni.-FKEIGHT-TRAIN  RESISTANCE. 


628.  The  d.agran,  is  especially  useful  ,o  afford  some  indication  as  to  the 
comparat.ve  tram  resistance  in  winter  and  summer,  as  to  which  there  are  „" 
expenmencal  records.  Since  the  diagram  fixes,  as  it  were,  a  superior  li^t  for 
the  r,ct,o„  of  ratlroad  journals,  we  might,  on  studying  it,  fairly  d  aw  hr« 
conclusions  :  ^     »      .    -inj'  uidw    mrec 

I.  Since  friction  can  in  no  case  be  less  than  zero   lines  reoresentin.,  »11 
poss.ble  loads  on  railroad  journals  must  lie  in  the  narrorspae'lt   h     .'ft  o 
the  diagram  between  the  zero  line  and  that  for  40  lbs.  per  square  inch  pre  sure 

He  betwe:„^  «  """■     T-    """'  "■"  ^''  -"-^■i<'-"a.  friction  oug.; 
lie  Detvveen  these  narrow  limiis  : 


40 
100' 


Temperature  of  Coefficient  of 

„        J""*""*'-  friciio... 

Fahrenheit o  to  .035 


Pounds  per  ton  train 
resistance. 

o  to  7.0  lbs. 
o  to  3.6  lbs. 


Fahrenheit o  to  .018 

froP,'!  TtZ  ^'^^^^'P""'^  ^^^^^  '^^  "«"!'  of  all  the  latest  tests,  which  sho^ 
from  3^  to  6  lbs.  per  ton  resistance. 

629.  2.  Within  the  temperature  limits  of  40°  and  100°.  the  effect  of  the 
higher  temperature  ,s  to  decrease  materially,  and  of  the  lower  temperature  to 
increase  matenally.  the  amount  of  loss  by  friction.  At  40  lbs.  per  square  inch 
the  friction  is  nearly  twice  as  much  at  the  lower  temperature,  while  at  still 
lower  pressures  of  i  to  10  lbs.  per  square  inch  it  is  from  three  to  four  times  as 
much.  Extendmg  the  indications  of  these  tests  to  the  higher  pressures  of  rail- 
way practice,  we  might  expect  that  the  effect  of  a  fall  of  temperature  in  the 
journals  from  100°.  which  we  may  call  an  average  summer  temperature  to  40° 
which  we  may  call  an  average  winter  temperature,  would  be  to  make  journal- 
friction  in  summer  and  winter  railway  service  compare  somewhat  as  follows  : 

Loaded.  Empty. 

summer,  as  shown  by  various  tests,  say 4  lbs.  6  lbs. 

Winter  (not  directly  shown  by  any  tests),  say 5^  to  6  lbs.         8  to  9  Ibs.^ 

630.  Whether  this  conclusion  be  true  or  not  cannot  be  proven  by  direct 
evidence,  for  lack  of  recorded  train-resistance  tests  which  have  been   made  in- 
cold  weather,  but  the  circumstantial  evidence  that  some  change  of  this  kind 
takes  place  is  very  strong.     Among  such  evidence  is  one  small  fraction  of  the 
series  of  tests  by  Mr.  Beauchamp  Tower,  above  alluded  to,  for  determining  the 
effect  of  temperature  on  journal  friction.     The  loads  and  journal-speeds  in  this 
case  closely  paralleled  railway  practice,  but  the  lubrication  was  vastly  more 
efficient,  being  by  a  bath  of  lard-oil.     Lard-oil  is  affected   by  temperature  much 
as  are  ordinary   railroad   lubricants,  but   the  superior  method  of  lubrication, 
in  addition  to  giving  rates  of  friction  which  are  far  below  the  possibilities  of 
railway   practice,    would    be    likely   to  have   the   effect    of  exaggerating  the 
beneficial    effect  of   high  temperature,    since  the   more  perfect    the  supply  of 
oil,    the   greater  might  be   expected  to   be  the  advantages   of  great   fluidity. 


4 


. 


CHAP.    XIII.— FREIGHT-TRAIN  RESISTANCE. 


507 


Nevertheless,  with  these  allowances  remembered,  some  of  Mr.  Tower's 
results,  as  summarized  in  Table  163,  are  very  instructive.  Translating  co- 
efficients of  friction  into  pounds  per  ton  of  train  resistance,  as  in  Fig.  155, 
by  multiplying  them  by  200,  and  translating  the  journal-speeds  into  train- 
speeds  by  multiplying  by  10  (these  methods  being  approximate  only,  but 
sufficiently  exact),  we  have  in  Table  163  some  very  definite  indications  of  the 
effect  of  temperature  on  axle-friction. 

631.  To  draw  any  positive  conclusions  from  this  table  we  must  make  a  cer- 
tain "scientific  use  of  the  imagination,"  by  making  allowances  both  in  the 
temperatures  and  in  the  observed  friction  for  the  difference  in  manner  of 
lubrication.  As  these  allowances  might  or  might  not  be  correct,  we  will  not 
attempt  them;  but  it  is  clear  that,  be  the  allowances  thus  made  what  they  may, 
these  results  support  the  general  conclusion  strongly,  that  the  external  tem- 
perature of  the  air  may  have  a  most  important  influence  on  the  normal  rolling- 
friction,  as  do  experiments  by  Professor  Jhurston  and  others.  On  the  other 
hand,  there  are  many  experiments  which,  at  least  in  appearance,  would  tend 
to  controvert  these  conclusions,  for  one  has  only  to  look  long  enough  to  find 
experimental  records  to  support  or  controvert  almost  anything.  But  such  con- 
troverting evidence  is  in  this  case  not  abundant,  nor  of  the  highest  class,  and 
as  a  general  rule  the  apparent  discrepancies  all  result  from  two  apparent, 
anomalies  which  are  in  no  respect  inconsistent  with  what  has  preceded  : 

1.  At  a  certain  temperature  not  far  above  100°  Fahr.,  and  with  some  fluid 
oils  below  it,  the  law  changes,  and  increase  of  temperature  causes  a  rapid  in- 
crease of  resistance. 

2.  At  very  slow  speeds,  especially  when  combined  with  very  high  pressures, 
the  law  often  changes,  and  a  higher  temperature  has  an  injurious  effect, 
apparently  because  a  certain  viscosity  is  necessary  for  efficient  lubricatioa 
under  such  circumstances. 


Table  163. 
Effect  of  Temperature  on  Journal  Friction. 

[Deduced  from  tests  of  Beauchamp  Tower;  bath  of  lard  oil;  load,  100  lbs.  per  sq.  in.  (about 

that  of  an  ordinary  empty  freight-car  journal.)] 


Train  speed. . 

At  120°  Fahr, 
At  60°  Fahr. , 

Difference. , 


Pounds  Per  Ton  of  Train  Resistance  at  Speeds  in  Miles 

Per  Hour  of — 


8.8 

0.48 
1. 18 


0.70 


13-2 

0.58 

1.68 


17.6 

0.70 
2.06 


I. 10..      1.36 


21. 9 

0.80 

2.38 


1.58 


26.3 

0.88 
2.60 


1.72 


35-1 

1.02 
2.96 


1.96 


39-5 

1.08 
3-12 


2.04 


I  * 


if 


■i 


508  C//AP.    XIII.-FREIGHT-TRAIN  RESISTANCE. 

632.  Zero  temperatures  are  not  favorite   ones   for  dynamometer   experi- 
ments, but  experience  in  the  running  of  trains  in  winter  and  summer  indicates 
in  the  most  positive  manner  that  summer  trains  must  be  cut  down  by  two  to 
four  cars  in  winter,  or  say  10  to  15  per  cent,  in  order  to  run  them  at  all      This 
practice  has  not  become  universal  without  some  real  necessity;  but  it  is  more 
difficult  to  account  for  the  necessity  than  is  generally  realized,  for  some  of  the 
explanations  which  are  given  will  certainly  not  hold  water,  as  pointed  out  in 
par.  345.     It  need  only  be  added,  that  the  loss   by  radiation   from  the  loco- 
^Tiotive  will  hardly  explain  any  part  of  this  need  for  cutting  down  trains   since 
the  difference  between  winter  and  summer  temperatures  is  a  small  and  unim- 
iportant  one  to  the  locomotive,    though  a  very  important  one  to  the  human 
body. 

633.  Let  us  see  how  radical  is  the  difference  in  its  effect  on  them  The 
■human  body  can  manage  to  sustain  for  a  short  time  a  temperature  of  sav  40' 
below  zero,  or  138°  below  its  natural  temperature,  and  it  can  do  this 'only 
when  "  lagged  "  with  skins  and  such  like,  to  the  last  degree  of  perfection  at 
•every  exposed  point.  The  boiler  is  subjected  to  an  equally  unpleasant  extreme 
of  temperature  when  the  external  temperature  is  350  -  138  =  212^  Fahren- 
heit, or  just  hot  enough  to  cause  water  to  boil  in  the  open  air.  To  get  a 
fair  parallel,  we  must  consider  how  much  warmer  the  average  man  would  think 
It  with  the  temperature  140°  below  zero  than  when  it  was  down  to  200°  below 
zero.  It  is  not  probable  that  he  would  find  that  the  difference  was  of  great 
consequence. 

To  be  sure,  the  fire  inside  the  boiler  is  more  efficient  than  the  fire  inside 
the  human  body,  but  the  demands  on  it  are  greater  and  the  difference  of 
winter  and  summer  less.  The  average  winter  temperature  of  Pittsburgh,  for 
example,  is  about  38°  and  the  average  summer  temperature  72  degrees  so  that 
we  have  as  the  difference  between  the  inside  and  outside  temperature  of  the 
boiler — 

I"^'"^^"" 350'  -  38°  =  3i2« 

In  summer 350.  _  ^^o  ^  ^yS' 

Difference «-«»  _  o 

or  about  11  per  cent. 

This  difference  is  far  too  small  to  explain  the  necessity  for  any  material 
difference  in  winter  and  summer  loads.     Assuming  that  as  much  as  20  per  cent 
of  the  heat  generated  is  lost  by  external  radiation,  which  is  a  large  estimate 
not  more  than  2  per  cent  difference  of  load  could  be  accounted  for  in  this  way! 

634.  We  seem  driven,  therefore,  as  a  net  result  of  all  the  preceding,  to  this 
interesting  and  important  conclusion,  to  directly  support  which  there  is.  as 
already  stated,  little  or  no  experimental  evidence,  although  the  circumstantial 
evidence  in  favor  of  it  is  very  strong :  that  a  difference  in  the  rolling-friction 
of  cars  is  the  chief  reason  why  trains  must  be  cut  down  in  winter.     As  this 


X  Ir 


CHAP.   XIII.— FREIGHT-TRAIN  RESISTANCE.  509- 

probably  results  from  difference  of  temperature  of  the  journals,  and  this  again 
from  radiation  from  the  boxes  of  the  heat  which  the  journals  are  constantly 
generating,  and  as  radiation  can  be  checked  by  a  very  slight  covering  whicb 
will  hold  a  little  dead  air  around  a  hot  metallic  surface,  we  have  in  these  facts 
indications  which  might  lead  to  the  important  practical  conclusion  that  some 
very  slight  covering,  which  would  merely  check  radiation  from  the  journal- 
boxes  somewhat,  might  have  an  appreciable  effect  on  the  loads  which  can  be 
hauled  in  severe  cold  weather. 

635.  In  Appendices  A  and  B  will  be  found  further  and  more  detailed  infor- 
mation as  to  the  laws  of  journal-friction,  and  especially  as  to  the  important 
question  of  starting  trains.  The  normal  journal-friction,  under  favorable  con- 
ditions, as  determined  in  various  series  of  tests,  is  summarized  in  Appendix 
B  as  follows,  for  velocities  greater  than  10  miles  per  hour,  or  90  ft.  per  minute^ 

journal-speed : 

Lbs.  per  ton. 

Beauchamp  Tower,  bath  of  oil o.  278 

♦'  '•         pad  or  siphon 1.9 

Thurston,  light  loads 2.75 

"  heavy  loads i-75 

Wellington  (gravity  tests  of  cars  in  service),  light  loads. . .  6.0 

"  «•  •«  "  *♦        heavy  loads..  3.9 

"  direct  tests  (as  shown  in  Appendix  B) j  ; " 

Thurston,  inferior  oils  ("  Friction  and  Lubrication, "p.  173)  \\'q 
Morin,  continuous  lubrication 6.0  to  10.8 

636.  The  great  discrepancies  in  these  results  will  be  seen  to  point  directly 
to  one  conclusion— that  the  character  and  completeness  of  lubrication  seems  to 
be  immensely  more  important  than  the  kind  of  the  oil.  or  even  pressure  and 
temperature,  in  affecting  the  coefficient  of  friction.  Mr.  Tower  found  that 
lubrication  by  a  bath  (whether  barely  touching  the  axle  or  almost  surrounding 
it)  was  from  six  to  ten  times  more  effective  in  reducing  friction  than  lubrication 
by  a  pad.  By  immersing  the  journal  in  a  bath  of  oil  Mr.  Tower  succeeded  in 
reducing  the  coefficient  in  a  large  number  of  tests  to  as  low  a  point  as  o.ooi— 
equivalent  to  only  0.2  lb.  per  ton  of  tractive  resistance;  and  the  general  average 
in  the  bath  tests,  under  all  varieties  of  load  and  speed,  is  given  as  only  0.00139, 
or  0.278  lb.  per  ton.  against  1.96  to  1.95  lbs.  per  ton  with  siphon  lubricator, 
or  pad  under  journal.    These  results  are  very  far  below  any  heretofore  reported. 

637.  The  overmastering  effect  of  minute  differences  in  the  condition  of  the 
lubrication  was  curiously  shown  in  two  ways  in  Tower's  experiments  : 

I,  It  was  accidentally  discovered  that  with  bath  lubrication  the  bearing  is 
actually  floated  on  a  film  of  oil  between  the  lubricated  surfaces,  which  is  so  truly 
a  fluid  that  it  will  rise  through  a  hole  in  the  top  of  the  bearing  in  a  continuous 


*H1 
9B1 


510 


CHAP,   XIIL—FREIGHT-TRAIN  RESISTANCE. 


stream  and  exert  a  pressure  against  a  gauge  equal  to  more  than  twice  the 
average  pressure  per  square  inch  on  the  bearing.  This  is  precisely  what  theory 
would  require  if  the  lubricant  were  a  perfect  fluid. 

2.  Tower's  apparatus  required  that  the  journal  should  be  revolved  first  one 
way  and  then  the  other.  It  was  found  that  the  friction  was  always  greater 
when  the  direction  of  motion  was  first  reversed.  The  increase  varied  consid- 
erably with  the  newness  of  the  journal.  "  Its  greatest  observed  amount  was  at 
starting,  and  was  almost  twice  the  nominal  friction,  and  it  gradually  diminished 
until  the  normal  friction  was  reached,  after  about  ten  minutes'  continuous  run- 
ning. This  increase  of  friction  was  accompanied  by  a  strong  tendency  to  heat, 
even  under  a  moderate  load.  In  the  case  of  one  brass  which  had  worked  for  a 
considerable  time  it  almost  entirely  disappeared."  It  is  with  apparent  justice 
concluded  that  the  phenomenon  must  be  due  to  the  interlocking,  point  to  point, 
of  the  surface  fibres  after  having  been  for  some  time  stroked  in  one  direction. 

638.  It  appears  not  impossible,  therefore,  that  a  great  further  reduction  in 
the  axle-friction  of  trains,  as  well  as  a  great  saving  of  oil,  may  result,  within 
a  few  years,  from  the  adoption  of  something  better  than  the  crude  and  wasteful 
axle  box  which  is  now  common.     The  objections  to  it  are  : 

1.  It  leaks  badly  at  the  back,  around  the  axle,  letting  oil  out  and  grit  in. 
Therefore — 

2.  The  oil  has  to  be  frequently  renewed,  requiring  a  loose  lid  in  front,  from 
which  more  oil  escapes  and  more  grit  gets  in. 

From  this  it  very  naturally  results  that  in  spite  of  the  large  expense  of  about 
a  cent  per  train-mile  (Table  78)  for  oil  there  is  often  very  little  or  it  where  it  is 
wanted,  and  that  dirty  and  gritty  ;  while,  on  the  other  hand,  the  ties  and  road- 
bed are  saturated  with  it  from  one  end  of  the  United  States  to  the  other. 

639.  In  Figs.  156-159  is  shown  a  French  oii-box  which  obviates  many 
of  these  objections  and  has  made  the  very  remarkable  record  given  below. 
The  Germans  have  similar  oil-boxes  in  extensive  use.  The  oil  reservoir  is 
entirely  below  the  axle,  so  that  oil  cannot  escape,  and  it  is  supplied  to  the  bear- 
ing by  a  pad  fed  by  wicks.  Could  an  oil-tight  stuffing-box  be  used  at  the  back 
of  the  box,  and  the  box  be  kept  completely  full  of  oil,  it  is  more  than  probable 
that  even  greater  reduction  of  axle-friction  and  waste  of  oil  would  follow. 

The  lower  half  of  these  boxes  is  furnished  inside  with  a  partially  horizontal 
diaphragm  in  the  portion  toward  the  wheel,  for  the  purpose  of  preventing  the 
forcing  out  of  the  oil  by  violent  side  blows.  They  have  proved  so  efficient 
that  the  consumption  of  oil  has  fallen  from  2.3  ounces  per  1000  miles  to  less 
than  one  fourth  that  amount  (41.25  grammes  per  1000  kilometres  to  9.93) — a 
most  remarkable  showing,  and  a  marvellous  contrast  to  the  results  obtained 
here.  The  dust  guard  is  formed  of  five  to  six  thicknesses  of  fluffy  woollen 
cloth,  held  between  two  leather  diaphragms  by  screws  like  those  used  for 
shoe  soles.     The  diaphragms  are  in  halves,  and  are  pressed  up  against   the 


^ 


•4  » 


i  i 


" 


'.    } 


CHAP.    XIIL—FREIGHT-TRAIN'  RESISTANCE. 


511 


.axle  by  steel  springs  behind  them,  and  the  leathers  on  opposite  sides  of  each 
half  diaphragm  break  joints  with  those  on  the  other  half. 

The  oiling  cushion  in  this  box  has  its  oiling  plush  firmly  tacked  to  a  beech 

I 

c. 


I ^y^i'—^X  -  BL .  _ 


Section  on  AB 


Section  on  CO. 


Section  on  EF. 


j»4Aic-> — 33/4:  _.i..2W — 4H.-a*»--4 
Lower  Part  of  9ex. 


Plan. 


Front  Elevjftion 


Lj.iM.t_JLJ*_iLJLJ_f-_/ _f_A_f -l_f  ^'-~ 
Figs.  156-159.— Standard  Journal-box  of  the  Eastern  Railway  of  France. 

block,  and  to  this  plush  are  fastened  several  little  tufts  projecting  above  its 
surface  and  keeping  the  plush  from  matting  down  by  too  hard  pressure  against 
the  journal.     The  plush  is  of  wool  with  a  long  silky  warp. 

640.  Tl'.e  important  question  of  the  comparative  resistances  in  start- 
\t\\r  trains  is  discussed  so  fully  in  Appendices  A  and  B  that  it  appears  un- 
necessary to  devote  space  to  a  repetition  of  the  same  matter  here.  From 
all  the  facts  there  given  the  following  conclusions  may,  it  is  believed,  be 
•drawn : 


512  CHAP,   XIIL— TRAIN  RESISTANCE^STARTINC. 


I.  The  resistance  at  the  beginning  of  motion  in  each  journal  is  equal, 
(as  before  stated)  to  about  20  lbs.  per  ton,  or  say  15  lbs.  per  ton  over  the 
average  friction  in  motion.     Except,  therefore,  for  the  elasticity  of  the 
springs  or  the  equivalent  effect  of  the  "  slack"  which  always  exists  in 
freight  trains,  enabling  the  cars  to  be  set  in  motion  one  at  a  time  such 
trains  as  are  usually  hauled  could  not  be  started  at  all  by  the  locomotive 
2.  A  velocity  of  0.5  to  3  miles  per  hour,  or,  as  an  average,  2  miles  per 
hour,  must  be  attained  before  the  journal-friction  falls  to  10  lbs.  per  ton 
or  5  lbs.  above  the  average  motion. 

The  average  during  this  period  may  be  taken  at  12  lbs.  per  ton. 
3-  At  6  miles  per  hour  the  journal-friction  is  at  least  i  lb.  per  ton 
higher  than  at  usual  working  speeds.     The  average  journal-friction  be- 
tween 2  and  6  miles  per  hour  may  be  taken  as  at  least  2\  if  not  x  lbs 
per  ton  higher  than  the  normal. 

4.  During  the  period  of  getting  up  speed,  the  normal  law  of  accelera- 
tion of  velocity  is  so  interfered  with  by  the  varying  coefficient  of  friction 
that  the  velocity  attained  at  any  given  point  may  be  rudely  taken  as 
directly  proportional  to  the  distance  run,  so  that  the  increase  of  velocity 
would  be  more  correctly  represented  graphically  by  a  right  line  than  by 
the  parabola  tangent  to  the  horizontal  line  of  normal  velocity  in  motion 
which  theory  requires. 

641.  Assuming  these  facts,  we  having  the  following  conditions  in  a 
freight  train  which  is  so  heavily  loaded  that  it  may  be  assumed  to  have 
to  run  3340  ft.,  or  f  of  a  mile,  to  acquire  a  velocity  of  10  miles  per  hour. 

1.  The  average  velocity  will  be  under  5  miles  per  hour  and  the  time 
occupif^d  over  7.6  minutes. 

2.  The  increased  tractive  force  needed  merely  to  accelerate  the  speed 
will  be  2  lbs.  per  ton;  since  communicating  that  velocity  is  equivalent 
(Table  1 18)  to  lifting  the  train  through  3.34  ft.  vertically,  and  i^^^  =  o.  la- 
per  cent  grade  =  a  resistance  of  2  lbs.  per  ton. 

3.  For  the  first  one-fifth  of  this  distance,  or  668  ft.,  the  total  demand 
upon  the  tractive  power  is — 

2  lbs.  per  ton  for  acceleration. 

12  lbs.  per  ton  for  extra  rolling-friction. 

14  lbs.  total  additional  tractive  resistance,  equal  to  a  grade  of  0.70,  or 
37  ft.  per  mile. 

4.  For  the  next  1336  ft.  the  total  demand  upon  the  tractive  power  is 
similarly  found  to  be  4.5  to  5  lbs.  per  ton  over  the  normal,  equivalent  to- 
the  effect  of  a  0.225  to  0.25  per  cent  grade,  or  12  to  13  ft.  per  mile. 


, 


CH.  XIII.— TRAIN  RESISTANCE— SIZE  WHEEL  AND  AXLE.     513 

642.  These  grades,  therefore,  represent  the  reduction  at  stations  or 
stopping-places  which  it  is  essential  to  make  to  fully  and  certainly  equal- 
ize the  demands  upon  the  tractive  power  of  locomotives  while  in  motion 
and  when  getting  under  way.  The  fact  that  such  heavy  reduction  of 
grade  at  stations  may  be  said  never  to  exist,  while  yet  such  heavy  trains 
are  hauled,  is  due  in  part  to  the  use  of  sand  in  starting,  in  part  to  the 
greater  starting  traction  which  is  realized  in  practice  from  the  same 
average  cylinder  pressure  (see  end  of  Appendix  B),  and  in  part  to  the  fact 
that  the  full  adhesion  of  the  locomotive  is  not  used  up  on  the  open  road 
(par.  557).  To  utilize  to  the  utmost  the  power  of  locomotives,  and  to 
make  the  hauling  of  heavy  trains  easy,  such  reductions  are  the  first 
thing  which  should  be  attended  to  in  laying  out  a  new  road  or  in  improv- 
ing an  old  one. 

Wherever  possible  the  reduction  of  grade  at  stations  should  be  liberal, 
since  there  is  in  no  case  danger  of  having  it  too  great  for  convenience. 
On  the  other  hand,  when  the  lower  grades  at  stations  are  only  obtainable 
at  the  certain  cost  of  higher  grades  between  stations,  then  it  becomes 
necessary  to  be  more  cautious,  although  the  tendency  will  always  be  to 
have  the  starting  resistances  the  true  limiting  cause. 

643.  Effect  of  Size  of  Wheel  and  Journal. — Theoretically,  the  less 
the  diameter  of  the  journal  and  the  larger  the  diameter  of  the  wheel  the 
less  the  axle-friction.  The  standard  diameter  of  car-wheels  in  America 
is  33  inches,  with  a  very  few  only  (chiefly  on  the  Baltimore  &  Ohio  lines) 
of  30  inches,  and  with  a  still  smaller  but  increasing  number  of  42- inch 
wheels  in  passenger-car  service.  The  weight  of  the  latter  is  more  than 
double  that  of  33-inch  wheels  (say  1200  lbs.  against  550,  as  an  average) 
and  their  primary  purpose  is  to  promote  easy  riding  of  cars. 

The  Master  Car-Builders'  Association  standard  journal  is  3f  x  7 
inches,  giving  a  nominal  bearing-surface  (the  horizontal  mid-section)  of 
i(i\  sq.  in.  A  very  few  4  x  8-inch  journals,  giving  32  sq.  in.  bearing,  are 
in  use  for  cars  carrying  very  heavy  loads,  and  a  verylarq^e  but  decreasing 
number  smaller,  down  to  as  small  as  3Jx6,  giving  19.5  sq.  in.  of  bearing. 

The  maximum  loads  which  are  carried  in  practice  on  these  journals, 
allowing  eight  per  car.  may  be  estimated  as  follows  : 


Journal. 

Square  Inches  Area. 

Maximum  Load. 

Load  Per  Square 
Inch. 

Maximum,  4    X8 

Standard,    3f  X  7 

Minimum,  3^  X  6 

32       X  8  =  256 
26^     X  8  =  210 
19.5  X  8  =  154 

64.000 
52,500 
38,500 

250  lbs. 
250   ♦• 
250  ** 

33 


514    CH.  XIIL— TRAIN  RESISTANCE— SIZE  WHEEL  AND  AXLE, 

As  an  average  of  the  entire  service  of  the  car  th.se  loads  will  hardly 
in  any  case  exceed  200  lbs.  per  sq.  in.,  but  they  will  often  run  up  to  300 
lbs.  This  pressure,  however,  is  very  unequally  distributed,  being  great- 
est (about  twice  the  average)  at  the  top  of  the  journal  and  running  down 
to  nothing  at  the  sides.  The  bearing,  in  fact,  for  this  and  other  good 
reasons,  is  never  made  to  cover  the  whole  semicircular  top  of  the  jour- 
nal. For  example  there  are  only  21.94  sq.  in.  of  bearing-surface  in  the 
American  standard  journal-bearing  against  26^  sq.  in.  in  the  section  of 

the  journal  itself. 

644.  The  only  purpose  in  increasing  the  size  of  the  journal  is  to  di- 


6.  Centre  of  axle.    (The  standard  axle  differs 

a  little  from  this,  tapering  more  toward 
the  centre.) 

7.  Flange. 

8.  Journal-box. 

9.  Journal-box  lid. 

46.  Brass  or  journal  bearing. 


Fic   t6o -Usual  Form  of  American  Car-whebl,  Journal,  and  Journal-box. 
Tc,  i«  the  so-called  dust-euard  bearing  ol  the  axle,  surrounded  by  a  flat,  square  dust-guard 
t  ^^^  A    i-tth«.r  r!r  vnlrlnfzed  fibre  which  is  slipped  in  from  above  throuKh  a  slot  in  the  cast- 

s!;r«  ^HS%^v^^  Sn;;fS 

dSiSId  out^oS  below^hL^rcvel  of  the  underlfJ?  of  th'e  axle  that  there  is  no  n.ore  to  escape.] 

minish  the  pressure  per  sq.  in.  so  as  to  prevent  heating.     Experience  has 
amply  shown  this  to  be  necessary,  with  such  lubrication  as  is  attained  in 


I 


Cff.  XIIL— TRAIN  RESISTANCE-SIZE  WHEEL  AND  AXLE.     5 1  5 

America,  because,  although  99  per  cent  of  the  car  mueage  may  be  said 
to  be  made.with  journals  in  good  order,  and  in  fact  with  surfaces  in  a 
high  state  of  perfection,  yet  the  inconvenience  and  danger  resulting  from 
possible  heating  of  the  remaining  one  per  cent  is  the  important  thmg  to 
obviate.  In  France  and  Germany,  where  much  more  carefully  con- 
structed axle-boxes,  insuring  far  more  reliable  lubrication,  are  in  use 
than  here,  as  shown  in  Figs.  156  to  159.  far  higher  pressures  are  likewise 
in  use,  without  evil  results,  up  to  fully  double  American  practice,  and  with 
great  economy  of  lubricants  ;  but  the  crude  form  of  axle-box  usual  in 
this  country,  shown  in  Fig.  160,  permits  fully  nine  tenths  of  the  oil  sup- 
plied to  the  journal  to  drip  out  upon  the  track  before  it  has  done  much 

service.  1    r  •  .• 

645.  The  coefficient  of  train  resistance  due  to  axle-friction 

__  coef!.  of  fric.  x  diam.  of  axle  ^.^  ^^^^   ^^^  ^^^^  ^  2000  or  2240 

■~  diam.  of  wheel 

=  journal  train  resistance  in  lbs.  per  ton.  With  the  same  axle,  therefore. 

by  increasing  the  diameter  of  the  wheel 

from  33  to  42   in.  we  should  decrease 

^xle-friction  to  H  of  its  former  amount, 

or  about  |.      With  the  same  wheel,  the 

comparative  axle-friction  is  directly  as 

ihe  diameter  of  the  journal. 

646.  If  the  average  journal-friction 
in  motion  be  taken  at  4  lbs.  per  ton,  the 
larger  wheels,  therefore,  will  save  about 
o  8  lb.  per  ton  of  rolling-friction,  but  they  will  add  possibly  10  per  cent 
to  the  weight  of  the  car,  and  therefore  to  grade  resistance.  Hence, 
wherever  the  grade  resistance  exceeds  about  8  lbs.  per  ton  (=  that  on  a 
0.4  per  cent  grade ;  21  feet  per  mile),  the  use  of  42-inch  wheels  is  a  losing 
operation,  so  far  as  mere  train  resistance  in  motion  is  concerned,  but 
there  still  remains  as  a  net  gain  the  improvement  in  riding  qualities  of 
the  cars  and  in  ease  of  starting— both  very  important  gains. 

647.  Many  circumstances  indicate  that  the  rolling-friction  proper,  between 
the  rail  and  wheel,  is  an  element  of  considerable  importance  in  the  aggregate 
of  the  so-called  "  rolling  friction."  One  is  the  known  and  great  effect  of  the 
.:ondition  of  the  track  on  the  resistance.  It  is  probably  largely  due  to  this 
cause  that  modern  determinations  of  rolling-friction,  both  in  this  country  and 
abroad  are  so  much  below  what  was  formerly  the  assumed  average.  Another 
is  the  ordinarily  very  perfect  condition  of  railway  journals  and  the  very  low  co- 
efficients which  have  been  obtained  by  Thurston,  Tower,  and  others  for  journal- 


^  JJSFt'ys  ^/S£..> 


Fig.  i6x. 


5l6    CH.  XIIL—TRAIN  RESISTANCE— SIZE  WHEEL  AND  AXLE. 

friction  proper,  as  above  given.  Another  is  the  high  tractive  coeflScients  of 
wheeled  vehicles  with  very  small  axles  and  very  large  wheels  on  the  most  per- 
fect roads.  On  the  other  hand,  the  close  correspondence  of  the  laws  of  varia- 
tion in  rolling  and  journal  friction,  together  with  the  laws  of  variation  in  jour- 
nal-friciion  o'nly,  seem  to  indicate  quite  the  contrary.  Thus,  in  both  cases,  as 
the  load  or  the  velocity  decreases  the  coefficient  cf  resistance  increases,  and  at 
about  the  saine  rates  (see  Appendix  B). 

648.  A  plausible  argument  may  be  made  to  show  that  no  theoretical  loss 
whatever  exists  from  the  compression  of  a  perfectly  elastic  substance,  such  as 

a  rail  may  be  arrumed  to  be,  and  to  a  great 
extent  the  permcn  .nt  way  as  a  whole,  under  a 
rolling  load.  In  Fig.  162,  the  compression  at 
any  point  of  the  surfaces  in  contact,  wher- 
ever it  may  be,  is  proportional  to  ordinates 
from  the  line  CCto  the  periphery  of  the  wheel 
P.  The  elastic  resistance  is  in  proportion  to 
these  ordinates,  and  the  semi-segments  FF 
represent  in  magnitude  and  position  the  total 
clastic  forces  operating  to  retard  and  to  accelerate.  The  resultants  R  and  R 
of  these  parallel  forces  must  pass  through  the  centre  of  gravity  of  these  semi- 
segments  F  and  F^  and  must  each  be  equal  to  half  the  total  load  resting  on  the 
wheel.  It  appears  to  follow  clearly  from  the  figure  that  the  moments  of  these 
accelerating  and  retarding  forces  are  equal,  so  that  they  neutralize  each  other. 

The  error  in  this  reasoning  is  in  part  that  at  high  speeds  the  element  of 
TIME  comes  in  to  modify  the  elastic  resistances,  increasing  that  in  front  of  the 
wheel  because  it  must  be  set  in  motion,  and  decreasing  that  behind  the  wheel 
because  the  elastic  resistance  requires  time  to  act,  and  hence  cannot  follow  up 
the  wheel  with  its  full  force.  In  part  the  error  is  that  any  irregularity  of  sur- 
face causes  an  irregularity  of  motion  which  is  known  to  very  seriously  aflfect 
both  wear  and  tear  and  friction. 

Any  attempt  to  determine  theoretically  the  amount  as  well  as  the  nature  of 
this  loss  would,  of  course,  be  impracticable. 

649.  The  work  of  Josef  Grossman,  Engineer  of  the  Austrian  Northwestern 
Railroad,  on  "  Lubricating  Materials  and  Metais  for  Bearings"  (Wiesbaden, 
1885),  treats  its  subject  with  a  good  deal  of  elaboration,  historically  and  ana- 
lytically, and  among  other  matters  discusses  quite  fully  the  question  of  train 
resistance,  although  not  always  with  correctness  and  good  judgment.  His 
results  indicate,  however,  that  the  axle-friction  is  at  any  rate  a  very  small 
clement.  In  this  connection  he  cites  a  remarkable  result  of  some  Bavarian 
experiments,  in  which  by  greasing  the  rails  on  the  curve  of  100  metres  (337  ft.) 
radius  a  reduction  of  the  total  curve  resistances  of  96  per  cent  was  attained;  61 
per  cent  of  the  total  resistance  due  to  the  curve  disappearing  when  the  inner 


CHAP.    XIII.— TRAIN  RESISTANCE— HIGH  SPEED.        517 


J.    K 


V   « 


i 


t 

\ 


■idice  of  the  head  of  the  outer  rail  was  greased,  and  31  per  cent  more  when  the 
other  rail  was  greased. 

The  striking  correspondence  of  these  experimental  results  with  those  de- 
duced theoretically  in  pars.  301-320  et  seq.  is  notable. 

THE  VELOCITY  RESISTANCES. 

650.  The  best  evidence  that  we  have  warrants  the  all  but  universal 
assumption  that  train  resistance  varies  as  the  square  of  the  velocity,  or 
that  its  equation  is  of  the  form 

R  =/7/»  +  c. 

This  is  still  merely  assumption,  not  only  as  respects  train  resistance  as 
a  whole,  but  as  respects  each  separate  constituent  element.  Air  resistance, 
for  example,  is  known  by  observations  on  projectiles  to  vary  more  nearly 
as  the  cube  of  the  velocity,  when  the  latter  is  very  great;  but  at  all  ordi- 
nary velocities  it  appears  to  vary  very  nearly  as  the  square,  and  as  re- 
spects oscillatory  resistance,  we  know  absolutely  that  the  amount  of  de 
structive  work  (or  of  any  other  kind  of  work)  which  a  train  is  capable  ot 
•doing,  either  by  a  dead  or  glancing  blow,  is  directly  as  the  square  of  the 
velocity.  These  two  elements  constituting  together  the  ord in a^-y  "  ve- 
locity resistance,"  it  is  but  natural  to  conclude  that  the  aggregate  also 
-varies  as  the  square  of  the  velocity,  and  all  but  certain  that  it  does,  al- 
though it  may  very  easily  be  as  7/'*",  or  v^'^,  or  even  z/'*',  or  may  fluctuate 
between  these  powers  at  various  speeds  or  according  to  circumstances. 
There  have  been  various  formulae  pui  forth,  and  some  of  them  on  very 
high  authority,  differing  widely  from  this  form,  some  of  them  giving  the 
velocity  resistance  directl)'^  as  v,  and  others  (only  one  of  which  is  known 
to  the  writer)  as  ^',  but  both  of  these  assumptions  lead  to  absurd  results 
when  extended  to  very  high  speeds,  and  are  unquestionably  erroneous. 

651.  One  instance  of  the  former  (as  respects  the  train  behind  the  engine)  is 
given  in  par.  662.  On  the  other  hand,  a  formula  deduced  from  Bavarian  experi- 
ments in  1876,  on  a  large  and  costly  scale,  reported  by  the  late  Baron  von 
Weber  in  a  somewhat  informal  paper,*  led  to  the  most  absurd  results,  not 
necessary  to  detail  here. 

652.  As  a  rule,  no  attempt  is  made  in  train-resistance  formulae  to 
separate  the  aggregate  velocity  resistance  into  its  constituent  elements, 
although  in  some  cases  they  are  in  such  form  as  to  assert  or  imply  that 
the  velocity  resistance  is  either  all  oscillatory  or  all  atmospheric.  A 
formula  devised  by  Mr.  Wm.  H.  Searles,  which  has  been  adopted  as  the 

*  See  Railroad  Gazette,  June  il,  25,  1880. 


I 


518       CHAP,   XIII.— TRAIN  RESISTANCE— HIGH  SPEED. 


1 


basis  for  the  computations  of  this  volume  as  having  a  truly  wonderful 
ran^e  of  application  to  all  speeds,  conditions,  and  classes  of  trains,  even 
if  it  is  not  precisely  correct,  is  open  to  the  sole  serious  objection  (and 
that  chiefly  theoretical)  that  it  in  effect  assumes  all  velocity  resistance  to 
be  oscillatory,  or  uniform  per  ton,  regardless  of  the  form  of  the  cars  (see 
pars  657-8; ;  while,  on  the  other  hand,  formulae  proposed  by  Mr.  O. 
Chanute  (in  Haswell's  "  Pocket- Book ")  are  distinctly  based  on  the 
assumption  that  the  velocity  resistance  is  wholly  atmospheric.  Both 
of  these  assumptions  are  unquestionably  erroneous,  although  which  is 
most  so  must  remain  doubtful. 

653.  The  writer  has  conducted  the  only  tests  as  yet  made,  and  known 
to  him,  which  have  been  distinctly  directed  to  the  end  of  determining 
the  amount  of  each  element  of  train  resistance  separately,  and  owing  to 
the  delicacy  of  the  apparatus  by  which  they  were  made,  and  the  extreme 
care  used  in  computing  them,  he  believes  them  (with  perhaps  a  natural 
bias)  to  be  still  the  most  trustworthy  indication  in  that  respect.  These 
experiments  are  given  in  full  in  Appendix  A,  and  their  general  results  are 
shown  graphically  in  Fig.  163,  their  most  striking  feature  being  perhaps 
the  positive  evidence  that  atmospheric  resistance  is  at  least  a  less  pro- 
portion of  the  velocity  resistance  than  is  commonly  assumed,  and  that 
the  resistance  arising  from  oscillation  and  concussion,  whatever  its  exact 
cause  and  nature,  is  a  materially  more  important  element. 

654.  Nevertheless,  there  is  a  fact  tending  to  disprove  these  conclu- 
sions, viz.,  the  enormously  greater  indicated  power  of  locomotives  at 
high  speeds  than  that  transmitted  backward  to  the  train  as  determined 
by  a  dynamometer.  Table  164  gives  one  record  illustrating  this  fact— a 
test  trip  of  a  fast  express  train  on  the  New  York  Central  &  Hudson  River 
Railroad,  made  by  Mr.  P.  H.  Dudley,  in  which  it  will  be  seen  that  only 
some  55  per  cent  of  the  indicated  power  passed  back  of  the  dynamome- 
ter  car  to  the  train  at  53  miles  per  hour.  Figs.  164,  165,  giving  the  re- 
sults of  some  elaborate  French  tests,  show  a  still  higher  proportion  of  en- 
gine-friction. Other  tests  of  the  kind  show,  according  to  the  speed,  from 
40  to  75  per  cent.  The  whole  subject  is  still  involved  in  much  obscurity 
and  doubt,  but  Figs.  164.  165  and  Table  165  will  illustrate  how  very  im- 
portant an  element  the  head  resistance  is  at  high  speeds. 

655.  According  to  the  best  evidences  which  the  writer  has 
been  able  to  secure,  the  ordinary  working  maximum  of  train  re- 
sistance, under  somewhat  adverse  conditions  as  respects  wind 
and  surfacing  of  track  and  rail,  may  be  considered  to  be  not  un- 


[^% 


t 


i 


As   DEDUCBD    FROM 


Fig.  163. 
D^c.cTAMrRsPERToN  OF  American  RoliBng-stock, 

DIAGRAM    SHOWING  THE  RESISTANCES  PeR  ToN  oXwAV,  AT  ClEVELANH,  OhIO. 

EXHERIMENO^  ON   THE    LaKE   ShORE  &   M.CH.GAN   SOUTHERN   Ra» 

Conducted  by  A.  M.  Wellington,  C^E.  ■  reproduced  in  AppendU  A.] 

c       rK    Vol  Vlll    No   CLXXVll.     lUe  substance  ol  t»»c  P*H^  ^ 

[For  original  paper,  see  Trans.  Am.  Soc.  C.E.,  \ol.  Vlll.,  wo.  k,x. 

30  lbs  Tier  ton  =  Qradeoft.sfteT-iOo 


-r 


/ 


^UJ- 


sv-^ 


e 


V 


I 


j^    M/Ls     io        HBH      -  ^^      ^^^"^    ^ 


s/tdiSxtijorxjar^olUngTf 


iation,  (^JEm^ify  Oars = 2_/  Us.]beyimi  fS.o in.  d^J 


y - ■ '' ~        \          istance  formulae,  and  was  for  a  long  time  regarded  as  standard.     More 

^'k  Clark's  formula,  shown  hereon,  is  one  of  the  oldest  and  best  known  of  all  train-res  ^^^^  ^^      ^,^^^^^  ,^,  ^^tter  is  more  doubtful.     See  par.  655 

modem  tests  indicate  that  it  is  far  too  high  at  low  speeds,  and  on  the  whole  somewhat  too  Ijp  g       P-    , 

et  seq. 


[\ 


CHAP.    XIII.— TRAIN  RESISTANCE— HIGH    SPEED.        5X9 


Table   164. 
Train  Resistance  of  Heavy  and  Fast  Passenger  Trains. 


Weight  of  Train. 

Engine  on  drivers 24.0 

entruck 12.0 


Tender 

Three  day-coaches  65 . 

Six  sleeping-coaches 185. 


± 
± 


Tons. 


36.0 
27.0 


250.0 


313  o 


Train  started  from  a 
state  of  rest.  Average 
speed  in  motion,  52  miles 
per  hour.  Slight  undu- 
lating grade  of  2  to  13 
ft.  per  mile,  the  effect 
of  which  is  corrected  be- 
low. 


Total  weight  of  train 

17  X  24  American  engine.    6  ft.  drivers,  135  lbs.  steam  pressure 

[Deduced  from  records  of  dynamometer  tests  by  P.  H.  Dudley  on  New  York  Central  &  Hudson 
River  Railroad,  Rept.  Am.  Ry.  M.  M.  Assoc,  1882,  p.  132.] 


Aver- 
age 
Mites. 

Aver- 
age 
Speed. 

Vel.- 

Head 

(Table 

118). 

Wo  k 

repre- 
sented 

by 

Speed . 

Vert.  ft. 

Grade. 

Dyn. 
Work 

on 

Train. 

Vert.  ft. 

Do.  ± 
Effect 

of 

Grade. 

Vert.  ft. 

Do.  ± 
Effect 

of 

Speed. 

Vert.  ft. 

Aver- 
ages 
Vert.  ft. 
Per 
Mile. 

Equivalent 
Resistance. 

Grade 
p.  c. 

Lbs. 
p.  ton. 

I 
3 

20.68 
38.31 

15.20 
52.10 

-- 15.20 
--36.90 

+  ■5*25 

48.23 
40.07 

48.23 

45-32 

33-03 
8.42 

3 

4 

43.90 
47-34 

68.42 
79  57 

■H-I6.32 
-l-ii.iS 

4-  5-25 

35-53 
31.81 

40.78 
31.81 

24.46 
20.66 

20.72 

.393 

7.86 

5 
6 

7 
8 

50.70 

49-31 
50.70 
52.89 

91.25 
86.32 
91  25 
99-3» 

-I-11.68 
-  4-93 
+  4-93 
-f  8.06 

-13.0 
4-18.0 
4-13.0 

29.74 

30 -57 
28.92 
26.44 

29.74 

17-57 

46.92 

39-44 

18.06 
22.50 
41.99 
31-38 
28.06 

34-57 
20.60 

22.56 

•427 

8.56 

9 
10 

IX 

53-70 
52.10 
52.89 

102 . 38 
96.36 
99  31 

+  3-07 
—  6.02 

+  2-95 

-1-  8.0 

4-  5-0 

23-13 
23-55 
23-55 

3'-i3 
28.55 
23-55 

28.48 

-540 

10.80 

12 

13 
»4 

16 

52.10 

51-43 
5143 
51-43 
51-43 

96.36 
93.91 

93-9' 
93-91 
93.91 

-  2.95 

-  2.45 

a    ■    ■    • 
•    •    •    • 

4-  8.0 

25.61 

24  78 
25.61 
26.85 
26.60 

33-6i 
24  78 
25.61 
26.85 
26.60 

36.56 

27-23 
25.61 
26.85 
26.60 

27.74 

•527 

10.54 

17 
18 

19 

52.89 
52.89 
52.89 

99-31 
99  31 
99-31 

4-  5-40 

4-  6"o 

-4-  2.0 

27.68 
26.44 
26.44 

27.68 

32.44 
28  44 

22.28 
32.44 
28  44 

28.56 

-541 

10. 82 

20 
21 
22 
23 

50.70 

49-31 
52.89 
53-70 

9»-25 
86.32 

99  31 
102 . 38 

-  8.06 

-  4.93 

-+12. 9Q 

+  3-07 

—  lO.O 

—  lO.O 

-^-lo.o 

29.68 
28.92 
24-78 
24-37 

1Q.68 
18.92 
24.78 
34-37 

11.62 

13.99 
11.79 

31-30 

27.72 
17.18 

•525 
-337 

10.50 
6.74 

Mr.  Dudley  found  the  traction  in  starting  to  be  11,000  to  12,000  lbs.  for  the  first  100 
to  200  feet,  falling  to  2800  to  3000  lbs.  at  50  miles  per  hour.     The  consumption  of  steam 

and  water  per  mile  was  : 

Ai  135  lbs.  pressure,  300  to  333  lbs.  water, 

40  to    50  lbs.  coal. 

=  7.5  to  6.67  lbs.  water  per  lb.  coal. 

He  notes  that  Swiss  and  German  locomotives  carry  165  to  180  lbs.  as  a  rule ;  some- 
times as  high  as  225  lbs. 

The  total  horse-power  developed  by  the  engine  is  given  in  the  same  table  as  the 
dynamometer  record,  but  computed  and  not  observed.  The  computation,  however,  ap- 
pears to  be  one  based  on  Mr.  Dudley's  own  investigations.     It  shows  a  total  horse-power 


i 


520       CHAP,   XIII.— TRAIN  RESISTANCE— HIGH  SPEED. 

developed  of  750  to  800  H.  P.,  and  taking  the  average  for  the  four  miles  13-16,  on  which 
the  grade  was  level  and  the  speed  uniform,  we  obtain  : 

Average  sf>eed.  miles  per  Average  horse-power  expended  on — 

hour,  51.43.  Train.  Engine.  Total.  P.  c.  enjf, 

340  426  766  55-6i 

lbs.  lbs.  lbs. 

Equivalent  total  traction  resistance 2,479  3,106  5,585  (=  i  adhesion.) 

Ditto,  in  lbs.  per  ton     9.92  4925  17.8 

This  is  considerably  lower  than  Table  166  indicates,  which  is  about  30  lbs.  per  ton; 
but  one  possible  explanation  of  this  discrepancy  is  that  Mr.  Dudley's  table  does  not  war- 
rant his  declaration  that  "at  50  miles  per  hour  the  traction  was  2800  to  3000  lbs.,"  but 
indicates  only  2500  lbs.  This  difference  alone  would  add  \\^  to  2  lbs.  per  ton  to  the 
resistance, 

Mr.  Dudley's  engine  and  head  resistance,  as  an  average  of  all  his  record  (not  all  given 

here),  amounts  per  engine  to  0.83  F^  lb.     The  writer's  tests  (see  Appendix  A  and  Fig. 

165)  give  a  somewhat  smaller  result  for  the  engine  resistances,  vir. : 

Lbs.  per  engine. 

For  head  resistance o.  a8  F* 

For  oscillation  and  concussion 0.35^^' 

Total 0.63^^*  4-  4  to  8  lbs.  per  ton  constant. 

By  comparison  of  a  variety  of  evidences,  however,  the  writer  believes  that  0.83  F«  lb. 
comes  very  close  to  giving  the  actual  total  velocity-resistance  of  the  engine  at  high  speeds, 
and  the  rapid  inroads  which  this  rate  makes  on  the  power  of  the  engine  is  shown  in 
Table  165. 

fairly  expressed  by  the  single  formula  of  Mr.  Wm.  H.  Searles 
just  referred  to  and  given  below.  For  the  more  favorable  con- 
ditions it  gives  unquestionably  far  too  high  resistance  ;  as  for 
example,  for  a  train  of  313  tons,  as  in  Table  164,  at  50  miles  per 
hour,  it  gives  a  tractive  resistance  of  30  lbs.  per  ton  for  the  en- 
tire train,  or  9390  lbs.  total  tractive  resistance,  equivalent  to  1280 
horse-power,  whereas  the  actual  horse-power,  as  given  beneath 
the  table,  was  less  than  800.  Further  evidences  to  the  same  ef- 
fect are  given  in  par.  659  et  seq.,  below  ;  but  the  ratios  of  the 
resistances  at  various  speeds  are  of  more  practical  importance 
than  their  absolute  amount,  and  these  will  not  be  affected  im- 
portantly by  any  reduction  in  the  latter.  Moreover,  nearly  all 
our  experimental  evidence  is  based  on  observations  taken  under 
the  most  favorable  conditions  for  low  resistance,  and  in  the  case 
of  European  tests  with  trains  of  much  smaller  cross-section  and 
with  cars  much  nearer  together.  The  bounding  rectangles  of  the 
average  American  and  European  passenger  cars  (a  fairer  basis  of 


i' 


I 


m 


m 


Kf 


CHAP.    XIII.— TRAIN  RESISTANCE— HIGH  SPEED,        $21 


Cn^nt  aloiw. 


Fig.  164.— Variation  in  Resistance  Per  Ton 
FOR  Various  Loads. 


SOTons  Load. 


10 


.1.4 J -C. 

%0  30 

Miles  per  Hour. 


Fig.  165.— Variation  in  Total  Traction  for 
Various  Loads. 


20 
Miles  per  Hour. 


French  Tests  of  Train  Resistance  at  Low  Velocities. 

[From  Annates  des  Fonts  et  Chaussies,  May,  1886.  '*  Etudes  Dynamometrique,"  par 
"M,  Desdoint,  Ing.  de  la  Marine,  adjoint  a  I'Ingenieur  en  Chef  du  Materiel  et  de  la  Trac- 
tion des  Chemins  de  Fer  de  l'£tat.] 

The  paper  showed  resistances  at  low  ordinary  speeds  of— 
Passenger  trains,  40)^"  wheels,  3J4  X  7"  axles,  4  tonnes  per  axle,  .      .      , 


Lbs.  per  ton. 


Freight 


ii 


ii 


i  3-4  U  2 


Temperature  of  axles  53.6»  Fahr. 

At  still  lower  velocities  of  5  ft.  per  second  (3^  miles  per  hour)  the  resistance  varied 
from  4.4  to  5.4  lbs.  per  ton,  this  being  in  fact  due  to  the  lower  journal  speed,  as  observed 
by  the  writer  in  his  tests  (par.  640  et  seg.  and  App.  A  and  B),  and  not  at  all  to  their  being 
*•  valeurs  toutes  exagerees  comme  on  va  la  voir,"  as  suggested  in  M.  Desdoint's  paper. 

Trains  of  300  tonnes,  with  70-tonne,  4-coupled  engine,  showed  a  mean  resistance  of 
4.4  lbs.  per  ton. 


522        CHAP,   XIIL-TRAIN  RESISTANCE-^HIGH  SPEED. 

Velocity  Resistances. 
The  following  grades  were  found  to  approximately  equajize  the  velocities  at  various 
speeds,  with  short  trains  : 

Grade  per  cent, 
o  to  o.s 
0.5  to  i.o 


Miles  per  hour, 
o     to  i8^ 
18H  to  37 


37 
See  also  par.  447. 


to  50 
to  63 


1.0  to  1.5 
1.5  to  2.0 


Equivalent,  lbs.  per  ton. 

ID 

10  to  20 
201030 
30  to  40 


comparison  than  the  precise  cross-section  area)  compare  aboat 

as  follows: 

American, 10  X  14  ft.  =  140  sq.  ft. 

European, 8  X  12  "     =    96     '^ 

656.  When  we  further  remember  that  the  car-bodies  of  Ameri- 
can cars  are  separated  by  over  six  feet  from  each  other  because 
of  the  platforms,  and  that  the  trucks  are  still  more  widely  sep- 
arated ;  and  when  we  remember  further  that  foreign  engines  have 
no  cabs',  and  a  smaller  cross-section  generally— the  foreign  evi- 

Table  165. 
Engine  Head-Resistance  at  High  Speed. 

[According  to  the  formula  R  =  0.83  ^ »  (see  foot-note  to  preceding  table)  in  which  R  =  the 

TOTAL  resistance  of  the  engine.] 


Speed. 

Milks 

Per  Hour. 


10. 
20. 

30. 
40. 

50. 
60. 
70. 


Total  Head 

Resistance. 

Lbs. 


83 
332 

747 
1328 

2075 
2988 
4067 


Horse- 
Power. 


2.213 
17.71 

59-77 
141.67 
276.70 
478.20 
759-30 


Lbs. 

Per  Ton 

of  Train 

(313  Tons). 


.266 
1.06 
2.38 

4.25 
6.64 

9-58 

13.05 


Since  the  resistance  in  pounds  increases  as  the  sguar^  of  the  speed,  the  horse-power 
demanded  will  necessarily  increase  as  the  cuie  of  the  speed.  It  takes  a  very  powerful 
engine  to  maintain  a  speed  of  70  miles  per  hour  on  a  level  for  any  distance,  and  no  engine 
can  do  it  long,  with  no  train  whatever  behind  it.  As  the  horse-power  corresponds  very 
correctly  to  the  conditions  at  this  maximum  speed  it  must  necessarily  correspond  very 
correctly  with  the  facts  at  the  lower  speeds.    See  end  of  par.  664. 


CJIAP.   XIIL— TRAIN  RESISTANCE— HIGH  SPEED.        52J 

dence  below  given  (par.  660  et  seq.)  seems  to  rather  support  than 
disprove  the  resistances  given  by  the  formulae  summarized  in 
Table  166  below,  although  nominally  smaller. 

657.  It  has  tiierefore  seemed  best  to  use  as  the  basis  for  all 
train-resistance  computations  in  this  volume  the  formula  above 
referred  to  (par.  652),  proposed  by  Mr.  Wm.  H.  Searles  in  his 
"  Field-Book,"  since  this  formula  in  a  single  simple  equation 
seems  to  approximate  very  closely  to  what  experiment  indicates 
to  be  an  ordinary  working  maximum  for  the  resistance  of  trains 
of  all  classes,  at  all  speeds,  and  with  all  forms  and  weight  of  cars. 
It  is  recommended,  with  justice,  by  Mr.  Searles  as  accomplishing 
this  end,  in  the  following  words: 

"  It  is  an  empirical  formula,  based  upon  a  careful  investigation  of  all 
such  records  of  experiments  on  the  subject,  several  hundred  in  number, 
as  have  come  under  the  author's  notice,  and  is  believed  to  give  results 
agreeing  closely  with  the  average  experience  and  practice  of  the  present 
day.  It  is  designed  to  give  the  resistances  per  ton  for  all  trains,  whether 
freight  or  passenger,  and  at  any  velocity,  under  ordinary  circumstances. 
Accidental  circumstances,  such  as  the  state  of  the  weather,  and  the  con- 
dition of  the  road-bed,  rails,  and  rolling-stock,  may  largely  modify  the  re- 
sistance, but  these,  of  course,  are  not  taken  account  of  in  the  formula." 

The  formula  (simplifying  its  form  somewhat)  is  as  follows 
for  velocities  in  miles  per  hour: 

Average  resistance  of  entire  train  in  lbs.  per  ton  of  2240  lbs.,  for 
all  weights  in  gross  tons, 

.0006  F"  (wt.  eng.  and  tender)'^ 
gross  wt.  of  train  * 

Average  resistance  of  entire  train  in   lbs.   per  net  ton,  for  all 
weights  in  net  tons, 

JP  =  4.82  +  .00535 7  V  +  •°°°4783K'(wt.eng.andtender> 

'         '^^^'         '  gross  wt.  of  train 

This  formula,  with  a  comparison  of  others  below  it,  is  tabu- 
lated in  Table  166. 

658.  It  will  be  seen  that  this  formula  gives  the  same  result  whether 
a  given  weight  of  train  be  made  up  of  light  empty  box  cars,  weighing 
perhaps  9  tons  each,  or  loaded  coal  cars  weighing  three  or  four  times  as- 
much  and  exposing  only  one  third  or  one  half  the  area  to  air  resistance; 


^  =  5.4    -|-.oo6r'        + 


524        CHAP,   XIII.^TRAIN  RESISTANCE-HIGH  SPEED. 


Table  166. 
Train  Resistance  on  a  Level  as  Affected  by  Velocity. 

A^.^  ac  thP  ordinary  working  maximum,  as  computed  from  the 

Giving  what  may  be  ^°"^f  ^^^"^^'^'J^^^^^^^  closely  with  the  apparent  indications 

P-eneral  formula  of  Wm.  H.  Searles,  comciaing  ^i       /  f  ^^cwtanrM 

of  the  most  recent  tests,  but  possibly  as  much  as  one  th^rdtoo  h^gh  for  the  resistances 

at  high  speeds  under  favorable  conditions  (par.  655  et  seq.). ^^^ 

Resistance  Per  Short  Ton,  for 
Velocities;  Miles  Pek  Hour. 


Freight  Train*. 

Heavy 
Consolidation  Engine. 


Engine  only  • 

"     and  10  loaded  cars 


(I 

it 
it 


it 
it 

4i 
it 


20 
30 

40 

75 
100 


it 

it 
it 

ii 


%t 
it 

it 

it 
ti 

it 


Total  Weight 
OF  Train. 


Long 
Tons. 


70 
270 
470 
670 

870 

1070 

1570 
2070 


Short 
Tons. 


78.4 
302.4 
526.4 
750- 4 


Equation  of 

Resistance. 

Per  Short  Ton. 


974-4 
I 198. 4 

1758.4 
2318.4 


it 
it 

ti 

it 
i« 
it 


.0428^" 

.oi5iF« 

.oiogKa 

.oo928K'» 

.00837^' 

.0078 P^' 

.  00703  f^' 

.oo653r» 


For  formulae 
coefficient  of  V^ 


of  resistances  for  trains  of  flat  cars,  suitract  about  oox.  from 
For  resistances  and  formute  per  long  ton,  add  12  per  cent. 


Pawenger  Train*. 

17  X  24 
Americ'nEngine. 


Total  Wt. 
OF  Train. 


Long 
Tons. 


Engine  only 

"    and    2  cars. 
it 

it  it  o       it 


ii 
it 


ii 


4 
8 
12 
16 


50 
100 

150 
250 

350 
450 


Short 
Tons. 


Equation  of 

Resistance. 

Per  Short  Ton. 


Resistance  Per  Short  Ton  for 
Velocities;  Miles  Per  Hour. 


56 
112 
168 
280 
39* 
504 


4.82+ 


.03214^'^ 
.01875^' 

.0143^' 

.0107 ^^' 

.00Q18F' 

.  00833 '^^ 


15 

12. 05 
9.04 
8.04 

7-23| 
6.89 
6.70 


20 


25 


17.68 

12.32 

10.54 

9. II 

8.49 
8.16 


30      40 


24.91 
16.54 
13.75 
11.52 
10.56 
10.03 


33-75156.25 
2i.7o'34  82 
17.68:27.69 
14.46121.96 

13.09119.51 
12.32  18.15 


For  resistances  and  formuloe  per  long  »»». '"^'' "  f*'/™'" 
Weight  of  cars  talcen  at  .5  long  tons,  56,000  lbs.  each,  loaded. 

Any  of  the  formnl.  compared  on  the  following  page  P- P'-''""^;^^^,*;^.  ^^^ 
e,cept^  Mr.  CHanu.e.  '—  trfJX^X^T^^::^^^  Xh 
feToc'L  tr^^jr:^  Z  r  UiL,  glve^he  res.ta„ce  of  freight  trains  a.  high 
velocities  at  only  Hi  to  M  as  much  per  ton  as  passenger  Uains. 


CHAP.   Xin.— TRAIN  RESISTANCE— HIGH  SPEED.        525 


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^26       CHAP.   XIIL^TRAIN  RESISTANCE— HIGH  SPEED. 

in  other  words,  it  attaches  no  weight  whatever  to  atmospheric  resistance 
and  the  form  of  the  train.  The  writer's  experiments  (Fig,  163)  indicate 
positively  that  this  is  more  nearly  true  than  is  generally  suspected,  but  in 
going  to  such  an  extreme  the  formula  is  unquestionably  defective.  It 
would  seem  also  to  be  theoretically  defective — or  if  not  that,  certainly  to 
go  a  long  way  beyond  experimental  authority — in  multiplying  one  im- 
portant term  of  the  equation  by  the  square  of  the  weight  of  engine.  No 
theoretical  justification  for  this  is  apparent.  The  constant  for  rolling- 
friction,  4.8  lbs.  per  ton,  is  also  a  little  too  high  for  loaded  trains, 
although  fair  for  a  mean  between  loaded  and  empty. 

But  with  all  these  minor  imperfections  the  formula  is  certainly  one  of 
wonderfully  exact  application  to  a  wide  range  of  trains,  from  an  engine 
running  light  to  the  longest  freight  trains,  and  at  all  speeds.  The  writer 
maybe  overmuch  disposed  to  look  on  it  with  favor,  since,  as  examination 
of  Fig.  165,  Appendix  A,  and  Table  165  will  show,  it  could  hardly  agree 
better  with  all  the  conclusions  of  his  own  tests,  made  in  1879,  had  it  been 
based  on  them  alone;  yet  the  comparison  given  in  and  below  Table  166 
with  the  formulae  given  by  Mr.  O.  Chanute  in  Haswell's  "  Engineer's 
Pocket-Book"  shows  that  it  compares  equally  well  with  some  other 
modern  formulae.* 

A  variety  of  further  evidence  as  to  the  absolute  amount  of  train  re- 
sistance at  high  speed  is  given  below  : 

659i  The  tests  of  Mr.  J.  W.  Hill  on  an  American  freight  train  at  slow 
■speeds,  given  in  Tables  146-7  and  Fig.  115,  check  very  closely  with  the  formula. 
Mr.  Hill's  tests  were  on  a  freight  train  weighing  782.94  tons  in  all,  with  an  engine 
and  tender  weighing  55.72  tons.  The  observed  and  computed  resistances  com- 
pare as  follows: 

Resistance  in  Lbs,  Per  Ton, 
Velocity  in  Miles 
Per  Hour. 
17.23 

22.67 

23.00 

The  observed  resistances  should  be  reduced  5  to  10  per  cent  for  the  internal 
friction  of  the  locomotive.  They  indicate  that  the  formula  is  substantially  cor- 
rect at  slow  speeds,  but  increases  too  fast  with  speed. 

660.  Mr.  Stroudley's  tests  on  a  train  weighing  335.7  tons  of  2240 lbs.  gross, 

*The  examples  of  the  application  of  these  formulae  to  various  trains  given 
in  the  above  *'  Pocket-Book"  contain  some  serious  errors  which  are  liable  to 
deceive. 


CHAP.   XIII.— TRAIN  RESISTANCE— HIGH  SPEED.        527 


Observed. 

Computed. 

7.57 

6.97 

7.27 

8.54 

7.55 

8.66 

'With  an  engine  and  tender  weighing  60.05  tons  of  2240  lbs.  (Fig.  114)  should,  ac- 
cording to  Mr.  Searle's  formula,  have  had  the  following  resistance: 

-^  =  5-4  +  .012445  r« 

=  5'^  +  83:3i- 

For  40  miles  per  hour  this  gives  25.3  lbs.  per  ton,  which  amounts  to  906 
horse-power,  whereas  the  average  horse-power  is  recorded  as  only  529  horse- 
power, and  the  maximum  shown  by  any  diagram  was  668;  but  then  the  draw- 
bar traction  on  the  same  train  is  given  as  an  average  of  4477  lbs.,  which  at  the 
average  speed  of  44.3  miles  per  hour  foots  up  528  horse-power  (13.36  lbs,  aver- 
age traction)  transmitted  through  the  draw-bar  to  the  train  alone,  excluding  all 
engine  and  head  resistance.  If  the  latter  bore  anything  like  the  ratio  to  the 
car  resistance  that  it  does  in  Fig.  165,  the  total  resistance  should  have  been 
fully  up  to  what  Mr.  Searle's  formula  gives. 

661t  The  Engineer  (April  4,  1884)  states  it  to  be  a  figure  "accepted  by  lo- 
comotive superintendents,"  that  with  a  total  train-load  of  336  long  tons  the  train 
resistance  at  60  miles  per  hour  is  40  lbs.  per  ton,  which  corresponds  closely  to 
Table  131. 

662i  In  a  French  paper  on  the  subject  of  train  resistance  and  economy  of 
grades*  we  have  the  following  formulae  given,  which  appear  to  have  been  deduced 
from  very  carefully  made  tests  : 

**  The  resistance  of  an  engine  and  tender  is  given  by  the  formula 

'       1000    '     \20  / 

in  which 

E  =  Indicated  tractive  force  in  kilogrammes, 
R  =  Resistance  per  tonne  in  kilogrammes, 
V=  Velocity  in  kilometres  per  hour. 
*'  For  the  train  hauled  we  have 

R  =  2  +  — ." 

40 

For  a  speed  of  80  kilos,  per  hour,  which  is  very  nearly  50  miles  per  hour, 
and  calling  2  lbs.  per  ton  =  i  kilo,  per  tonne,  as  it  is  almost  exactly,  we  have 
from  this  formula  for  the  train  tested  by  Mr.  Dudley  (Tables  146-7) : 

Per  Ton.  Total. 

For  engine  resistance 60  lbs.  3,780  lbs. 

For  train  resistance 8   *'  2,000   " 

Total  (for  313  tons) 18.5  lbs.         5,780  lbs. 

*  "Notice  sur  les  Prix  de  Revient  de  la  Traction,  et  sur  les  Economies  reali- 
s6es  par  I'Application  de  Diverses  Modifications  aux  Machines  Locomotives. 
Par  M.  Ricour,  Ing6nieur  en  Chef  des  Fonts  et  Chaussees,"  Annales  des  P.  et 
■C.,  Sept.,  18S5. 


< 


528        CHAP.   XIIL— TRAIN  RESISTANCE— HIGH  SPEED. 

This  corresponds  very  closely  to  what  we  have  just  deduced  (Table  164)' 
from  Mr.  Dudley's  tests. 

663i  Another  French  formula,  based  on  the  experiments  referred  to  beneath 
Figs.  164-165,  gives  still  lower  results,  indicating,  at  50  miles  per  hour, 

For  engine,  tender,  and  rear  car 31.0  lbs.  per  ton. 

For  interposed  cars  ... .   7.1  "  ** 

It  is  stated  in  the  same  paper  that  at  about  18.6  miles  per  hour  the  resist- 
ance is  double,  and  at  31  miles  per  hour  triple,  what  it  is  at  6  to  9  miles,  and 
that  "at  still  higher  velocities  the  increase  is  rapid."  This  is  far  from  true 
for  American  rolling-stock,  and  probably  for  any  other,  up  to  30  or  40  miles 
per  hour,  and  the  exact  figures  given  may  be  rejected  as  untenable,  except  that 
they  may  serve  as  cumulative  evidence  that  the  resistances  at  high  speeds  are 
not  so  great  as  many  formulae,  including  those  of  Table  i66,  give  them,  at  least 
for  European  trains  under  favorable  conditions. 

664.  A  test  was  made  in  1884,  upon  the  Bound  Brook  route,  between  Phila- 
delphia and  New  York,  to  ascertain  the  difference  in  the  consumption  of  coal 
between  an  express  train  running  on  schedule  time  and  the  same  train  run  at 
a  very  low  speed,  but  otherwise  under  the  same  conditions,  the  same  five  cars 
and  precisely  similar  engines  being  used.  The  trains  ran  in  each  case  from 
Philadelphia  to  Bound  Brook  and  back,  a  distance  of  119  miles.  The  slow  trip 
was  made  in  9  hours  and  23  minutes,  4420  lbs.  of  coal  being  consumed.  The 
train  stopped  at  the  same  places  as  the  regular  express  trains,  the  only  unusual 
feature  of  the  trip  being  the  funereal  pace,  averaging  a  little  over  12^  miles  an- 
hour. 

The  performances  compared  as  follows  : 


Speed. 
Slow  trip 12^  m.  per  h. 

Fast  trip 50±  ••     " 


Coal  burned. 
4,420  lbs. 

6.725   " 


Difference. . .     37^  m.  per  h.     2,305  lbs.  =  34.2  per  cent  saved. 

The  engine  and  tender  weighed  75  tons,  and  the  five  cars  126  tons. 

According  to  D.  K.  Clark's  formula,  R  = f-  8  (for  gross  tons),  the  com- 
parative resistances  at  these  speeds  should  have  been  about  31  to  13^  lbs,,  or 
more  than  double,  and  this  gives  a  much  less  rapid  increase  with  speed  than 
most  modern  formulae.  (See  Fig.  163.)  By  Table  166  the  difference  should 
have  been  more  than  three  to  one.  This  appears  to  indicate  very  low  velocity 
resistances.  Coal  consumption,  however,  is  but  a  very  vague  guide  to  train  re- 
sistance, it  being  quite  certain  that  the  power  is  developed  more  economically 
at  the  higher  speeds.  Still  this  test  certainly  tends  to  show  that  the  resistances 
due  to  speed  are  not  as  great  as  supposed,  as  do  also  the  facts  presented  be- 
neath, Table  164,  Figs.  164,  165,  and  the  tests  already  referred  to  (par.  444)  as- 


CHAP.   XIII.— TRAIN  RESISTANCE— HIGH  SPEED.        529 


made  on  the  Lake  Shore  &  Michigan  Southern  Railway  {Transactions  Am.  Soe. 
C.  £.,  Oct.,  1876,  p.  344,  ♦•  Experiments  and  Tests,"  by  P.  H.  Dudley),  in  which 
tests  the  conclusions  reached  were  expressed  as  follows  : 

"  We  found  that,  with  the  long  and  heavy  trains  of  650  to  700  tons  it  re- 
quired less  fuel  with  the  same  engine  (Mogul)  to  run  trains  at  18  to  20  miles 
per  hour  than  it  did  at  10  or  12  miles  per  hour.  The  engine  at  the  highest 
rate  of  speed,  seems  to  produce  its  power  more  economically." 

Table  167. 
Speed  of  the  Fastest  Trains  in  England  and  America. 

[From  Mr.  E.  B.  Dorsey's  paper  on  "  English  and  American  Railroads  Compared,"  Trans. 

American  Soc.  C.  E.,  1885-6.] 

English  Railways. 


LiNB. 

Termini. 

Miles. 

Time, 

including 

Stops. 

Average 

Speed, 

incl.  Stops. 

London&N.  W 

London  to  Liverpool 

'*         Glasgow 

"         Edinburgh... 

"         Holyhead 

"         Glasgow 

"         York 

201.75 
406 
401 
264 

444 
188.25 

397 
216 

118.5 

50 
76.5 
125 

h.    m. 

4    30 

10    00 

9    55 

6    40 

10    20 

3     55 
9    00 
6    00 
2    36 

1  05 
»     47 

2  30 

M                       •« 

44-8 
40.6 

«l                       tt 

it                        <( 

40.4 
39-6 

Great  Northern 

it 

43 
48.1 

«• 

'♦          Edinburgh  . . . 
"         Swansea 

Bristol 

"         Brighton 

Dover 

*•         Nottingham  . . 

Great  Western 

44* 

36 

45.6 

46.  IS 
42.6 

u 

London,  Br.  &  S.  Coast 

London,  Ch.  &  D 

Midland 

50 

American  Railways. 


N.  Y.,  N.  H.  &H. 
Pennsylvania 


it 
tt 


N.  Y.  Central  &  H.  R. 
tt  it 


Central  of  New  Jersey . 
Baltimore  &  Ohio 


New  York  to  Boston . , 
Jersey  City  to  Phila.. 

"  Pittsburg 

"  Chicago. 

New  York  to  Albany  . . 

"  Buffalo.. 

**  Chicago. 

Jersey  City  to  Phila.... 
Baltimore  to  Washington 


6  00 

1  59 
"  45 
25  15 

3  30 

II  00 

25  30 

2  00 

o  45 


39 
44-9 
37-7 
36.x 

40.9 
40.1 

38.4 

45 

53-33 


These  runs  are  in  every  case/rom  terminus  tc  *ermtnus,  which  makes  a  difference  of 
5  to  8  miles  an  hour  from  the  speed  obtained  by  selecting  only  the  most  favorable  parts 
of  the  run.     See  summary  on  following  page. 

34 


Va 


lltl 


530        CHAP.    XIIL— TRAIN  RESISTANCE— HIGH  SPEED. 


The  aggregates  of  the  preceding  tables  compare  as  follows : 

12  English  trains,  averaging  240^  miles  run  at  43.33  miles  per  hour. 
9  American     "  "  374V6      "  "     41.71     "  " 

Or,  omitting  the  two  long  runs  of  over  900  miles  from  Chicago  to  New  York : 

7  American  trains,  averaging  214  miles  run  at  42.90  miles  per  hour. 

While  this  table  correctly  indicates  that  the  fastest  trains  in  England  and  America 
make  substantially  the  same  time,  the  average  speed  of  all  trains  is  undoubtedly  consider- 
ably higher  in  England,  owing  chiefly  to  the  fact  that  there  are  almost  no  grade  crossings 
or  highway  crossings,  and  in  part  to  the  shorter  runs,  which  always  justify  and  require 
higher  speed  for  equal  convenience. 


665.  According  to  Table  165,  the  difference  in  the  horse-power  demanded 
to  overcome  the  engine  resistances  only  in  the  Bound  Brook  lest  just  mentioned 
would  have  been: 


Trip.  Time  V  Horse-power. 

Slow 9.4  hours  X      5  H.  P 

Fast,     ....     2.4  hours  X  271.7  H.  P.    =  652 


"  Hour  Horse-powers." 
=     47 


Total  difference  in  head  resistance, 


605 


The  total  difference  in  coal  consumption  being  2305  lbs.,  we  have 


2305 
605 


3.62  lbs.  as  the  coal  burned  per  horse  power  per  hour,  without  making  any 
allowance  for  the  increased  car  resistance  due  to  speed  on  the  one  hand,  or  for 
the  greater  economy  with  which  steam  is  used  at  high  speed  on  the  other  hand. 
As  3.62  lbs.  is  about  a  fair  rate  of  coal  consumption  under  the  circumstances 
(rather  high),  these  two  latter  may  have  approximately  balanced  each  other. 

666.  Table  167  shows  the  fastest  regular  trains  in  England  and  America, 
every  train  on  the  list  probably  reaching  a  speed  of  60  miles  per  hour  on  short 
stretches  of  almost  every  run.  The  fastest  trains  do  not  haul  over  125  tons  to 
train,  but  even  then  they  could  not  probably  make  the  lime  they  do  if  the 
resistances  were  quite  as  high  as  in  Table  166.  When  all  proper  allowances 
are  made,  however,  the  facts  do  not  necessarily  imply  any  materially  lower 
resistance. 

ENGINE-FRICTION. 

667.  In  computing  train  resistance  it  is  not  essential  to  assume  any 
diflerent  rolling-friction  for  the  engine  than  for  the  cars.  The  tender- 
friction  should  of  course  be  the  same,  and  the  engine  truck  friction  sub- 
stantially the  same,  while  for  the  driving-wheel  base  we  have  only  to 


CHAP.   XIII.— TRAIN  RESISTANCE— ENGINE. 


531 


consider  the  rolling-friction  between  wheel  and  rail  only,  and  not  the 
journal  friction,  since  the  latter  does  not  tax  the  adhesion  (par.  608). 
The  same  is  true  of  all  the  internal  machinery-friction  of  every  nature 
.and  kind  ;  so  that,  as  we  have  plenty  of  steam-power  in  freight  service,  or 
can  have  by  reducing  the  speed,  and  only  lack  tractive  force  in  pounds, 
the  machinery  and  driving-journal  friction  is  of  slight  importance  for 
freight  service,  whether  much  or  little.  For  passenger  service  it  may  be 
•of  more  importance,  and  it  will  at  least  be  profitable  to  summarize  the 
•evidence  as  to  its  amount. 

668.  The  locomotive  is  a  simple  machine,  and  the  evidence  does  not 
make  it  probable  that  more  than  5  to  8  per  cent  of  its  indicated  power 
fails  to  reach  the  periphery  of  the  drivers.  Ten  per  cent  is  often  allowed. 
In  complicated  low-pressure  compound  engines  the  machinery-friction  is 
flo  to  15  per  cent.  In  small  stationary  engines  (Table  168)  the  loss 
/ranges  from  12  to  20  per  cent. 

In  16x24  American  locomotives,  the  tests  of  John  W.  Hill  (Tables 
146-7)  show  that  some  13  lbs.  per  ton  of  locomotive  and  tender  was  act- 
ually required  to  propel  it  without  load  at  speeds  of  17  to  23  miles  per 

Table  168. 
Estimated  Cost  of  Power  and  Efficiency  of  Stationary  Engines. 

[[Abstracted  from  a  careful  and  detailed  paper  by  Charles  E.  Emery,  Ph.D.,  M.  Am.  So.  C.  E., 

Trans.  Am.  So.  C.  E.,  November,  1883.] 


H.P. 

Kind. 

Cost  in 

Mass. 
1874. 

Loss 
per 
cent  by 
Fric- 
tion. 

Indi- 
cated 
H.  P. 

Feed- 
Water, 

per 
I  H.P. 

Coal 

I.  ffV. 

Evap. 

per  lb 

Coal. 

Cost 

309 

days. 

5 

Portable  Upright 

S645 

20 

6.25 

42 

5.60 

7-5 

$176.46 

lo 

M                              »l 

988 

20 

12.50 

38 

5- 10 

7-5 

109.96 

«5 

ii                              it 

1,487 

18 

18.29 

36 

4.80 

7-5 

90.14 

ao 

"         Horizontal... 

1,981 

15 

23 -53 

34 

425 

8. 

7328 

as 

ti                  tt 

2.441 

14 

29.07 

32 

4.00 

8. 

67.28 

50 

Stationary  Non-cond'g. 

5,331 

12 

56.8a 

27 

327 

8.25 

52.15 

100 

Condensing  Single 

9,207 

II 

112.36 

23 

2.61 

8.8 

36.02 

200 

(i              It 

16,785 

10 

220.99 

22.2 

2.52 

8.8 

28.64 

300 

ti             tt 

23,899 

9-5 

331-49 

22.2 

2.52 

8.8 

2682 

400 

It              ti 

29,958 

9-5 

441-99 

22.2 

2.52 

8.8 

26.01 

500 

it              it 

36,220 

9-5 

SS-?- 49 

22.2 

2.52 

8  8 

25.66 

This  table  is  carried  out  in  the  paper  in  much  more  detail,  but  the  above  are  the  most 
important  data. 


532 


CHAP.  XIII, —  TRAIN  RESISTANCE— ENGINE. 


hour,  whereas  the  average  resistance  of  the  train  behind  it,  at  the  same 
speeds,  was  only  some  6f  lbs.  per  ton.  Assuming  that,  owing  to  the 
greater  weight  on  the  locomotive  drivers,  the  rolling-friction  proper,  be- 
tween rail  and  wheel,  was  at  least  as  much  as  the  rolling  and  axle  fric- 
tion combined  of  the  train  behind  it,  we  may  divide  up  this  i8  lbs.  ap- 
proximately as  follows : 

Lbs.  Per  Ton.    Total  Lbs. 
Taxing  adhesion : 'RoWxn^-ix'xcxXon 7  3^2 

"  "  Head  and  oscillatory  resistance,     .     .      2  1 1.2. 

Not  taxing  adhesion :  Friction  of  engine  running  light,      4  224 

"  "  Assumed  addition  due  to  load,    .      5.  280 


Total, 18  1,008 

Actual  average  tractive  pull  (nearly  |  load  on  drivers),     .     .     .     6,250 
Maximum  tractive  pull  in  ordinary  work  (i  weight  on  drivers),    11,200 

This  would  indicate  that  when  the  engine  is  working  fairly  hard  the 
internal  friction  consumes  about  9  per  cent  of  the  indicated  power,  but  it 
is  almost  certainly  too  high.  When  an  engine  is  working  light  and  run- 
ning fast  a  much  larger  proportion  of  the  energy  developed,  up  to 
nearly  \,  would  appear  to  be  used  up  by  internal  friction,  and  no  doubt 
is — a  waste  well  worthy  of  attention,  but  not  of  that  ruinously  injurious 
character  that  an  equal  tax  on  the  adhesion  would  be. 

669.  The  friction  ok  the  slide-valve  is  one  of  the  chief  sources  of  loss 
by  machinery-friction;  but  by  the  rapid  introduction  of  "  balanced  "  slide-valves, 
or  those  which  have  the  pressure  excluded  or  counteracted  on  the  top  side  of 
the  slide-valve,  this  loss  is  being  largely  eliminated.  The  slide-valve  exposes  an 
area  of  from  70  to  100  sq.  in.,  averaging  perhaps  90  sq.  in.,  to  the  steam-pres- 
sure in  the  steam-chest,  which  may  be  taken  to  average  at  least  100  lbs.  per  sq. 
in.,  giving  some  9000  lbs.  pressure.  With  good  lubrication  this  pressure  would 
create  no  great  amount  of  friction,  but  with  the  imperfect  lubrication  which 
alone  is  possible,  it  is  far  more  serious.  The  coefficient  is  probably  in  the 
neighborhood  of  o.i  to  0.2  in  ordinary  working,  causing  a  resistance  to  motion^ 
in  both  steam-chests,  of  900  to  1800  lbs.  With  sin.  travel  of  valve  and  50-in. 
drivers  the  slide-valve  travels  about  ^V  as  far  as  the  engine,  which  would  make 


this  loss  equivalent  to 


900  to  1800 
16 


=  say,  55  to  no  lbs.  of  tractive  resistance,. 


amounting  to  something  like  i  per  cent  of  the  ordinary  work  done,  which  in 
starting  is  no  doubt  often  much  more. 

Direct  experiments  on  the  Boston  &  Albany  road  gave  a  resistance  to- 
motion  of  2100  lbs.  in  starting  under  the  worst  conditions — full  stroke  with 
throttle  wide  open;  while  with  the  Richardson  balanced  slide-valve,  which  is 
one  of  the  most  approved,  325  lbs.  sufficed.     When  once  in  motion  it  is  prob- 


CHAP,   XIII— TRAIN  RESISTANCE— ENGINE. 


533 


able  that  the  contrast  is  much  less  striking,  but  the  saving  in  wear  as  well  as 
resistance  is  so  great  that  balanced  slide-valves  promise  to  be  soon  practically 
universal. 

670.  Otherwise  than  this  it  is  difficult  to  account  for  any  great  loss  by  fric- 
tion at  any  one  part  of  the  machinery.  Therefore,  since  no  difficulty  is  found 
in  obtaining  correspondingly  favorable  results  with  stationary  engines  of  equal 
power  and  more  complication,  we  may  conclude  with  some  certainty  that  5  to  8 
per  cent  of  the  indicated  power  represents  the  full  extent  of  the  loss  by  ma- 
chinery.friction  proper,  in  ordinary  cases. 

671.  Tests  at  the  works  of  Messrs.  Schneider  &  Co.,  Creusot,  reported  by 
Mr.  M.  F.  Delafield  in  a  notable  paper  published  in  the  Annales  des  Mines  (and 
most  other  scientific  journals  of  the  world),  1885.  made  on  a  22  X  44  in.  Corliss 
engine,  which  could  be  worked  either  condensing  or  non-condensing,  gave  the 
following  relation  of  indicated  and  effective  power: 

Condensing  engines,  effective  H.  P.  =  .902  I.  H.  P.  —  16 
Non-condensing  "  "  '•       =  .^45  i.  h.  P.  -  12 

This,  however,  is  not  known  to  apply  correctly  to  other  than  engines  ap- 
proximately  similar  to  that  tested,  which  developed  140  to  250  H.  P.  with  about 
60  revolutions  per  minute,  according  as  it  was  condensing  or  non-condensing. 

672.  Tests  purporting  to  give  very  high  or  low  engine  friction  must  be 
looked  on  with  extreme  scepticism.  There  is  especial  danger  of  error  in  inter- 
preting  the  apparent  results  of  such  tests  Thus,  tests  of  an  apparently  very 
accurate  character  by  the  Locomotive  Superintendent  of  the  Eastern  Railway 
■of  France*  show  that  of  the  total  indicated  horse-power  only  42.5  and  41.6  per 
cent  was  delivered  to  the  draw-bar,  in  two  successive  tests,  out  of  which  it  was 
assumed  that  34.2  and  35.6  per  cent  was  consumed  by  the  bare  friction  of  the 
engine  mechanism,  after  deducing  the  assumed  resistance  of  the  engine  and 
tender  considered  as  vehicles.  The  error  lay  in  an  insufficient  allowance  for 
the  latter,  and  especially  in  an  insufficient  allowance  for  head  resistance,  which 
at  high  passenger  speeds,  such  as  that  of  the  tests,  consumes  a  large  part  of  the 
power. 

673.  An  investigation  by  the  writer  given  in  par.  128  shows  that  20  lbs.  X 
^5  lbs.  per  car  gives  the  ordinary  consumption  in  passenger  service;  indicat- 
ing a  very  small  loss  by  internal  friction. 

674.  To  get  at  the  collective  resistance  of  the  bearings  of  a  locomotive 
under  steam,  and  to  separate  it  into  its  constituent  elements.  Messrs.  VuiUemin, 
Guebhard.  and  Dieudonn6  made  some  experiments,  narrated  in  a  work  by  Josef 
<jrossmann,f  showing  the  following  results: 

*  Engineen'ttg  Sitxd.  Engineer,  18S5. 

t  "  Die  Schmiermitiel  und  Lagermetalle  fttr  Locomotiven,  Eisenbahnwagen 
Sch.flfsmachinen,  etc."    Von  Josef  Grossmann,  Ingenieur  der  osterreichischeii 
Nordwestbahn.     Wiesbaden,  C.  W.  Kreidels'  Verlag.  1S85. 


534 


CHAP.    XIIJ.— TRAIN  RESISTANCE— ENGINE. 


, Pounds  Per  Net  Ton. , 

Non-coupled        4-coupled        6-coupled 
^   ^   ,         .                                   ,  ,                .  pass.  enRines.       engines.  engines, 

lotal  resistance  per  ton  of  locomotive 16.0  25.2  3044 

Resistance  of  cold  engine  (connecting-rod 

removed) 6.0  10.44  12.30 

Percentage  of  latter  to  total  resistance 375  p.  c.      41.5  p.  c.     40.5  p.  a 

These  figures  are  for  speeds  of  17  to  21  miles  per  hour. 

If  now  the  collective  resistance  of  the  axle  and  parallel  rod  bearings  and  of 
the  valve-gear  be  deducted  from  the  resistance  of  the  cold  engine,  as  above 
given,  the  remainder  ought  to  give  the  resistance  due  to  rolling-friction;  and  if 
this  be  deducted  from  the  total  resistance  of  the  above  table,  the  remainder 
should  be,  approximately,  the  total  resistance  of  all  bearings  in  the  engine  at 
work. 

The  axle-friction  coefficient  was  assumed  at  0.009  and  the  proportion  of  the 
diameter  of  axle-journal  to  that  of  the  wheels  at  y^,  giving  for  the  axle-friction- 
li  lbs.  per  ton  weight  of  engine.  The  friction  of  the  valve-gear  of  the  cold 
engine  was  taken  as  i  lb.  per  ton  of  engine,  and  the  crank  pin  friction  for  four- 
coupled  engines  at  02  lb.  and  for  six  coupled  engines  at  0.4  lb.  per  engine  ton. 
Adding  together  these  resistances,  and  deducting  them  from  the  resistances 
of  the  cold  engines  without  connecting-rods,  the  following  table  was  obtained. 

' Pounds  Per  Net  Ton. » 

Non -coupled  4-coupled  6-coupled 

pass,  engines.         engines.  engines. 

Total  resistances  per  ton  of  locomotive,  as 

*^ove     .  16.0  25.2  30.44 

Resistance  of  rolling-friction  per  ton  of  lo- 

^^o'^o^'^e 3.50  7.74              9.40 

Percentage  of  last  to  the  total 21.87  30. 71  p.  c.  30  88  p.  c. 

Resistance  of  oiled  parts  (in  steam)  per  ton 

oflocomoiive 12.50  17.46  21.04 

Percentage  of  last  to  the  total 78.13  69.29  p.  c.  69. 12  p.  c. 

These  figures  were  assumed  to  show  how  large  a  portion  of  the  engine  re- 
sistances those  of  the  oiled  parts  constitute,  which  do  not  tax  adhesion. 

The  experimental  evidence  as  to  the  comparative  rolling  and  internal  fric- 
tion of  coupled  and  uncoupled  engines  is  interesting  and  possibly  correct,  but 
the  exact  figures  given,  as  with  all  such  single  statements,  must  be  received 
with  much  allowance. 

With  regard  to  the  increased  amounts  of  rolling  friction  indicated  for  four- 
and  six-coupled  engines,  the  author  reasonably  remarks  that  it  is  in  accordance 
with  what  might  be  expected,  since  the  coupled  wheels,  on  account  of  their 
slight  difference  of  form  and  of  imperfections  in  the  track,  cannot  roll  as  per- 
fectly as  the  uncoupled  ones,  and  must  slip  more  or  less. 


CHAP.    XIII.— TRAIN  RESISTANCE— ENGINE. 


535 


675.  The  following  record  of  some  other  French  tests  gives  very  different 
results  :  * 

For  determining  engine  resistance,  the  locomotive  to  be  tested  was  set  in 
motion  at  4  or  5  miles  per  hour,  and  change  of  velocity  determined  by  accurate 
apparatus,  from  which  the  following  resistances  were  computed: 

, Pounds  Per  Ton  of  Resistance. , 

Passenger  engine,       Locomotive  tor  mixed      Freight  engine, 
3  axles,  2-coupled,    service,  3-coupled  axles,    4-coupled  axles, 
78-in  drivers,  59-'n-  drivers,  50-in.  drivers, 

52  tonnes.  48  tonnes.  70  tonnes. 

Engine  in  working  order. ..  6.4  7.2  8.0 
Eccentrics  and  connecting- 
rod  disconnected 4.7                               4.5                           6.2 

Difference  1.7  2.7  1.8 

Coupling-rods  also  discon- 
nected   4.7  4.4  6.2 

In  all  these  tests  the  effect  of  disconnecting  the  coupling-rods  is  inappreci- 
able. The  tender  resistance  was  found  to  be  only  5.0  to  5.6  lbs.  per  ton.  All 
the  above  are  the  mean  of  a  number  of  tests,  not  differing  greatly  in  result. 
The  following  are  from  still  larger  averages: 

/ Resistance  in  Pounds  Per  Ton. « 

Drivers.       No.  axles     Coned  tread.  Cylindrical  tread. 

coppled.  Link-  Link-  Walchaert*s 

motion.  motion.  valve-gear. 

Passenger  engine..  78"  2  6.2  ..  5.2 

Mixed  engine 59"  3  7.2  7.2  ... 

Freight  engine 51!"  3  9.4 

Freight  engine 50"  4  ...  ...  8.2 

The  tests  measured  the  resistances  between  velocities  of  2\  to  5  miles  per 
hour.  The  resistances  include  machinery-friction,  and  the  very  low  speed 
would  tend  to  make  the  resistances  considerably  higher  than  at  working  speeds, 
notwithstanding  which  fact  it  would  appear  as  if  the  results  must  certainly  be 
too  low. 


*  "  Application  de  la  M6thode  rationale  aux  Etudes  dynamom6triques.  Par 
M.  Desdouits,  Ing6nieur  de  la  Marine,  adjoint  a  I'lng^nieur  en  Chef  du  Materiel 
et  de  la  Traction  des  Chemins  de  Fer  de  I'Etat,"  Annates  des  Ponts  et  Chaussees^ 
Mai,  1886. 


536 


CHAP,    XIV.^EFFECT  OF  GRADES  ON   TRAINLOAD, 


til 


CHAPTER  XIV. 

THE    EFFECT    OF    GRADES    ON    TRAIN-LOAD. 

676.  The  absolute  effect  of  gradients  to  increase  the  load  on  the  engine 
IS  constant  and  easily  determined.  Under  the  theory  of  the  inclfned 
plane  (or  rather  under  the  general  theory  of  the  equilibrium  of  forces) 
any  body  W,  F.g.  167,  resting  on  such  an  inclined  plane,  is  acted  on  by  at 


Fig.  167. 


least  two  forces :  the  force  of  gravity,  vertically  downward  ;  and  the  re- 
action of  the  supporting  plane  s,  acting  at  right  angles  thereto 

Since  a  body  acted  on  by  two  forces  only  cannot  remain  at  rest  (see 
any  treatise  on  n.echanics)  unless  the  forces  are  (,)  equal  in  magnitude. 
(2)  opposite  in  direction  to  each  other,  and  (3)  lie  in  the  same  riiht  line 
motion  must  ensue  under  these  conditions  down  the  plane  .;  and  the  force 
/necessary  to  resist  motion  (or  impelling  the  body  down  the  plane,  if  equi- 
wilTffi  T  7'""*t'"'''.>  '^  represented  by  the  length  of  any  line  /,  which 
will  suffice  to  close  the  triangle  of  forces.  The  direction  of  this  force  is 
ordinanly  fixed  by  the  conditions,  and  in  the  case  we  are  now  considlrLg 
It  must  he  parallel  with  the  plane  s.  as  represented  in  the  cut ;  but  a  force 


Fig.  168. 


CHAP.    XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD.      53/ 

acting  in  any  other  direction,  as/7",  Fig.  i68,  will  suffice  for  the  same 
end,  provided  it  will   form  with  the  forces  g  and  w'. 
Fig.  167,  a  closed  triangle ;  the  magnitude  only  of  the 
force  /  required  varying  thereby. 

677.  If  the  body  W,  Fig.  167,  be  an  angular  body,  this 
necessary  force  /  will  be  supplied  by  the  friction  of  con- 
tact between  the  body  and  the  plane,  and  the  body  will 
remain  at  rest  until  the  angle  becomes  very  considerable, 
as  in  sliding  a  brick  down  a  board.  If  the  body  be  a 
wheeled  vehicle,  the  journal  and  other  rolling-friction 
subserves  the  same  purpose,  so  far  as  it  goes,  as  respects 
motion  down  the  plane ;  but  since  the  rolling-friction  is 
a  very  small  portion  of  the  total  weight  of  the  body,  the  angle  of  the 
slope  on  which  the  rolling-friction  alone  will  suffice  to  maintain  equi- 
librium must  be  very  small.  When  it  does  not  suffice  for  this  purpose, 
the  body  is  impelled  down  the  plane  by  the  difference  between  the  force  / 
of  gravity  and  the  retarding  force  of  friction. 

When  a  body  is  caused  to  move  up  the  plane  it  is  obvious  that  the 
resisting  friction,  whether  much  or  little,  plays  no  part  in  reducing  the 
iorce  /,  tending  to  cause  the  body  to  move  down  the  plane ;  for  in  that 
case  the  two  forces  resisting  motion  coincide  with  each  other  in  direction, 
and  their  sum  instead  of  their  difference  has  to  be  overcome  by  the  im- 
pelling force,  whatever  it  may  be. 

678.  These  are  the  conditions  under  which  the  locomotive  acts  in 
hauling  a  train  up  a  grade ;  and  in  Fig.  167,  if  ^  be  made  to  represent  the 
^weight  of  any  vehicle  W  or  of  all  the  vehicles,  W  will  represent  the 
•force  with  which  they  press  against  the  rails ;  /,  the  "grade  resistance"  or 

■force  impelling  them   downward,   or   resisting    motion  upward ;  — ,  the 

,     .             ,           .                       ,           -   ,          2000/         2240/  ,. 

ratio  of  the  grade  resistance  to  the  weight ;  • or ,  according 

g  g 

to  the  number  of  pounds  m  the  ton,  the  grade  resistance  in  pounds  per  ton,' 

iv 

— ,  the  ratio  of  the  reaction  against  the  rails  to  the  actual  weight  of  the 

«body,  which  is  given  numerically,  for  various  grades,  in  Table  119. 

679.  All  grades  are,  in  the  technical  work  of  American  and  Continen- 
tal engineers,  expressed  in  the  rate  per  cent,  although  m  common  American 
practice  the  words  "  per  cent"  are  (somewhat  unfortunately)  omitted,  the 
grades  being  known  as  a  0.5,  0.8,  or  i.o  grade.  A  grade  so  expressed  is 
andependent  of  the  particular  unit  of  measure  employed,  whether  feet, 


.i:i.i 


\    \ 

'r  '  H 


wmtm 


538      CHAP.   XIV.^EFFECT  OF  GRADES  ON   TRAIN-LOAD. 


metres,  miles,  or  any  other.  In  popular  American  and  English  language 
grades  are  expressed  by  feet  per  mile,  which  (since  there  are  5280  feet  in 
a  mile)  is  52.8  times  the  rate  per  cent.  The  use  of  this  awkward  unit, 
especially  among  engineers,  is  in  every  way  to  be  regretted.  Enghsh 
enc^ineers  are  also  much  given  to  a  still  more  awkward  habit-expressing 
grades  as  rising  "  i  in  80,"  or  some  other  horizontal  distance.  (See  par. 
683.)  These  may  be  turned  into  grades  per  cent  with  a  table  of  recipro- 
cals.    In  Fig.  167  the  rate  of  grade  is  given  by  -. 


If   we  let  d  =  100 


(whether  feet  or  any  other  unit),  then  r  will  give,  in  the  same  unit,  the 

rate  per  cent  of  the  grade.  ^ 

680.  Since  gravity.^,  in  the  diagram  of  forces  in  Fig.  167.  is  repre- 
sented by  the  hypothenuse  of  a  right-angled  triangle,  it  follows  that  the 
pressure  of  the  wheels  on  the  rails.  W,  can  never  be  quite  equal  to  the 
weight  of  the  body.  The  loss,  however,  is  not  on  any  ordinary  grade  a 
serious  or  even  an  appreciable  one.     It  may  be  determined  as  follows: 

Ratio  of  pressure  on  rails  to  real  weight  ^^  (Fig.  167)=  j;but^=  ^/d^^rh\. 


exactly.    Or,  approximately  (i), 


7.d 

.y  =  —=  +  a. 
2d 


whence  (2), 

681.  This  latter  is  determined  by  a  rule  of  great  convenience,  which  is  too 
little  known,  and  which  the  student  will  do  well  to  fix  indelibly  in  his  memory, 
for  the  multitudinous  uses  of  which  it  is  capable,  viz. :  .    ,  •  . 

To  SOLVE  A  RIGHT-ANGLED  TRIANGLE  OF  SMALL  ALTITUDE  :  Square  the  hetght 
or  rise  and  divide  by  twice  the  base  or  hypothenuse  (whichever  is  known).  The 
quotient  will  be  the  difference  between  the  base  and  hypothenuse,  whence 
the  unknown  side  is  obtained  from  the  known  by  direct  addition  or  subtrac- 
tion.     Frequently,  however,  in  solving  such  triangles  the  difference   only  is- 

'^"^Exfmples  showing  the  range  of  error  in  this  rule  are  given  in  Table  168^. 
The  extreme  examples  of  the  latter  part  of  the  table  are  intended  only  for  lUus- 
trative  purposes,  but  show  that  even  in  such  an  extreme  case  as  the  *  3.  4.  and 
5  triangle"  the  error  is  only  ^  or  i\  per  cent.  For  a  multitude  of  engineering 
computations,  where  the  altitude  of  the  triangle  is  below  i  the  base,  the  formula 
is  sufficiendy  approximate  for  all  purposes,  the  error  with  base  4  and  altitude 
I  being  less  than  half  of  one  per  cent  and  varying  as  the  square  of  the  alti- 
tude. 


CHAP.   XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD.      539 


Table  I68|, 

Examples  showing  Range  of  Error   in  the  Approximate  Formula  of 
Par.  681  FOR  Solving  Right-angled  Triangles. 


Given— 

Hypothenuse. 

Error 
Per  Cent. 

Base. 

Height. 

By  Approxi- 
mate Rule. 

Exact. 

10 
xo 
10 
to 
so 
zo 
10 

I 
2 
4 
5 
6 
8 
10 

10.05 
10.2 
10.8 
11.25 
II. 8 

13-2 
15.0 

10.049 
10.198 
10.770 
11.180 
11.662 
12.806 
14.142 

O.OI 

0.02 
0.03 

0.6 

1.2 
30 

5-7 

4 
(hyp.) 

5 

3 
3 

5^ 
(base.) 

4^ 

5- 
4- 

^ 

A 

All  these  examples  are  far  beyond  the  range  of  the  highest  rates  of  grade.     For  exam- 
ples of  the  latter,  see  Table  119,  page  341. 


682.  Comparing  the  two  similar  triangles,  drs  and  W'tg,  Fig.  167, 

we  have,  since  r'.dwt:  IV', 

W'r 


/  = 


d 


W  being,  as  we  have  seen,  not  the  true  w^eight  or  gravity  of  the  body,, 
but  the  component  thereof  at  right  angles  to  the  plane,  or  the  force  with 
which  it  presses  against  the  plane. 

On  any  grade  practicable  for  locomotives,  however,  W  and  g  are 
practically  equal  to  each  other,  the  difference  even  on  a  10  per  cent 
grade  being  only  one  half  of  i  per  cent,  and  on  a  i  per  cent  grade  (52.8 
feet  per  mile)  only -r|^  as  much,  or  ^^^  of  i  per  cent.  Therefore  it  is 
universally  customary  to  consider  that  for  all  practical  purposes  r:^:  '.t\g. 
Fig.  167,  whence 

with  suf!icient  exactness,  and  we  have  the  rule  already  given  in  par.  382:. 
The  rati  of  grade  in  ft.  per  100  =  the  grade  resistance  in  lbs.  per  100  Ihs.,^ 
whence,  evidently, 


540      CHAP,   XIV,— EFFECT  OF  GRADES  ON   TRAINLOAD. 


The  grade  resistance  in  lbs.  per  ton  =  the  rate  of  grade  per 
cent  X  20,  or  =  2  lbs.  per  o.i  per  cent. 

This  last  formula  should  likewise  be  indelibly  engraven  on  the  memory 
of  the  engineers  having  to  do  with  railway  work,  making  reference  to  a 
table  needless. 

683.  The  grade  resistance  in  lbs.  per  ton  on  a  grade  given  in  feet  per  mile 

/                                               grade  in  feet  per  mile\ 
is  Isince  the  rate  per  cent  = —- 1 

grade  in  feet  per  mile  grade  in  feet  per  mile 

equal  to  the tt^ X  20  =  *• 


Or,  since 


2.64 


52.80 
=  0.3788,  we  have — 


2.64 


Grade  resistance  in  lbs.  per  ton  =  grade  in  ft.  per  mile  X  0.3788  =  grade  in 
sft.  per  mile  -7-  2.64. 

For  the  long  ton  of  2240  lbs.  we  obtain,  in  the  same  way. 

Grade  resistance  in  lbs.  per  ton  =  grade  in  ft.  per  mile  X  .4242. 

For  a  grade  expressed  in  a  horizontal  distance  for  a  rise  of  i,  as  i  in  80,  i  in  100, 

or  I  in  d,  the  total  grade   resistance  is  — -, ,  or  —  of  the  weight ;  or  in  lbs. 

'  °  80   100        a 

per  ton, or  — —,  for  the  short  and  long  ton  respectively.    This  method  of 

d  d 

expressing  grades  is  used  nowhere  in  the  world  but  by  English  engineers,  and 
has  nothing  to  commend  it. 

684.  From  the  preceding  it  follows  that  the  effect  of  grades  UPON 
THE  grade  resistance  is  directly  as  the  rate  of  grade.  On  a  grade  of 
i.o  per  cent,  the  grade  resistance  is  just  twice  as  much  as  on  a  grade  of 
0.5  ;  and  by  whatever  percentage  the  rate  of  grade  be  reduced  the  grade 
resistance  will  be  reduced  as  much. 

To  determine  the  effect  of  the  grade  resistance  ON  THE  POWER  OF 
engines,  the  rolling-friction,  a  constant  element  per  ton  on  both  grades 
and  levels,  must  first  be  considered,  in  addition  to  the  grade  resistance. 

685.  Assuming,  for  reasons  already  stated  (par.  623),  that  the  rolling- 
friction  at  ordinary  freight  speeds  of,  say,  15  miles  per  hour  is  8  lbs.  per 
ton  (=0.4  per  cent  grade),  which  is  a  high  resistance  to  assume,  and 
much  higher  than  the  ordinary  resistance  of  the  train  behind  the  engine 
only,  the  total  train  resistance,  and  hence  gross  weight  of  trains  on  any 
two  rates  of  grade,  will  be  as  the  rate  of  grade  per  cent  +  0.4,  or  as 

^  +  04 

On  grades  of  0.5  and  i.o  per  cent,  adding  0.4  to  each,  we  have  0.9 and 
a .4  as  the  equivalent  gradient  in  each  case,  including  the  rolling-friction. 


CHAP.   XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD.      54I 

The  gross  weight  of  trains  on  these  grades,  consequently,  will  be  as  0.9: 
1.4  or  I  to  1.556,  and  not  as  0.5  :  1.0  or  i  to  2.00. 

With  grades  of  0.3  and  0.6  per  cent,  we  have  for  the  comparative 
gross  weight  of  trains  0.7:  1.0  or  i  to  1.43,  instead  of  i  to  2.00.  With 
grades  of  1.0  and  2.0  per  cent  we  have,  similarly,  1.4  :  2.4,  or  i  to  1.714  for 
the  comparative  gross  weight ;  whereas  in  this,  as  in  the  two  former  ex- 
amples, the  grade  resistance  only  is  as  i  to  2. 

686.  It  will  be  seen  from  these  examples  that  as  the  grades  are  higher 
the  comparative  gross  weight  of  trains  comes  nearer  and  nearer  to  the 
ratio  of  the  grade  resistance  only,  as  is  but  natural,  since  the  rolling-fric- 
tion becomes  a  less  and  less  important  fraction  of  the  total  resistance. 
Thus,  in  grades  of  2.00  and  3.00  per  cent,  the  comparative  gross  loads  are 
as  2.4 :  3.4  or  2  :  2.833.  But  on  the  lower  gradients  this  is  far  from  beings 
the  case. 

687.  So  far,  we  have  considered  only  the  gross  weight  of  train,  in- 
cluding engine;  but  it  is  apparent  that  the  true  measure  of  the  cost  of 
gradients  is  their  effect  upon  the  net  or  revenue-earning  load 
of  cars  and  freight,  and  the  ratio  of  the  net  loads  on  any  two  gradients^ 
depends  upon  an  additional  variable,  viz.,  the  ratio  of  the  gross  weight 
of  engine  and  tender  (or  rather,  of  engine,  tender,  and  caboose)  to  the  trac- 
tive power  of  the  engine.  Whatever  the  absolute  weight  of  the  engine,  if 
its  ratio  to  the  tractive  power  be  the  same,  the  ratio  of  the  net  loads  will 
be  the  same  on  any  two  given  grades,  whether  the  engine  be  light  or 
heavy. 

For  the  gross  weight  of  train  on  any  given  grade  is  directly  as  the 
tractive  power,  and  if  the  ratio  of  the  weight  of  engine  to  the  tractive- 
power  be  the  same,  the  resulting  net  loads,  as  well  as  gross  loads,  will  be 
to  each  other  directly  as  the  tractive  power. 

688.  The  ratio  of  the  tractive  power  to  the  total  weight  of  engine  is 
not  a  constant,  but  varies, yfrj/,  with  the  pattern  of  engine,  and,  secondly ^ 
with  the  ratio  of  adhesion,  which  is  itself  a  variable  quantity;  but  assum- 
ing the  constant  ratio  of  adhesion  of  ONE  fourth,  which  we  have  seen 
(par.  530)  to  be  that  justified  by  ordinary  American  experience,  the  ratio- 
is  readily  determined  for  any  pattern  of  engine,  and  will  be  seen  from 
the  following  Table  169  to  vary  from  i  to  10^  to  i  to  4,  according  to  the 
pattern  of  engine,  the  ratio  for  the  more  usual  patterns  of  freight  engines 
being  about  i  to  7. 

In  the  former  edition  of  this  treatise  it  was  assumed  as  i  to  10,  the  average 
ratio  of  adhesion  being  taken  at  ^,  but  conditions  have  greatly  changed  since- 
then  (1872-6). 


) 


542      CHAP.   XIV,— EFFECT  OF  GRADES  ON  TRAIN-LOAD, 


CHAP.    XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD.      543 


Table  169. 
Ratio  of  Weight  of  Engine  and  Tender  to  the  Tractive  Power,  for 

Various  Types  of  Engines, 
As  assumed  in  the  headings  of  Table   170,  substantially  in  accordance  with  the  data  of 

Tables  1 27-131. 


Kind  of  Engine. 

Tractive  Power. 

(^  Weight  on 

Drivers.) 

Total  Weight 

of  Engine  and 

Tender 

in  Service. 

Ratio  of  Weight 
to  Tractive  Power. 

T  icrht  American •■••«••■ 

tons. 

5 
6 

7 
8 

9 
10 

II 

12 

13 

tons. 
52 
58 
60 

64 

67 
70 

75 
80 

87 

•  •  •  • 

•  •  •  • 

trac.  power  =  i.o. 
10.4 

A verace  American .*•••••••■ 

9.67 

Light  Ten-wheel   

Averaffp  Ten- wheel  ..••«•••• 

8.57 
8.0 

I  iurht  IVf ncriil       ...........•■> 

A verace  Mocul ....••■•••«•• 

7-44 

I  lorHt  f^r>n«r»liflation  ......... 

7.0 

A  vi»ra«y«»            *'                ...«...•• 

6.82 

Si'nddSS?)   •«            

6.67 

Hpavv  \f  astodon.  .•••••••••• 

6.69 

Tank  Consolidation 

TankSwiich-engine(aU  weight 
on  drivers^ ••••• 

•  •  •  • 

•  •  •  • 

about  4 .  50 
4.00 

1 

If  any  one  of  these  constant  ratios  be  subtracted  from  the  fourth  column  of  the  long 
Table  170,  it  will  give  a  column  of  ratios  of  net  loads  to  tractive  power  which,  when 
multiplied  by  the  tractive  power  of  any  engine  whatever  of  the  same  proportion  of  weight 
on  drivers  to  total  weight,  will  give  its  hauling  power.  

689.  From  the  preceding  it  will  be  clear  that  if  we  know  merely  the 
RATIO  of  the  net  load  to  the  tractive  power  we  can  determine  by  what 
per  cent  a  given  increase  or  decrease  of  grade  will  modify  the  necessary 
tractive  power,  without  determining  the  absolute  amount  of  either  the 
one  or  the  other,  and  tliis  method  was  followed  in  the  first  edition  of  this 
treatise.  It  obliges  us  to  assume,  however,  that  this  ratio  is  constant ;  and 
as  it  is  commonly  the  case  that  with  every  considerable  variation  in  the 
weight  of  engine  the  ratio  of  its  power  to  its  weight  will  also  vary,  it  is  prac- 
tically much  better  to  study  the  effect  of  gradients,  and  of  the  changes 
therein,  directly  from  a  table  showing  the  tons  of  net  load,  exclusive  of 
engine,  tender,  and  caboose,  which  various  patterns  of  engine  can  handle 
on  various  grades.  Such  a  table  is  given  in  the  following  long  Table  170, 
in  which  the  net  load  in  tons  for  nine  different  patterns  of  engines,  varying 
from  liglit  American  to  the  heaviest  Mastodon  engines,  is  shown  for  every 
0.02  per  cent  of  grade  up  to  4.0  per  cent,  and  from  that  to  10  per  cent  at 
wider  intervals. 


690.  Table  170  is  computed  under  the  following  assumptions  : 
Rolling-friction 8  lbs.  per  ton. 

Adhesion  or  tractive  power i  weight  on  drivers. 

Weight  of  tender  (about  two-thirds  loaded),  as  noted 

in  the  heading  to  the  table 21  to  25  tons. 

It  gives  also,  in  addition  to  the  grade  per  cent,  the  corresponding 
grade  in  feet  per  mile,  the  resistance  in  pounds  per  ton  on  each  grade  due 
to  gravity  only,  and  to  gravity  and  rolling-friction  (8  lbs.)  combined,  and 
the  ratio  of  the  gross  load  to  the  tractive  power,  or 

2000  

total  resistance  in  lbs.  per  ton' 
This  ratio  x  tons  of  tractive  power  of  each  engine  (=  \  weight  on 
drivers)  =  gross  weight  of  train  in  tons  which  the  engine.can  haul.  Sub- 
tracting from  it  the  total  weight  of  each  engine,  as  given  in  the  first  line 
of  each  heading,  we  have  the  net  load  of  train  in  tons,  as  given  in  the 
nine  columns  which  constitute  the  body  of  the  table. 

691.  This  Table  170  we  shall  make  the  basis  of  our  ensuing  study  of 
the  effect  of  gradients  on  net  loads.  Experience  has  clearly  shown  that 
•only  by  the  aid  of  such  tables  or  by  diagrams  can  the  effect  of  gradients 
be  comprehended,  since  the  number  of  variables  entering  into  such  a 
table  is  so  great  that  formulae  become  very  intricate  in  form,  and  carry  no 
impression  to  the  mind.  The  weight  of  the  caboose  at  the  rear  of  the 
train,  which  is  practically  only  another  tender,  and  almost  universally  used, 
might  well  have  been  included  as  a  part  of  the  gross  weight  of  the  engine 
and  tender  in  Table  170;  but  there  are  two  styles  of  caboose  in  use, 
4- wheel  and  8-wheel,  differing  considerably  in  weight,  and  for  other  rea- 
sons it  seemed  better  not  to  include  it. 

692.  In  Table  138  a  variety  of  records  of  actual  performances  of  en- 
gines has  already  been  given,  which  justify  the  claim  made  at  the 
head  of  Table  170,  that  it  represents  the  fair  working  capacities  of  the 
various  engines  on  the  given  grades  in  good  American  practice.     The 

CAUTIONS  at  the  HEAD  AND  FOOT  OF  THE  TAlCE  MUST  BE  FULLY 

REMEMBERED,  however,  that  the  grades  must  be  the  de-facto  or  virtual 
grades,  not  increased  in  effect  by  unreduced  curvature  or  by  stops  on  or 
near  the  grade,  nor  decreased  in  effect  by  the  assistance  of  momentum 
(see  par.  413  ^/  al.),  either  of  which  contingencies  may  make  the  nominal 
grades  of  the  profile  anything  but  the  true  governing  gradients.  Fig. 
169  with  its  accompanying  note  will  serve  better  than  Table  170,  perhaps, 
to  make  the  effect  of  grades  on  train-load  clear  to  the  eye. 


ft 


544     CHAP.  XIV,— EFFECT  OF  GRADES  ON  TRAIN^LOAD. 


CHAP.   XIV.— EFFECT  OF  GRADES  ON  TRAIN-LOAD.      545 


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35 


546      CHAP.   XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD. 


CHAP.   XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD.      547 


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M    000 

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m  CO  M     O  00  so 
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m  ro  M 
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♦  ♦♦    ♦♦♦    ♦  ♦  •♦ 


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mmm 


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548      CHAP.   XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD. 


o 


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cococo    cocoro    cocoe* 


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n  e«  n 


00   O   «      •♦VO  00 
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ci  ei  «     «  «  ct 


C//AP.   XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD.      549 


t^ 

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r^  t^vo 


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PI    PI    C« 


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0  VO   PI     _- 

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552      CHAP.   XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD. 


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Grade  in  Feet  per  Mile. 


CHAP.   XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD.      553 


Notes  to  Fig.  169. 

Regarding  the  bottom  of  the  page  as  the  base-line  of  the  diagram,  or  axis  of  x,  as  ex- 
plained beneath  the  title  to  it : 

1.  r/ie  lower  heavy  line  represents  the  progressive  increase  of  train-load  (behind  ten- 
der) as  the  grade  is  reduced,  for  the  lightest  American  engine  given  in  Table  170,  which 
begins  at  o  at  a  grade  of  480  ft.  per  mile,  and  ends  at  1198  tons  on  a  level,  just  beyond  the 
limits  of  the  diagram.  * 

2.  The  upper  heavy  line,  marked  A,  represents  the  same  thing  for  the  heaviest  Mas- 
todon engine  given  in  Table  170,  so  nearly  that  it  is  not  in  error  by  more  than  its  own 
width  at  any  point.  It  was  not  plotted  for  that  purpose,  however,  but  was  one  of  the 
lines  of  the  original  diagram,  as  below,  made  blacker  to  correspond  with  line  i. 

Similar  lines  for  all  the  other  nine  engines  whose  tractive  capacities  are  given  in  Table 
170  would  fall  between  these  two  lines  at  approximately  regular  intervals.  It  has  not 
seemed  necessary  to  plot  them. 

The  remaining  lines  of  the  diagram  give  the  cyhnder  and  adhesion  tractive  powers  sep- 
arately for  the  three  different  engines  below  detailed,  as  computed  by  Mr.  G.  W.  GUSH- 
ING, Supt.  M.  P.  No.  Pac.  Ry.,  on  the  following  assumptions : 

Rolling-friction,  6^  lbs.  per  ton  in  place  of  8  lbs.  per  ton,  as  in  this  volume. 

Ratio  0/ adhesion,  >4,  as  in  this  volume. 

The  difference  in  the  rolling-friction  makes  the  train-loads  somewhat  greater  than 
those  given  in  Table  170,  especially  as  a  level  is  approached,  but  makes  no  great  differ- 
ence on  the  higher  grades.     The  three  engines  are  as  follows  : 


Engine. 

Cylin- 
ders. 

Drivers. 

Trac.  Pr. 

in  Lbs., 

Per  Lb.  of 

Effective 

Pressure. 

No. 
Drivers. 

Weights. 

On 
Drivers. 

Total        Tender, 
Engine.   1  Loaded. 

! 

Total. 

A 

B 
C 

2a" X  26" 
22" X  26" 
20"  X  24" 

49" 
49" 
49" 

256.8 
256.8 
196 

8 

10 

8 

ioo,ocx> 

110,000 

96,000 

112,000 
112,000 
108,000 

65,000 
65,000 
65,000 

177,000 
177,000 
i73i"«> 

The  lines  marked  A,  B,  C  indicate  the  loads  corresponding  to  the  adhesion  tractive 
power  of  these  three  engines,  computed  on  the  basis  of  one  fourth  the  weight  on  drivers. 

The  remaining  lines  indicate  the  cylinder  tractive  powers  for  the  same  engines  at 
various  points  of  cut-offs,  cis  follows  : 

Engine  Qi,  2o"x24",  Gonsolidation,  48  tons  on  drivers.  At  half-stroke  the  cylinder 
power  is  somewhat  less  than  the  adhesion,  and  at  70  per  cent  very  slightly  over.  Only  at 
very  slow  speed  can  such  an  engine  furnish  steam  for  running  at  70  per  cent  cut-off. 

Engine  A,  22"  x  26",  Consolidation,  50  tons  on  drivers,  or  5  tons  less  than  B,  but  iden- 
tical in  cylinder  capacity,  showing  that  the  latter  is  in  excess. 

Engine  B,  22"  x  26",  Mastodon,  55  tons  on  drivers.  The  two  lines  for  cylinder  tractive 
power  apply  alike  to  engines  A  and  B.  In  both  of  these  engines  the  cylinder  power  is 
much  greater  in  proportion  than  in  engine  C,  and  cannot  be  fully  utilized  at  one  fourth 
adhesion.     As  the  working  adhesion  on  a  good  rail  often  rises  much  higher  thiin  one  fourth 


554      CHAP.   XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD. 

THE  PERCENTAGE  OF  CHANGE  IN  THE  NET   LOAD  RESULTING  FROM  A. 

CHANGE   IN   THE  RATE  OF  ANY  GRADE. 

693.  Assuming  Table  170  as  a  basis,  we  can  readily  determine 
from  it,  in  the  manner  below  outlined,  the  two  following  laws,, 

which  are  the  foundation  for  a  correct  estimate  of  the  value  of 

« 

reducing  grade: 

First.  When  the  rate  of  any  one  given  ruling  grade  is  increased  or 
decreased^  the  corresponding  percentage  of  increase  or  decrease  in  ther 
engine-mileage  required  to  handle  any  given  tonnage  varies  almost  di- 
rectly  as  the  change  in  rate  of  grade ^  however  much  or  little  the  change 
may  be,  slightly  increasing,  however,  as  the  increase  is  greater  and  de^ 
creasing  as  the  decrease  is  greater. 

For  example,  if  a  0.6  per  cent  grade  be  increased  to  0.8  the  increase  in  en- 
gine-tonnage required  is,  for  Consolidation  engines,  ^^  =  21.73  per  cent  in- 
crease, or  10.9  per  cent  per  o.  i  per  cent  of  grade  ;  but  if  it  be  increased  to  1.5 
percent,  the  increase  is  Yff^  =  103. 37  per  cent  increase,  or  11.48  per  cent  per 
0.1  per  cent  of  grade  ;  being  about  5i  per  cent  more  per  o.i  per  cent  of  grade 
than  for  the  smaller  increase. 

If  the  entire  weight  of  the  engine  be  on  the  drivers,  or  if  only 
the  load  on  the  drivers  be  considered  the  engine,  and  the  re- 
mainder a  part  of  the  train,  this  law  is  exact,  and  the  engine-ton- 
nage varies  precisely  with  the  change  in  rate  of  grade,  as  may 
be  seen  in  Table  172. 

Second.   The  amount  of  this  percentage  of  increase  or  decrease  in 


CHAP.   XIV.— EFFECT  OF  GRADES  ON   TRAIN-LOAD,      555 


however,  this  surplus  cylinder  power  is  likely  to  be  very  useful  in  handling  heavy  trains 
easily,  and  indicates  that  engine  B  at  least  is  better  designed  than  engine  C  for  the  most 
efficient  freight  service. 

Where  and  why  tank  engines  are  advantageous  may  be  very  clearly  seen  from  this^ 
diagram  as  follows : 

Referring  to  the  head-lines  to  Table  170,  it  will  be  seen  that  the  total  weight  of  the' 
lightest  American  engine  and  the  weight*  on  drivers  of  the  heaviest  Mastodon  are  the 
same,  52  tons.  A  tank  engine  of  the  same  total  weight,  all  of  it  on  drivers,  while  it  will 
be  a  much  lighter  and  cheaper  machine  than  the  Mastodon,  and  be  equal  to  much  lower 
speeds  only,  will  have  a  greater  net  tractive  power  on  all  grades  by  the  constant  amount 
of  35  tons  (saved  in  dispensing  with  a  tender  and  leading  truck).  Therefore,  plotting  on 
Fig.  169  a  line  for  35  tons  greater  loads  than  for  the  upper  heavy  black  line,  we  find  that 
on  the  higher  grades  it  makes  an  enormous  difference  in  the  percentage  of  net  load 
hauled,  but  as  the  lower  grades,  below  2  per  cent  (106  ft.  per  mile),  are  reached  the  two 
lines  become  almost  coincident. 


the  engine-tonnage  required  varies  considerably  with  each  grade,  being 
nearly  five  times  as  much  on  a  level  as  on  a  3  per  cent  grade  j  and  is 
about  as  given  in  the  following  Table  171,  where  these  percentages 
are  given  for  all  grades,  determined  in  a  manner  we  will  shortly 
review. 

964.  These  two  facts  being  definitely  ascertained,  we  have,  ire 
order  to  determine  the  effect  of  any  change  of  grade  upon  the 
engine-mileage  required  to  handle  a  fixed  tonnage,  simply  to» 
multiply  the  percentage  given  in  Table  171  (which  see)  by  the 
xxumh^v  oi  tenths  per  cent  change  of  grade  to  obtain  the  total  in- 
crease in  engine-mileage  which  will  be  required  for  any  given? 
change  of  grade  ;  or,  the  same  fact  may  be  still  better  deter- 
mined directly  from  the  actual  load  on  each  grade,  given  in 
Table  170.  This  percentage,  multiplied  by  the  proportion  of  the 
expenses  which  varies  with  the  number  of  trains  or  engine-ton- 
nage (the  car-mileage  and  traffic  remaining  constant),  i.e.,  by  the 
portion  of  the  expenses  which  would  be  doubled  if  the  engine- 
tonnage  were  doubled,  will  give  the  annual  cost  of  a  proposed' 
increase  of  grade,  or  the  annual  saving  of  a  proposed  decrease. 

695.  Table  171  (see  p.  556)  is  determined  from  Table  170  in  the  fol- 
lowing simple  manner: 

Taking  only  three  types  of  engines,  the  lightest  "American,"  heaviest 
Consolidation,  and  a  tank  engine  of  the  same  weight  on  drivers  as  the 
latter,  but  with  no  tender  nor  truck,  and  comparing  the  net  loads  given 
for  grades  of  Level,  0.5,  i.o,  1.5,  and  2.0  per  cent,  we  have  the  following 
net  loads  hauled  : 

Light  American,  .    .    . 
St'nd  Consolidation, 
Heavy  Tank  Engine,    . 

Then  it  is  evident  that,  whatever  the  total  tonnage  to  be  moved,  the 
percentage  of  increase  in  the  engine-mileage  required  to  move  it  will  be^ 
with  a  1.5  per  cent  instead  of  i.o  per  cent  ruling  grade, 

American.  Consolidation.  Tank. 

777         .   ..„  857 


Grades  of 

Level. 

0.5. 

I.O. 

1.5. 

2.0. 

1198 

504 

305 

211 

156 

2920 

1253 

777 

552 

420 

3000 

1333 

857 

632 

500 

305  , 

—  =  1.446, 

211  ^^ 


552 


=  1.408, 


times  that  required  on  a  i  per  cent  grade,  or 
44.55  per  cent,  40.8  per  cent, 


632  _  =  '-357, 
35.7  per  cent. 


'556      CHAP.   XIV.-EFFECT  OF  GRADES  ON  TRAIN-LOAD, 


1 


rf  fW 


Table  171. 
Percentage  of  Increase  (or  Decrease)  in  the  Engine-Mileage  required 

WHICH    RESULTS   FROM   ANY   CHANGE   IN  THE    RaTE   OF   ANY   GrADE. 
[Deduced  from  the  long  Table  170  in  the  manner  explained  in  Table  172.] 


INCREASE  Pek 
Mileage  Per  0.1 

Cent  in  Engine- 

Grade 

DECREASE  Per  Cent  in 

•J 
Enginb- 

of  Change  in  Grade 

to  be 

Mileage  Per  0.1  of  Change 
resulting  from  a  Total  Ch 

in  Grade 

KESULTING  FROM  A 

Total  Change  of — 

Changec 

ange  of — 

79.2 

52  8 

26.4 

5. 28   ■ 

Ft.  Per 

Mile. 

\   5.28 

26.4 

52.8 

79.2 

+  1.5 

+  1.0 

+  0.5 

+  0.1 

Per  cent 

-  0.1 

-0.5 

-  1.0 

-  1.5 

28.68 

27.62 

26  64 

25.9 

Level. 

•  ■  •  • 

■ . .  • 

■  ■  ■ 

23.16 

22.30 

21.46 

20.9 

.10 

20.6 

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19 -43 

18.73 

18.02 

17-5 

.20 

17.3 

•  •  •  • 

16.80 

16.15 

15.54 

»5.i 

.30 

14.9 

-  •  •  • 

.... 

•  •  •  • 

14.84 

14.25 

13.72 

13.3 

.40 

13.1 

•  ■  •  • 

.... 

13-30 

12.76 

12.26 

II. 9 

.50 

11.8 

11.42 

. . .  • 

12.05 

11.58 

II. 16 

10.8 

.60 

10.6 

10.36 

«... 

•  •  •  • 

11.05 

10.60 

10.22 

9.8 

.70 

9-7 

9.48 

.    •    a    . 

•  •  •  • 

10.24 

9.81 

9-44 

9.2 

.80 

9.0 

8.74 

.... 

■  •  •  • 

9- 50 

9.13 

8.76 

8.5 

.90 

8.4             8.14 

.... 

.... 

8.93 

8.56 

8.22 

8.1 

1.00 

7.8 

7.60 

7-34 

*  •  •  • 

7.91 

7-59 

7.26 

7.0 

1.20 

6.9 

6.76 

6.52 

•  •  •  • 

7.18 

6.86 

6.60 

6.3 

1.40 

6-3 

6.10 

5.88 

6.58 

6.27 

6.02 

5-8 

1.60 

5-8 

556 

5-37 

5  17 

6.09 

5.80 

5.60 

5.5 

1.80 

5.4 

5.14 

4-95 

4.77 

5.67 

5.38 

5.20 

5-1 

2.00. 

5.0 

4.80 

4.62 

4-44 

5.35 

5.01 

4.86 

4.8 

2.20 

4-7 

4.50 

4.31 

4.14 

5.05 

4-79 

4.66 

4.6 

2.40 

4-4 

4.22 

4.07 

3.92 

4.85 

4.58 

4.44 

4-4 

2.60 

4-2 

4.00 

3.85 

3.71 

4.68 

4-39 

4.24 

4.2 

2.80 

4.0 

380 

3.67 

3-55 

4.50 

4.23 

4.06 

4.0 

3.00 

3-8 

3.62 

3.50 

3.37 

4.03 

3.80 

3.66 

3-6 

3.50 

3.5 

3.38 

3.19 

3.07 

3.79 

3-57 

3-34 

3-4 

4.00 

3.3 

3-10 

2.97 

2.83 

3-5« 

330 

3-14 

'■' 

5.00     1 

3.0 

2.80 

3.63 

2.51 

These  percentages  are  computed /or  an  average  Consolidation,  havine  11  tons  trac- 
ed i^s'^^'"s7  ^'°^^''^-  ''''  drivers,  but  they  are  substantially  the  same  for  all  freight 

By  interpolation  any  desired  percentajje  can  be  determined  from  the  above  very  ao- 
-iproximately.     Thus  for  an  increase  of  0.75  in  a  0.75  grade  we  have 
10.41  +  9.63 

^  =  10.02  X  7-5  =  75  +  per  cent  increase  in  engine-mileage. 

-Exactly,  it  is  (Table  170)  ?-^  =  74.64  per  cent,  increase. 

552 


CHAP.   XIV.— EFFECT  OF  GRADES  ON  TRAINLOAD.      557 

total  increase  of  engine-mileage,  equivalent  to  an  average  increase  A'' 
0.1  oj  increase  of  grade  of 

8.91  per  cent,  8.16  per  cent,  7.14  per  cent. 

For  an  increase  from  a  i.o  per  cent  to  a  2.0  per  cent,  we  have 

American.  Consolidation.  Tank. 


305 


=  I-PSS* 


m 


=  1.850, 


^57 

5^= '•7^4, 


156         '"  420 

a  total  increase  per  cent  ot 

95-  5  per  cent,  85.0  per  cent,  71.4  per  cent, 

or  an  increase  per  o.i  per  cent  of  increase  of  grade  of 

9. 55  per  cent,  8.50  per  cent,  7. 14  per  cent. 

696.  Proceeding  similarly  for  other  changes  of  grade,  viz.,  o.i,  0.3^ 
0.5,  and  1.0  per  cent  of  increase  from  a  i  per  cent  grade  (making  the" 
maximum  change  considered,  from  a  1.0  per  cent  to  a  2.0  per  cent)*,  and 
computing  also  the  comparative  engine-tonnage  required  for  correspond- 
ing decrease  in  a  i  per  cent  grade,  this  extreme  reduction  being  to  Level 
we  obtain  the  following  Table  172,  in  which  the  computations  in  the  last 

Table  172. 

Showing  the  Effect  of  Various   Changes    in  a  One  Per  Cent  Grade 

ON  the  Engine  Tonnage  required  for  Three  Patterns  of  Engines. 


For  a  Decrease  in 
A  I  00  Per  Cent 

Making 

the 
Grade 

The  Per  Cent  of  Change  in 
Engine  Tonnage  needed  is— 

And  the  same  Per  o.  i  Per 
Cent  of  Change  in  Grade  is— 

Gradb  of — 

Light 
Ameri- 
can 

Heavy 
Cons'n. 

Heavy 
Tank. 

Light 
Ameri- 
can. 

Heavy 

Cons'n. 

Heavy 
Tank. 

1.0  per  cent 

Level. 

0.3 
0.5 
0.7 
0.9 

1.00 
x.x 

«.3 
X.5 
»-7 
3.0 

74.5 
53-9 
39-5 
24  3 
8.4 

8.5 
36.0 

44.6 

64.0 

95-5 

73-4 
52.4 
38.0 

23.1 
8.8 

7-9 
24.1 

40.8 

58.2 

85.0 

71.4 
50.0 

35-7 
21.4 

7-14 

7.14 
21.4 

35.7 
50.0 

71.4 

7.45 
7.70 
7.90 
8. II 
8.41 

8.53 
8.68 
8.91 
9.14 
9.55 

7.34 

7.49 
7.60 

7.71 
783 

7.92 
8.04 
8.16 
8.31 
8.50 

0.7    "    •'     

7.14 

0.5    "    "     

7.14 

0.3    "    "     

7.14 

0.1    "    ••     

7.14 

And  for  an  Increase 
of 

7.t4 

O.I  percent 

0.3    "    ♦•    

7.14 

0.5    "    "    

7-14 

0.7    "    •»     

1.0    "    •»    

7.14 
7.14 

1 

7.»4 

Computed  from  Table  170  n\  the  manner  explained  in  par.  695.     The  results  of 
lar  computations  for  all  rates  of  grade  are  condensed  in  Table  171. 


simi' 


S58      CHAP.   XIV.^EFFECT  OF  GRADES  ON  TRAIN-LOAD. 


CHAP.   XIV.— EFFECT  OF  GRADES  ON  TRAIN-LOAD.      559 


mm 


column  but  one  correspond  substantially  with  one  line  (that  for  a  i.o 
grade)  of  Table  171.  All  the  other  lines  of  Table  171  were  computed  in 
the  same  way  from  Table  170,  the  figures  only  differing. 

697.  It  will  be  seen  in  Table  172  that  a  tank  engine  which  has  all  its 
-wreight  on  drivers  gives  exactly  the  same  per  cent  of  change  in  motive- 
power  per  unit  of  change  of  grade,  whether  it  be  great  or  small.  In  pro- 
tion  as  the  dead  weight  of  the  engine  becomes  a  larger  proportion  of  the 
weight  on  drivers,  the  absolute  per  cent  of  change  in  motive-power  in- 
creases, and  likewise  the  irregularity  of  the  percentage. 

698.  By  interpolation  in  Table  171,  the  percentage  for  almost  any 
kind  of  a  change  of  grade  can  be  readily  determined.  These  percentages 
do  not  vary  to  any  important  extent  with  the  pattern  of  engine,  within 
the  range  likely  to  be  used  for  freight  service,  nor  even  for  considerable 
differences  in  the  assumed  ratio  of  adhesion.  Moreover,  as  it  is  now  well 
established  that  \  is  the  proper  ratio  to  assume,  for  American  practice 
at  least,  no  other  should  be  assumed. 

699.  Ordinarily  the  changes  of  grade  which  the  engineer  is  called 
upon  to  consider  are  not  very  great.  The  typical  percentage  for  any  or- 
dmary  change  in  any  grade,  for  use  in  estimating  the  value  of  a  reduc- 
tion or  the  cost  of  an  increase,  may  therefore  be  taken  to  be  that  due  to 
a  change  of  o.i  per  cent  in  it.  as  shown  in  Table  178.  which  is  practically 
the  same  for  either  an  increase  or  a  decrease  of  grade.  For  extreme  dif- 
ferences of  conditions,  of  any  kind,  the  actual  percentage  of  change  in 
engine-tonnage  should  be  directly  computed  from  the  relative  train-loads 
given  in  Table  170. 

We  are  now  prepared  to  consider  the  cost  of  changing  the  hauling 
power  of  engines  by  changes  of  grades. 

700.  Table  173  will  illustrate  how  enormously  the  virtual  gradient  as  well 
as  the  work  of  the  engine  may  be  increased  by  frequent  stops  and  quick  starts 
On  the  New  York  Elevated  Railway  the  stops  are  so  close  together  that  it  is  ab- 
solutely essential  that  speed  should  be  gotten  up  very  quickly  indeed  if  reason- 
ably fast  time  is  to  be  made.  Accordingly  we  find  that  the  work  done  in  get- 
ting  up  speed  is  equivalent  to  an  addition  to  the  actual  grade  of  2.63  per  cent, 
or  139  feet  per  mile— an  addition  so  great  that  whether  the  actual  grade  be  i 
per  cent  up  or  i  per  cent  down  makes  comparatively  little  di£ference  in  the 
working  of  the  engine.  Table  173  gives  an  extreme  example  of  conditions 
which  obtain  very  largely  in  passenger  service,  and  which  make  frequent  stops 
a  very  serious  disadvantage.  Due  allowance  for  this  effect  should  never  b«» 
forgotten  in  attempting  to  determine  what  the  actual  grades  are. 


Table  173. 

"Handling  of  Trains  on  Manhattan  (Elevated)  Railway  (Third  Avenue 

Line). 
[From  a  paper  by  Mr.  Frank  J.  Sprague  before  the  Boston  Society  of  Arts,  1886.] 


Length  of  line 8.48miles. 

Toul  lift,  up  track 144-42  ft. 

Lineal  distance  for  same 13,160        ft. 

Total  lift,  down  track 137.60  ft. 

Lineal  distance  of  same ...  16,510        ft. 

Level  on  each  track 15,100       ft. 

Number  of  stations 27 

Number  of  stoppages 26 

Average  Times  : 

Single  trip 42  min. 

Per  station 97  sec. 

Under  way 80    " 

Stop ,7    " 

Time  due  to  a  run  without  stop  at 

max.  speed  of  19.2  m.  per  hour..  26,56  min. 

Total  time  standing  still  at  sta- 
tions, at  17  sec.  each 7.37    " 

Time  lost  in  slowing  up  and  get- 
ting under  way 8.07    *• 

Total 42.00  min. 


Average  distance  between  stations.     1,722  ft. 
Divided  nearly  as  follows  : 

Getting  up  to  10  miles  per  hour 130  ft. 

Thence  to  full  speed  (19.2  miles  per 

P.ho"'')  •- 495ft. 

Full  speed 808  ft. 

Slowing  to  stop 289  ft. 

Average  Speed — miles  per  hour : 

Getting  under  way 

Full  speed 

Slowing  to  stop 

Mean  between  stations 


»3-4 

19.2 

9.6 

14-7 


Daily  Work  of  One  Engine  : 

Round  trips  made 9 

Coal  used 5,760  lbs. 

Hours  on  duty 20 

Hours  steam  on 6 

Av.  consumption  of  coal  per  trip, . . .    640  lbs. 
Total  horse-power  per  round  trip. , .         6,184 

Horse-power  per  pound  of  coal -^^  =      9.66 


Pounds  of  coal  per  H.  P.  p.  h. 


640 
60 

9.66 


=        6.3X 


For  a  speed  in  miles  per  hour  of. 
The  velocity-head  (Table  118)  is  , 


Divided  by  distance  to  acquire  that  speed , 

Gives  as  the  virtual  gradient  due  to  that  acceleration,  in  excess 

of  the  actual  grade         

If  the  actual  grade  be  i  per  cent  up,  the  same  speeds  will  be 

acquired  in  a  distance  of , 

Or  if  1  per  cent  down,  in 

Even  so  extreme  a  difference  in  grade  makes  comparatively  little  difference,  therefore,  in 
practical  operation. 


xo.o 
355  ft. 

19. 2 
13.10  ft. 

135  ft. 

495  ft. 

2.63  p.  c. 

2.64  p.  c. 

918  ft. 
98  ft. 

Sooft. 
360  ft. 

Getting  up  speed  to  19.2  miles  an  hour  26  times  is  equivalent  to  lifting  the  train  ver- 
tically 13. 10  X  26  =  340.6  ft,  in  a  run  of  8.5  miles,  or  40  ft.  per  mile,  whereas  the  total 
tractive  resistance  in  motion  at  that  speed,  at  10  lbs.  per  ton,  is  equivalent  to  some  26  ft. 
per  mile  only. 


56o   CHAP,  XV.— TRAIN-LOAD   ON  OPERATING  EXPENSES, 


CHAP,XV.—  TRAIN.LOAD   ON  OPERATING  EXPENSES.    561 


Hi 


liffln 


CHAPTER  XV. 

THE   EFFECT   OF    TRAIN-LOAD   ON   OPERATING   EXPENSES. 

701,  The  increase  in  train  resistance  which  results  from  an  increase 
of  ruling  grade  can  be,  and  is,  overcome  in  either  of  two  ways:  (i)  By  an 
increase  in  the  weight  and  power  of  engines  ;  (2)  by  decreasing  the  weight 
and  increasing  the  number  of  trains. 

The  first  of  these— increasing  the  weight  of  engines— is  by  much  the 
cheapest,  but  is  only  possible  to  a  limited  extent  and  under  special  cir- 
cumstances. Ordinarily,  it  is  not  fair  to  assume  that  heavier  engines 
are  used  on  one  alternate  grade  than  on  another,  because,  whatever 
advantage  may  be  gained  by  using  heavier  engines  on  one  grade  may  be 
equally  well  gained  on  the  other  grade.  It  is  far  more  frequently  possi- 
ble to  fairly  assume  the  use  of  heavier  engines  on  heavier  grades  with 
passenger  than  with  freight  service,  but  passing  (until  par.  732)  the  ques- 
tion of  when  it  is  or  is  not  possible  to  adopt  the  cheaper  expedient,  we 
will  estimate  the  cost  of  each  separately. 

THE   COST   OF   INCREASING  THE   WEIGHT  OF   ENGINES. 

702.  The  following  items  will  not  be  increased  at  all  by  an  increase  of 
weight  of  engines  to  suit  the  requirements  of  a  higher  grade,  the  weight 
of  train  remaining  the  same:  The  cost  of  (i)  repairs  of  cars;  (2)  train- 
wages  ;  (3)  general  expenses  ;  (4)  maintenance  of  way  and  works,  exclusive 
of  rail  and  tie  renewals  and  lining  and  surfacing;  (5)  that  portion  of  the 
inaintenance-of-way  expenses  last  excepted  which  is  caused  by  the  cars 
and  not  by  the  engines. 

The  most  reasonable  estimate  which  can  now  be  made  of  the  relative 
erfect  of  engine  and  cars  upon  the  track  is  (pars.  115,  116)  that  consider- 
ably over  half  of  the  deterioration  of  track  comes  from  the  passage  of  en- 
gines over  it,  and  the  remainder  only  from  the  passage  of  cars,  which  may 
weigh  ten  or  twenty  times  as  much.    Assuming  one  half  only,  we  are  led 


to  the  conclusion  (see  Table  175)  that  more  than  three  quarters  of  the 
total  expenditure  is  unaffected  by  an  increase  of  the  weight  of  engines  in 
any  visible  and  direct  way. 

703.  The  effect  on  cost  of  maintenance  of  track  of  increasing 
the  weight  of  engines  has  been  greatly  modified  and  much  reduced  since 
the  publication  of  the  first  edition  of  this  volume  (prepared,  as  it  neces- 
sarily was,  from  records  which  were  some  years  old  in  1876)  by  the  now 
universal  use  of  steel  rails  in  place  of  iron.     The  causes  and  extent  of  the 
changes  thus  brought  about  have  been  already  summarized  in   par.  109 
et  seq.     The  most  important  of  all,  as  respects  the  use  of  heavy  engines. 
IS  that  the  nature  of  the  wear  of  rails  has  changed.     With  iron  rails,  the 
wear  took  the  form  of  a  crushing  or  lamination,  which  destroyed  their 
surface  long  before  the  direct  abrasion  had  become  a  serious  matter.   This 
crushing  was  very  greatly  hastened  by  heavy  loads  per  wheel,  and  in- 
creased in  much  faster  ratio— to  the  extent  that  iron  rails  which  would 
sustain  the  passage  of  light  engines  for  many  years  would  be  crushed  out 
by  heavy  engines  in  a  few  months.     On  the  other  hand,  with  steel  rails 
(excluding  those  of  inferior  quality,  of  which  far  too  many  have  been  and 
are  laid)  the  wear  is  merely  direct  abrasion,  which  is  not  materially  in- 
creased per  ton  of  train  either  by  load  per  wheel  or  speed.     As  respects 
the  last  at  least,  there  is  very  good  reason  to  believe  that  it  increases  in 
much  less  than  direct  ratio. 

704.  For,  as  respects  speed,  when  the  question  is  one  merely  of  abrasion 
and  not  of  destruction  impact,  the  less  the  time  to  which  the  rail  is  exposed  to 
load  the  less,  undoubtedly,  the  normal  crushing  effect,  for  the  same  reason 
that  journal  and  other  (i.e..  brake)  friction  is  less  at  high  speeds  or  that  it  takes 
more  force  to  rupture  a  specimen  in  a  test- 
ing-machine quickly  than  slowly.  Impacts 
proper  play  their  part,  no  doubt,  in  the  wear 
of  steel  rails  as  of  iron  rails,  but  so  long  as  the  p,c 

surface  remains  tolerably  good  (as  it  does  almost  indefinitely  with  the  best  steel 
rails)  it  is  a  small  part.     When  the  surface  becomes   seriously  impaired    steel 
rails  go  almost  as  quickly  as  iron;  but  either  with  steel  or  iron  the  effect  of  the 
impacts  is  not,  as  is  often 
assumed,  as  Mv'^.     This  is 
true  of  a  body  impinging 
directly  upon  another;  but 

one     caused     to    impinge  Fig.  171. 

upon  another  in  jumping  from  ^  to  ^  under  conditions  outlined  clearly  enough 
in  Fig.  170  impinges  at  a  different  angle,  which  has  the  effect  of  reducing  the  im- 
pact communicated  to  B  to  the  approximate  ratio  Mv  ;  and  when  we  assume  a 
36 


562    CHAP.  XV.—  TRAIN.LOAD   ON  OPERATING  EXPENSES. 


case,  as  in  Fig.  171,  still  more  closely  approaching  average  practical  conditions, 
the  communicated  impact  becomes  more  nearly  in  the  ratio  M  \^v^. 

That  this  is  so  follows  clearly  from  experience  on  tracks  where  the  varia- 
tions of  speed  are  considerable,  as  notably  on  the  four  tracks  of  the  New  York 
Central  &  Hudson  River  Railroad,  two  of  which  are  used  for  passenger  ser- 
vice only,  and  two  for  freight  only.  The  observed  rate  of  wear  per  ton  is  nearly 
constant  on  these  tracks,  in  spite  of  the  fact  that  the  proportion  of  engine-ton- 
nage is  several  times  greater  on  the  passenger  tracks. 

As  respects  efifect  of  increase  of  load,  abrasion,  other  things  being  equal, 

should  be  in  some  approximately  exact  ratio  to  the 
maximum  fibre-strain.  If  we  assume  an  elastic  cyl- 
inder or  sphere  to  be  rolling  on  a  plane,  a  distor- 
tion of  form  will  result  from  compression,  rudely 
outlined  in  Fig.  172.  The  volume  of  this  solid, 
shown  in  plan  in  Fig.  173,  will  be  in  direct  ratio 
to  the  total  load,  but  the  maximum  fibre-strain  will 
be  in  proportion   to    the  maximum   ordinate  CC\ 

which  varies  more  nearly  as    \/L  or  even  '4/Z,  ac- 
cording to  the  assumptions  as  to  the  surfaces  in  contact. 

The  subject  is  too  obscure,  and  too  unimportant  for  our  immediate  purpose, 
to  consider  further. 

705.  The  observations  of  the  Pennsylvania  Railroad  on  the  wear  of 
rails  on  grades  (par.  457)  also  tend  to  show  that  not  more  than  half,  or  at 
most  two  thirds,  of  the  total  cost  of  rail  wear  can  be  considered  to  vary 
directly  with  the  engine-tonnage,  the  car-tonnage  remaining  constant; 
whereas  in  the  first  edition  of  this  treatise,  based  in  the  main  on  iron- 
rail  statistics,  the  whole  cost  of  rails  was  assumed  (and  the  writer  be- 
lieves with  substantial  correctness)  to  vary  as  the  square  of  the  weight 
on  drivers,  or  at  the  rate,  for  small  increments,  of  200  per  cent.*  This 
change  is  one  small  evidence  of  the  immense  advantages  which  have  re- 
sulted from  the  introduction  of  steel  rails. 

706.  Of  the  remaining  items  of  the  cost  of  track,  lining  and  sur- 
facing, in  spite  of  apparent  reasons  to  the  contrary  (discussed  in  par. 
125),  is  affected  by  increased  weight  of  engines  in  a  considerably  greater 
ratio  than  the  rail  wear,  and  tie  renewals  to  a  very  considerable  extent, 
although  not  quite  so  largely.  We  may  not  improperly  take  half  the  total 
cost  of  rails,  ballast,  ties,  adjusting  track,  and  switches,  frogs,  and  sidings, 
as  varying  directly  with  the  average  weight  on  drivers,  car-tonnage  being 

*  For  the  reason  (to  those  familiar  with  the  elements  of  the  calculus)  that 
<&*  =  2xdx.     See  p.  90,  old  edition. 


Tfc, 


CHAP.  XV.—  TRAIN-LOAD   ON  OPERATING  EXPENSES.    563 


constant.  With  inferior  steel  rails  it  may  be  much  more,  but  with  such 
rails  as  may  be  had  at  the  same  cost  by  adequate  care  in  inspection  this 
estimate  is  a  sufficient  one. 

707.  The  remaining  items  of  maintenance  of  way,  for  bridges  and 
BUILDINGS,  are  very  slightly  affected,  certainly  by  not  more,  in  ordinary 
cases,  than  \  ct.  per  train-mile,  the  whole  being  an  allowance  for  interest 
and  maintenance  charges  on  heavier  bridges. 

708.  Repairs  of  engines  are  affected  much  less  than  would  be  sup- 
posed by  the  weight  of  engines.  Renewals  constitute,  as  per  Table  55  and 
others,  from  40  to  50  per  cent  (under  normal  conditions,  which  can  hardly 
be  said  as  yet  to  exist  on  account  of  the  rapid  growth  of  traffic)  of  what  ap- 
pears charged  to  "repairs."  Table  174  affords  the  means  for  estimating 
that  considerably  less  than  50  per  cent  of  the  Jirs/  cost  of  engines  varies 
directly  with  weight,  the  remainder  being,  within  moderate  limits  of 
variation,  a  constant. 

Of  the  remaining  cost,  repairs  proper,  it  is  indicated  in  Table  ^\etseq. 
and  a  number  of  others,  that  between  50  and  60  per  cent  is  for  labor  only  : 
an  item  which  will  be  somewhat,  but  very  slightly,  affected  by  the  weight 
■of  engines.  The  remaining  expenditures,  for  raw  materials  and  for 
wheels,  axles,  and  tires,  will  vary  nearly,  but  not  quite,  directly  as  the 
M'eight. 

It  would  appear  from  these  facts  that  50  per  cent  of  the  cost  of  repairs 
may,  with  sufficient  exactness,  be  assumed  to  vary  directly  with  weight 
of  engines,  the  remainder  being  constant,  as  has  been  already  stated  in 
par.  134. 

709.  The  cost  of  fuel  for  heavier  engines  hauling  the  same  train 
behind  them  will  not  be  largely  increased.  In  not  a  few  cases  there 
would  be  an  actual  decrease.  It  is  to  be  remembered  that,  even  if  heavier 
-engines  are  used  to  overcome  a  somewhat  higher  grade,  it  is  only  for  a 
short  distance  that  the  extra  power  is  required.  On  all  up  grades  below 
the  maximum,  and  in  descending  all  grades,  the  power  required  and  ex- 
erted will  be  no  greater  than  with  the  smaller  engine,  except  the  slight 
addition  due  to  the  weight  of  the  engine  itself,  and  this  power  will  be 
somewhat  more  economically  exerted  (par.  579),  owing  to  the  heavier  en- 
gine being  less  pushed.  The  constant  wastage  from  radiation,  stopping 
and  starting,  etc.,  estimated  in  par.  344  et  seq.,  at  50  per  cent  of  the  fuel 
consumption,  will  remain  for  the  most  part  constant. 

For  all  these  reasons  together,  on  something  like  two  thirds  of  the 
length  of  ordinary  railways  the  fuel  burned  per  mile  would  be  but  slightly 
if  at  all  affected  by  moderate  (not  over  20  per  cent)  differences  in  weight 


564  CHAP.  XV.— TRAIN-LOAD  ON  OPERATING  EXPENSES. 


Table  174. 

Comparative  Cost   Per  Ton  of  Various  Sizes  of  Engines,  Broad  and- 

Narrow  Gauge. 

[Compiled  from  information  furnished  by  the  Baldwin  Locomotive  Works.] 

American   Type — Standard  Gauge. 


Weight  (net  tons). 

Cost,  1886. 

Cylinders. 

Total. 

On  Drivers 

Engine. 

Tender. 

Per  Ton  on 
Drivers. 

12  X    22 

13  X  24 

14  X  24 

15  X  24 

16  X  24 

17  X  24 

18  X  24 

24. 
27. 

295 

32.5 

36. 

38. 

41. 

15. 

l8. 

19.5 
22. 

245 

25.5 
27.5 

$5,750 
6,000 
6.250 
6,500 
6,750 
7,000 
7,250 

$950 
1,000 
1,050 
1,100 
1,150 
I,200 
1,250 

$383 
333 
321 

295 
276 

275 
264 

20  X  24 

21  X  24 


11  X  16 

12  X  16 

13  X  16 

14  X  16 

15  X  16 


Mogul  Type — Standard  Gauge. 


16  X  24 

37. 

32.5 

$7,250 

$1,150 

$223 

17  X  24 

39- 

34.5 

7.500 

1,200 

217 

18  X  24 

42. 

37. 

7.750 

1,300 

209 

19  X  24 

45. 

40. 

8,000 

1,350 

200 

Consolidation   Type — Standard  Gauge. 


53. 
59- 


46. 

52. 


$9,250 
9.750 


$1,400 
1,400 


Narrow-Gauge  Engines. 
American   Type. 


Mogul  Type. 


$201 
188 


10  X  16 

16.5 

II. 

$4,750 

$750 

$432 

II  X   16 

18. 

12. 

5,000 

775 

417 

12    X    16 

19-5 

13. 

5.250 

800 

404 

13  X   16 

22.5 

15.5 

5.500 

850 

355 

14  X  16 

24. 

16.5 

5.750 

900 

357 

$5,250 

$800 

$362 

5.500 

850 

334 

5,750 

900 

295 

6,000 

950 

278 

6,250 

1,000 

255 

CHAP.  XV.-TRAIK.LOAD  ON  OPERATING  EXPENSES.    565 


•    J--  J 

Table  174 — Continued. 
Consolidation   Type. 

Cylindeks. 

Weight  (net  tons). 

Cost,  1886. 

Total. 

On  Drivers. 

Engine. 

Tender, 

Per  Ton  on 
Drivers. 

15  X  18 

16  X  18 

28. 
34. 

24. 
29. 

$6,750 
7,250 

$950 
1,000 

$282 
250 

i^i-\rvk«-k'«  «»■»»._          /■ 

it               • 

Narrow 
Gauge. 

$182 

100 

ICX) 


Comparison  of  the  above  table  shows  that  the  cost  of  enHn^c  Kr.  ~.  " 

rate  of  $250  per  inch  of  cylinder  diameter,  about  $'0  '^eZ  f  "'"'''  ''" 

per  extra  truck-axle;  which  are  builder^  aZroI^L       /  ^""'"^-^^^^'  ^"^  $250 

American  engine  as  the  standard  or  u^Ttypf    "^""'^  '''''''*  ''^'"'^^  ^^°™  ^^^  ^7^^ 

Comparing  the  lightest  and  heaviest  engines  of  each  tyt>e  we  finH  th.t  tT, 
on  drivers  of  extra  weight  is  but  little  over  fxoo  per  ton,  1  :  ^'  '^^ 

Standard 
American Gauge. 

Mogul,     ....'*****. ^^^ 

Consolidation, ^°° 

roads  have  been  contemplated  h  wn  .Idt.  ^  "'^  *"""  ■■»"°»'-S»"ge  rail- 

CHi:t^tt:r'-'-r~ 

>Ae  have,  therefore,  given  much  attention  to  the  subject  of  your  question      Our  . 

™.v^  h,  the  ^ater  cross.n,easu.n,ents,  is  <,ui.e Z^^Ledlr^^^^^^^^^ 
Wheel-base  enables  the  engine  to  curve  more  readilv   r.,,,^  ^^°''*^'" 

are  offered  at  the  same  price."  equivalent  narrow-gauge  engines,  and  which 

Of  engines,  and  on  the  remaining  distance  not  more  than  50  per  cent  of 
the  fuel  burned  would  vary  directly  with  the  weight  and  power  exerted 
As  an  average  of  entire  runs,  it  is  entirely  adequate  to  asspme  that  2    per 


' 


566   CHAP.  XV.^TRAIN-LOAD   ON  OPERATING  EXPENSES. 


% 


cent  of  the  total  fuel  consumption  varies  directly  with  the  weight  of  engines 
hauling  the  same  train  over  for  the  most  part  the  same  grades,  and  that 
the  remaining  75  per  cent  is  unaffected.  On  this  basis,  an  engine  20  per 
cent  heavier  would  average  for  entire  runs  not  over  5  per  cent  more  fuel 
to  liaul  the  same  trains.  The  cost  of  supplying  oil  and  water  would  vary 
in  about  the  same  proportion. 

710.  These  various  items  are  summed   up  in  the  following 
Table   175.     As  already  stated,  however,  it  is  only  under  very 
exceptional  circumstances  and  on  a  limited  scale  that  it  is  proper 
to  assume  that  differences  of  grade  can  or  will  be  overcome  in 
practice  by  the  cheap  and    apparently  simple  expedient  of   in- 
creasing the  weight  of  engines  for  freight  service,  and  on  roads 
enjoying  a  moderately  large  passenger  traffic  the  same  is  very 
nearly  true  of  passenger  trains.     The  engines  will  in  any  case  be 
made  as  powerful  as  is  deemed  feasible  or  expedient,  for  conveni- 
ence in  stopping  and  starting,  and  for  occasional  exigencies,  if  for 
nothingelse;  and  anything  which  reduces  their  hauling  capacity  at 
the  requisite  speed  between  stations  will  be  apt  to  result  directly 
or  indirectly  in  running  shorter  trains  and  more  of  them.     This  is 
far  from  an  unmixed  disadvantage  under  many  circumstances 
(par.  89),  but  nevertheless  it  is  a  real  disadvantage. 

711.  Table  175  itself  makes  clear  why  it  is  entirely  improper 
to  assume  the  use  of  heavier  engines  to  meet  the  demands  of 
heavier  grades,  by  indicating  that  there  is  always  a  great  econ- 
omy in  using  the  heaviest  engines  which  the  traffic  will  warrant. 
To  double  the  weight  of  engine  to  haul  the  same  train  will  only 
add  some  14  per  cent  to  expenses,  according  to  Table  175.  If  by 
doubling  the  weight  of  engine  we  can  also  halve  the  number  of 
trains,  we  immediately  effect  an  immense  economy  in  train-wages, 
engine  repairs,  fuel,  and  maintenance  of  way,  exceeding  more 
than  threefold  (Table  176)  the  increased  expense  per  train-mile 
due  to  the  heavier  weight  of  engine.  It  is  only  when  the  grades 
are  so  very  low  (approximating  closely  to  a  level)  that  even  a 
light  engine  can  haul  the  fifty  or  sixty  loaded  cars,  which  are 
as  many  as  can  be  conveniently  handled  with  the  present  bad 

styleof  coupling,  that  heavier  engines  can  be  legitimately  assumed 
to  meet  the  requirements  of  a  heavier  grade;  if  even  then. 


__CHAP  XV.-7KAINL0AD   ON   OPEKA  IVX^KXPENSF...    567 

Table  175. 

EST,„ATH.    AVEKACE   COST   Pkk   Tha,X-M„.E   OP    DoUBL.NG   THH   We.GHT  OP 

Engines  to  Haul  the  Same  Train. 


Item. 
(As  per  Table  80,  page  179.) 


FuqI 

Oil,  waste,  and  water. . . .... . ', 

Engine  repairs '.. 

Switching-engines *." 

Train  wages  and  supplies. ... . 
Car  maintenance  and  mileage. 

Renewals,  rails ' 

Adjusting  track 

Renewals,  ties ..**.'.' 

Earthwork,  ballast,  etc. ..  .. 

Switches  and  sidings ]  ] ' 

Bridges  and  buildings.  ....... 

Station,  terminal,  and  general. 


Average 

Cost  of  Item. 

Cents  or 

Per  Cent, 


Per  Cent  Added  by 

Doubling  Weight 

of  Engine. 


Total. 


7.6 
1.2 

5.6 

5.2 

15-4 
12.0 

2.0 
6.0 
3.0 
4.0 

2.5 

5.5 

30.0 


100. o 


25  per  cent. 

<  > 

50  per  cent. 
Unaffected. 


50  per  cent. 


Added 

Cost. 
Cents  or 
Per  Cent. 


14. 1  percent. 


1.9 

0.3 
2.8 


i.o 
30 

1-5 
2.0 

1.3 
03 


14. 1 


Perhaps  one  further  exception  should  be  made-when  thre 
traffic  ,s  so  very  light  that  it  is  not  practically  convenient  to  run 
very^heavy  trains,  as  when  it  is  less  than  three  \o  five  freight  trZ 


712.  Table  175  also  explains  why  there  is  so  great  a  tendency 

o  increase  the  weight  of  passenger  trains  by  Applying  to'e 

luxurious  accommodations.     It  is  because—  ^^  >  "^  "^^^^ 

Hght  ot7TabTe?;S'  ^"^'"^  ^°"^  ''"'  ""'^  -°-  '°  -"  '•'-  a 

2.  Coal  consumption  is  but  little  increased  by  material  differ- 
ences in  the  weight  of  cars  (par.  ,29)  ^  ^^ 

untn  ?yr^u     ""^"^  ''"'  ""■'  '"""^"^  "P°"    passenger  trains 
unt  1  they  become  very  long  (par.  397  et  seg.),  and  by  slight  re 

ca„r::7'°"'r"''^^'^''"''«'-^'''-«-'°f -creased  Light 
as"te    doT  'in     "  """"^^  ^''^"'^  '">'  -""'"^  -"-'- 


I  mi 


568  C//AP.  XV.—  TRAI^-LOAD   ON  OPERATING  EXPENSES. 


CHAP.  XV.^TRAINLOAD   ON  OPERATING  EXPENSES.  569 


4.  It  encourages  traffic  to  run  more  passenger  trains  (par.  89), 
and  discourages  it  materially  to  attempt  to  crowd  the  traffic  upon 
a  few  trains. 

5.  And  more  important  than  all,  the  increased  luxury  is  a 
great  attraction  to  travel,  and  added  travel  thus  secured  is  of 
immense  value  to  the  property  (pars.  37-40- 

713.  The  cost  of  increasing  the  number  of  engines  to  haul 
THE  SAME  TRAFFIC,  OH  account  of  E  heavier  grade,  may  be  estimated  as 

follows : 

The  number  of  trains  is  supposed  to  be  increased  by  a  change  of  maxi- 
mum grade  only,  which  will  not  ordinarily  extend  over  one  third  of  the 
distance.  While  running  over  the  remaining  distance,  the  work  done  on 
the  train  behind  the  engine  will  vary  according  to  the  weight  or  number 
of  cars.  While  running  on  the  maximum  grade  the  power  exerted  by  the 
engine  will  be  the  same,  since  in  each  case  the  engine  is  supposed  to  be 
fully  loaded  on  that  grade. 

714.  Fuel.— For  reasons  already  enumerated  (par.  344),  about  one 
half  of  the  consumption  of  fuel  will  vary  directly  with  the  tonnage  of  the 
train ;  the  other  half,  consisting  of  the  fuel  burned  in  stopping  and  start- 
ing (in  part),  getting  up  steam,  loss  by  radiation,  loss  by  head  resistance, 
etc.,  making  up  in  the  aggregate  the  50  per  cent  which  is  unaffected  by 
the  length  of  the  train. 

If,  therefore,  the  maximum  grade  be  increased  on  about  one  third  the 
length  of  the  road,  while  on  the  remainder  the  grades  remain  about  the 
same,  about  half  the  consumption  on  two  thirds  of  the  distance,  equal  to 
all  the  consumption  on  one  third  of  the  distance,  or  33  per  cent  of  the 
entire  consumption  will  vary  directly  with  the  net  weight  of  the  train  ;  so 
that,  if  the  grade  were  so  increased  as  to  take  two  locomotives  instead  of 
one  to  handle  the  same  traffic,  the  fuel  consumption  would  be  as  i.o  to 
1.67  at  most,  and  not  as  i.oto  2.0,  as  might  be  over-hastily  assumed. 
The  aggregate  cost  of  oil,  waste,  and  water  will  vary  in  about  the  same 

proportion. 

715.  Train-wages  will  of  course  vary  directly  with  the  number  of 
trains,  unless  the  change  of  grade  in  contemplation  were  so  great  as  to 
shorten  up  trains  so  as  to  dispense  with  one  brakeman,  which  can  rarely 

happen. 

716.  Station,  terminal,  and  general  expenses  will  remain  unaf- 
fected by  any  moderate  change,  but  there  is  nothing  by  which  they  are 
so  quickly  affected  as  by  a  decided  increase  in  the  number  of  trains,  and 


a  full  20  per  cent  of  their  aggregate  may  be  considered  as  varying  directly 
therewith. 

717.  Of  the  cost  of  maintenance  of  way  we  cannot  directly  account 
for  an  increase  of  more  than  one  half  to  two  thirds  as  a  result  of  doubling 

theenginemileage,  the  car-mileage  remainingconstant;  but  the  facts  given 
in  par.  125  and  its  accompanying  Tables  41-44  indicate  that  there  is  an  in- 
direct effect  from  multiplication  of  the  number  of  trains  which  seems  to 
cause  all  expenses  for  maintenance  of  way  to  increase  pari  passu  there- 
with, including  some  items,  such  as  those  for  policing,  maintenance  of 
ballast,  road-bed.  and  ties,  etc.,  etc.,  which  should  be  affected  but  little, 
if  any,  apparently,  by  the  precise  number  of  trains  over  the  road.    It  is  to  be 
remembered,  in  considering  the  tables  referred  to,  that  during  the  years 
which  they  cover  the  weight  as  well  as  the  number  of  trains  has  increased 
enormously,  which  should  naturally  tend  to  keep  maintenance  of  way  per 
train-mile  at  a  high  figure  ;  but  after  making  all  allowances  for  this  differ- 
ence, the  chief  cause  for  the  singularly  constant  ratio  of  increase  in  main- 
tenance of  way  and  maintenance  of  rollmg-stock  is  probably  this  :  A  con- 
tinually advancing  standard  of  maintenance  is  indispensable  as  the  volume 
of  traffic  increases,  and  the  cost  of  each  step  toward  perfection  increases 
about  as  the  square  of  the  number  of  steps.     A  very  slight  expenditure 
suffices  to  make  track  good  enough   for  the  passage  of  one  train  a  day. 
A  slight  addition  suffices  for  two  or  three  trains  a  day,  and  makes  a  great 
improvement  in  the  condition  of  the  track.    A  much  greater  expenditure 
is  necessary  to  fit  the  track  for  ten  trains  a  day,  and  yet  the  visible  ad- 
vance in  condition  is  much  less ;  and,  finally,  as  we  get  up  to  thirty  or 
forty  or  fifty  trains  a  day.  a  very  great  additional  expenditure  is  found 
necessary— or  at  least  expedient— although  the  visible  advance  of  condi- 
tion is  very  small.     At  any  rate,  the  fact  seems  to  be  that  even  in  so  ex- 
treme an  advance  as  from  six  trains  a  day  to  sixty  (see  top  of  page  128), 
the  cost  of  maintenance  of  way  per  train-mile  does  not  decrease,  but 
Tather  the  total  cost  per  mile  of  road  increases  tenfold  with  the  number 
•of  trains. 

718.  Investigation  clearly  indicates  this  to  be  the  fact.  We  are 
therefore  not  justified  in  going  behind  it,  to  see  whether  we  can  explain 
It,  but  must  take  it  as  it  is.  If  we  do  sj,  we  are  compelled  to  estimate 
that  if  by  a  change  of  grade  we  should  double  the  engine  mileage  needed 
^or  handlmg  the  same  tonnage,  we  should  also  double  the  entire  cost  of 
maintenance  of  way.  Making  a  concession  of  somewhat  doubtful  pro- 
priety to  the  fact  that  the  car-mileage  would  remain  the  same,  we  may  ex- 
clude the  cost  of  bridges  and  buildings  as  unaffected;  but  this  is  the  most 


mmm 


mm 


570  CHAP.  XV.—  TRAIN-LOAD   ON  OPERATING  EXPENSES. 


which  can  be  done.  Statistics  do  not  seem  to  indicate  that  the  total  cost 
per  train-mile  on  roads  which  handle  light  trains  is  sensibly  less  than  on 
roads  which  handle  heavy  trains. 

719.  Engine  repairs  should  apparently  vary  directly  with  the  miles 
run  ;  but  the  indications  are  (Table  42  et  al.)  that  as  a  matter  of  fact  it  is 
much  less  likely  to  do  so  than  maintenance  of  way,  owing  in  part  to  the 
large  proportion  of  incidental  expenses  (see  Table  57),  which  are  not  by  any 
means  doubled  to  maintain  a  double  number  of  engines.    There  will  also- 
be  a  certain  diminution  of  wear  and  tear  from  stopping  and  starting,  etc. 
(see  Table  85,  page  203),  from  the  fact  that  the  trains  to  be  handled  are- 
shorter.     Taking  both  of  these  causes  together,  it  is  not  probable  that 
doubling  the  number  of  engines  to  move  the  same  number  of  cars  would 
increase  engine  repairs  in  the  ratio  of  more  than  i.oo  to  1.75,  and  prol>- 
ably  somewhat  less. 

720.  Car  repairs  are  certainly  affected  beneficially  by  having  a  less^ 
number  of  cars  to  a  train.  By  referring  to  Table  86  (page  203)  it  will  be 
seen  that  more  than  one  third  of  the  total  cost  of  car  repairs  can  be  di- 
rectly traced  to  the  concussions  of  stopping  and  starting  and  making  up- 
trains.  Much  of  this  expense  may  disappear  with  the  introduction  of 
better  couplers ;  but  even  this  is  doubtful,  as  an  automatic  coupler  will 
permit  of  much  more  violence  in  running  cars  together,  since  a  brake- 
man's  life  between  the  cars  will  no  longer  have  to  be  considered.  A 
diminution  of  at  least  10  per  cent  may  fairly  be  estimated  as  a  result  of 
running  only  half  as  long  trains. 

721.  To  these  expenses,  properly  so  called,  is  to  be  added  an  inter- 
est charge  on  the  cost  of  the  additional  motive-power  re- 
quired by  the  higher  grade,  unless  the  first  cost  of  these  engines  be  in- 
cluded in  the  estimated  cost  of  constructing  the  higher  grade-line,  before 
determining  the  difference  in  the  capital  investment. 

This  should  be  done  because  the  addition  of  the  required  number  of 
engines  is  really  so  much  added  to  the  original  investment.  Before  tiie 
line  is  ready  to  handle  the  required  traffic  it  is  as  necessary  to  have  them 
as  it  is  to  have  the  track  laid  on  the  high  grade-line  and  not  on  the- 
other.  In  considering  differences  of  distance  (if  not  too  great),  orcurva-^ 
ture,  or  rise  and  fall,  this  is  not  so.  The  total  amount  of  equipment  will 
be  the  same  whatever  the  differences  in  that  respect.  We  therefore  es- 
timate the  expenses  regardless  of  interest  on  the  plant,  and  only  consider 
differences  in  the  cost  of  construction.  Of  the  car  equipment  the  same 
is  true  in  the  case  of  gradients.  Whatever  the  grades,  the  number  of 
cars  will  be  the  same  ;  but  as  the  number  of  engines  is  increased  because 


CHAP.  XV.- TRAIN  LOAD   ON  OPERATING  EXPENSES.  S7l 

of  the  grades,  and  not  for  any  ^^^^^^^^^fZ^f^^^ 
he  difference  m  the  cost  of  equipment  as  a  part  of  the  cost  of  construe! 
t.on,  or  add  an  interest  charge  to  expenses.     On  the  whole,  it  is  more 
convenient  to  add  the  interest  charge. 

722.  Putting  together  all  these  items  which  have  been  lust 
considered,  we  obtain  the  summary  given  in  Table  176,  as  the 
effect  on  operating  expenses  of  so  increasing  the  rate  of  grade 
as  to  double  the   number  of  engines  required  to  handle  a  given 

Table  176. 

Estimated  Average  Cost  Per  Train-Mile,  of  Doubling  th«  Nnmh.      r 
Trains  TO    Handle   a    Given   Traffic-    op    p"°"°""e^  *"«  Number  of 

iKAFFic,    OR    Proportion    of    Expfk<;i?c 
WHICH  Varies  Directly  with  the  Number  of  Trains    the  0^1x0^ 

NAGE   REMAIViKn-    r.^vTc-.K,^  iKAiwb,    THE    CAR- TON- 


NAGE  REMAINING   CONSTANT 
[The  percentage  by  which  any  i 
(or  weight  of  engines)  to  be  increased,  is  give^'in'TaWes  "17^  'and '178.] 


tl"!.^.?"*^.^^  '^  "^'^^  -y  ^--  change  of  grade  will  require  the  number  of  trains- 


Item. 
(As  per  Table  80,  page  179.) 


Fuel 

Oil,  waste,  and  water 

Engine  repairs 

Switching  engines 

Train  wages  and  supplies. . . . . 
Car  maintenance  and  mileage. 

Renewals,  rails 

Adjusting  track 

Renewals,  lies *  *  . 

Earthwork,  ballast,  etc... ... . 

Switches  and  si'Hngs ' 

Bridges  and  buildings. . '.  *.  *.*.'.'. 
Station,  terminal,  and  general! 

Total  of  operating  items. . 


Average 

Cost  of  Item. 

Cents  or 

Per  Cent. 


Per  Cent  Added  by 

Doubling  Number 

of  Trains. 


7.6 
1.2 
5.6 

5.2 

15.4 
12.0 

2.0 

6.0 

4.0 
2.5 

30.0 


100. 0 


67  per  cent. 

75  per  cent. 

Unaffected. 

100  per  cent. 

10  p.  c.  /ess. 

100  per  cent. 
«« 

«« 

<( 

<< 

Unaffected. 
20  per  cent. 


47-8  per  cent. 


Added 

Cost. 
Cents  or 
Per  Cent. 


5.1 
0.8 
4.2 

•    •    •    • 

15.4 
-1.2) 
2.0 
6.0 
30 
4.0 
2.5 

•    •    •    • 

6.0 


Toth 


is  is  to  be  added  the  interest  on  the  cost  of 


47.8 


'^   ^^^   average  passenger-engine   miieaaf*   tr^    k« 
40,000  m.les  per  year,  .e  have,  as  thf  interlst  chT^^et'per  mile? 


Making  the  grand  total. 


1-7 


49.5 


572  CHAP.  XV.— TRAIN-LOAD   ON  OPERATING  EXPENSES. 

traffic.  When  and  if  it  can  fairly  be  assumed  that  the  weight  of 
engines  can  be  increased  instead  (par.  711),  Table  175  gives  the 
percentage  of  increase  in  expenses. 

723.  In  the  former  edition  of  this  work,  this  summary  was  materially  dif- 
ferent, especially  as  respects  the  effect  of  increasing  the  weight  of  engines,  as 
shown  in  the  following  Table  177.  The  cause  of  the  discordance  'is  simply  the 
change  in  conditions,  in  the  writer's  view,  and  not  that  either  is  essentially  in- 
correct. 

Table  177. 

Estimated  Cost  of  Doubling  the  Engine-Tonnage  for  the  same  Car- 
Tonnage  USED  IN  THE   FORMER   EDITION  OF  THIS  TREATISE. 
[For  statistics  based  for  the  most  part  on  iron-rail  track.] 


Total 

Cost. 

Cts.  or 

Per  Cent. 

For  a  Double  Number 
OF  Engines. 

For  a  Double  Weight 
OF  Engines. 

Items. 

Percent  increas- 
ing with  Number 
of  Engines. 

Added 
Cost. 

Percent  increas- 
ing with  Weight 
of  Engines. 

Added 
Cost. 

Fuel 

lO.O 

2.0 
9.0 

13. 0 

13.0 

7.0 

7.0 

30.0 

90  per  cent. 
.      90    "      " 
90    "      " 
90    "      " 
100   "      " 
100    "      •' 
Included  above. 
Unaffected. 

9.0 

-     31. 0 

13.0 
7.0 

•    •    •    • 

50  per  cent. 

r  50  "     " 
]    33  "     " 

[   Unaffected. 

200  per  cent. 

100    "      " 
Included  above. 

Unaffected. 

50 

Oil,  waste,  etc 

Engine  repairs 

30 

Train-wacres 

Track  reoairs 

*>f\    Ck 

Road-bed  repairs 

7.0 

•  •  >  • 

•  •  •  • 

Yards  and  structure 

General  and  station 

Totals  

100. 0 

50  p>er  cent. 

50.0 

42  per  cent. 

42.0 

Assumed  average^  48  cents  per  train-mile,  or  48  per  cent  of  operating  expenses. 

724.  Assuming  that  under  all  ordinary  circumstances,  for 
moderate  changes  of  grade,  any  increase  must  be  met  by  an  in- 
crease in  the  number  and  not  in  the  weight  of  engines,  we  have 
49.5  cents  per  train-mile,  or  49.5  per  cent  of  operating  expenses, 
as  the  portion  of  the  total  expenses  which  will  vary  with  increase 
of  engine-mileage  to  handle  the  same  business,  which  is  not  far 
from  the  cost  of  running  an  engine  light,  as  it  should  be. 

Multiplying  this  amount  by  365  X  2,  we  have 

$0,495  X  365  X  2  =$361.35 

as  the  yearly  sum  per  daily  train  per  mile  of  road  which  varies  di- 
rectly with  an  increase  of  engine-tonnage  for   the  same  traffic. 


CHAP.  XV.—  TRAINLOAD   ON  OPERATING  EXPENSES.   57$ 

If,  now,  we  multiply  tliis  sum  by  the  percentage  of  the  in- 
crease in  engine-mileage  RESULTING  FROM  AN  INCREASE  OF  O.  I 
PER  CENT  in  any  ruling  grade,  we  shall  obtain  the  cost  per  daily 
train  per  mile  of  road  of  such  increase.  In  other  words,  we  ob- 
tain the  cost  per  train  of  increasing  the  number  of  trains  to  han- 
dle the  same  fixed  tonnage,  or  the  saving  per  train  by  decreasing 
that  number;  i.e.,  we  obtain  the  cost  of  using  i.i,  1.2,  1.5,  or 
2.0  trains,  instead  of  one,  to  handle  a  given  tonnage,  or  the  sav- 
ing by  using  0.9,  0.8,  or  0.6.  That  cost  or  saving  is  given  in 
Table  178,  and  when  multiplied  by  the  estimated  number  of  the 
trains  on  the  grade  for  which  the  traffic  was  estimated,  it  gives 
the  total  cost  or  saving. 

725.  The  cost  thus  obtained  is  not  an  absolute  value,  inde- 
pendent of  the  length  of  the  road,  as  in  the  case  of  the  similar 
values  deduced   for  distance  (Tables   ^^,  89),  curvature  (Table 
115),  or  rise  and  fall  (Table  124),  but  varies  with  the  length  of 
the  road  or  division,  inasmuch  as  the  ruling  grade  increases  the 
cost  of  operating  the  entire  road,  whatever  the  length  of  the  rul- 
ing  grade  itself  may  be.     Hence,  to  obtain  the  true  value  of  re- 
ducing grade,  it  must  be  multiplied  by  the  length  of  the  road. 
It  may  appear  that  it  should  be   multiplied   bv,  not  the  actual 
but,  the  equated  length,  according  to  pars.  195I9,  since  we  have 
there   seen   that   10    per    cent  more    distance  does    not  by  any 
means  add   10  per  cent  to  operating  expenses.      But  whife  this 
view  is  in  a  sense  correct,  yet  the  items  which  vary  with  a  change 
of  grade  vary  so  nearly  with  distance  likewise,  that  it  would  lead 
us  too  far  to  attempt  any  more  accurate  process  of  equating. 

726.  The  cost  per  year  in  Table  178,  divided  by  the  rate  of 
interest  on  capital,  0.06,  0.07,  etc.,  will  give  the  capitalized 
value  per  daily  train  of  avoiding  an  addition  of  o.i  per  cent  to 
the  ruling  grade.  Thus,  to  avoid  an  increase  of  o.i  per  cent  in 
a  10  ruling  grade,  at  6  per  cent  on  capital,  and  for  a  division  100 
miles  long,  we  have 


$2927       ^ 

-^-^  =  $48,873  per  daily  train, 


4.V 


11 


574  CHAP.  XV.^TRAIaW.LOAD    on  opera  TJ  AG  EXPENSES. 

Table  178, 

Estimated   Value  per   Daily   Train    of   Avoiding  an  Addition  of  O.i 
Per  Cent  (5.28  Feet  Per  Mile)  to  the  Rate  of  any  Ruling  Grade. 

[Cost  per  train-mile  assumed  at  $1.00.] 


i 

Rate  of 

Gkadk  to 

Bu  Changed. 

Per  Cent  of 

Increase  in 

Enjf.  Mileage 

lor  Each  o.i 

Per  Cent 

Added  10  the 

Grade  (from 

Table  171). 

Cos*  Per  Year  Per  O.I  Per 
Cent  Increase  in  Grade. 

Relative  No.  of 

Trains  to 

Haul  Same 

Traffic. 

Per  Daily  Train 

=  Preceding 
Per  Cent 

X  S361.35 
X  icx>  Miles. 

Per  looo  Ton- 
Miles  Daily  of 
Cart  and   Load 

as  per 
Table  170. 

Relative 
N^t  Load. 

Level 

25-9 

$9359 

$17.50 

1. 00 

100.00 

O.I 

0.2 
0.3 
0.4 

0.5 

0.6 

0.7 
0.8 
0.9 

20.9 

17.5 
15- 1 

13-3 
II. 9 

10.8 

9.8 
9-2 

8.5 

7.552 

6353 
5.456 

4.806 
4.300 

3.903 

3.541 
3  324 
3.072 

17-77 
18.03 
18.23 

18.48 

18.75 
19.03 

19  34 
19.74 
20.12 

1.26 
1.52 
1.79 

2.06 

2.33 
2.61 

2.89 
3-18 

3-47 

79-44 
65.72 

55-93 

48.60 
42.88 
38.32 

34.58 
31.48 
28.82 

I.O 

8.1 

2927 

20.38 

3-76 

26.58 

1.2 
1.4 

1.6 

1.8 
2.0 
2.2 

2.4 
2.6 

2.8 

7.0 

6.3 

5-8 

5-5 
5.1 
4.8 

4-6 

4-4 
4.2 

2.530 
2.277 
2.096 

1987 
1.843 

1.734 

1.662 
I  590 

1. 518 

20.87 

21.43 
22.26 

23.18 
24.26 
25.22 

26.23 
27.22 

28.21 

4  37 
4.99 
5-63 

6.29 
6.98 
7-69 

8.41 
9.16 
9-94 

22.88 
20.04 
17.76 

15.89 
14.32 

1301 

11.89 
10.92 
10.06 

3-0 

4.0 

1.445 

29.02 

10.74 

9-31 

3.5 
4.0 

50 

3.6 

3-4 
3.2 

1. 301 
1,229 

1. 156 

31.42 

35  10 
44.82 

12.92 
15.29 

20.74 

7.74 
6-55 

4.82 

Comparison  of  the  third  and  fourth  columns  will  show  that  while  the  cost 
per  daily  train  of  a  given  increase  of  grade  is  much  less  on  the  higher  grades,  because 
the  number  of  trains  is  so  much  greater,  yet  that  the  cost  per  unit  of  traffic  is  greater  as 
the  grades  are  higher,  as  it  naturally  should  be. 


CHAP.  XV.—  TRAIN.LOAD   ON  OPERATING  EXPENSES.   575 

THE  third  column  in  this  table  is  computed  for  a  division  100  miles 
long.  For  a  greater  or  less  length,  increase  in  direct  ratio  with  the  length.  Letting 
C  =  the  sum  thus  obtained,  we  have 

c  X  number  daily  trains  (each  way)  x  tenths  per  cent  of  change  of  grade 

rate  of  interest  on  capital  (0.06,  0.07,  etc.)  '  '  = 

capitalized  value  of  any  increase  or  decrease  in  the  rate  of  the  given  ruling  grade,  approx- 
imately.  For  greater  exactitude,  determine  the  correct  percentage  for  the  given  change 
of  grade  from  Table  171 ;  or,  for  still  greater  exactitude  compute  the  percentage  from  the 
train-loads  given  in  Table  170  for  the  two  given  grades  and  the  given  type  of  engine. 

The  fourth  column  is  independent  of  the  length  of  the  division,  and  may  be  de- 
duced from  the  third  column  by  dividing  it  by  the  total  weight  of  train  as  given  in  Table 
170,  X  aoo  +  1000. 

or,  for  the  moderate  traffic  of  10  daily  trains  per  day  (each  way 
in  all  cases),  $487,833. 

If  the  division  be  no,  no,  or  150  miles  long,  this  sum,  multi- 
plied  by  i.io,  1.20,  or  1.50,  will  give  the  capitalized  value,  as 
nearly  as  may  be.  If  the  change  in  grade  be  0.2  or  0.3  per  cent 
the  capitalized  value  will  be  again  increased  in  proportion! 
Thus,  if  the  division  be  150  miles  long,  and  the  comparison  be 
between  a  i.o  and  1.5  grade,  we  have 

$487,833  X  1.5  X  5  =  $3,658,750 
as  the  approximate  justifiable  expenditure  for  avoiding  the  in- 
crease, for  10  trains  per  day  and   at  $1  00  per  train-mile.     For 
greater  exactness  see  note  to  Table  178,  above. 

727.  Several  recent  French  and  German  estimates  of  the  value  of  reducing 
grades  might  be  given,  which  do  not  differ  radically  from  the  preceding  except 
in  the  constants  assumed;  in  which  latter  respect  they  do  differ  radically 
Table  179  gives  one  of  the  most  recent  and  most  nearly  correct  of  such  esti- 
mates.  1  here  are  no  estimates  in  English  known  to  the  writer,  of  an  at  all 
reliable  character. 

728.  The  greatly  inferior  loads  hauled  on  foreign  railways  compared  with 
American  practice  is  conspicuously  brought  out  in  this  table.  An  American 
engine  wiih  40  tons  on  the  drivers  will  haul  in  daily  practice  (Table  170), 

^                       .  "Toos.  Tonnes. 

On  a  0.5  grade 1041  )  Against  French  (  487 

On  a  2.0  grade, 347  (    by  Table  179.    (  131 

The  French  loads  are  explicitly  stated  to  be  based  on  velocities  of  25  kilos 
per  hour,  and  indicate  to  an  American  eye  very  bad  administration. 


57^  CHAP.  XV.-^TRAIN-LOAD  ON  OPERATING  EXPENSES. 

Table  179. 
Estimate  of  the  Value  of  Reducing  Grades  on  French  Railways. 

[By  M.  Ricour,  Ing.  en  Chef,  Corps  des  Fonts  et  Chauss^s.     Abstracted  from  the  pat>er 

referred  to  in  par.  662.] 


CHAP.  XV.— TRAIN-LOAD  ON  OPERATING  EXPENSES.    577 


Grade. 

Gross  Load 

C. 

Tonnes. 

Price  per 

Tram  Kilo. 

Francs. 

Price  per 

xooo  tonnes  gross, 

per  Kilo. 

Francs. 

•4 

568 

»-54<5 

2.72          Diffs. 

•5 

487 

1-465 

3.00             .28 

.6 

.7 
.8 

.9 

425 
375 
335 
302 

1.403 
»-353 
1-313 
1.280 

330             .30 
3.60              .30 

3  9»              -31 
4.23              .32 

1.0 

274 

1.252 

4-56              -33 

x.a 

«-4 
1.6 
X.8 

230 
196 

169 

»47 

X.208 
1. 174 
1.147 
1. 123 

5-25              .36 
5  98              .37 
6.78              .39 
7-65              .46 

2.0 

131 

1.109 

8.46              .43 

The  last  column  of  this  table  x  ii7-5  (i-6i  X  0.20  X  365)  will  give  a  column  corre^ 
spending  to  the  fourth  column  of  Table  178.  No  close  correspondence  can  be  expi.cted, 
because  the  French  loads  are  so  much  less  and  decrease  so  much  more  rapidly  with  grade. 

This  table  was  computed  for  a  6-driver  engine,  36  tonnes  (39.67  tons)  on  drivers  ; 
mean  total  weight,  50  tonnes  (55.10  tons).  The  values  in  the  last  column  are  of  a  more 
general  character.  They  are  independent  of  the  weight  of  the  engine — at  least  within 
the  limits  of  usual  French  practice. 

THE  PROPORTION  OF  TRAFFIC  AFFECTED  BY  THE  RATE  OF 

RULING  GRADE. 

729.  According  to  the  character  of  the  road,  this  may  vary 
under  certain  conceivable  circumstances  between  the  extreme 
limits  of  o  and  loo  per  cent,  for  both  passenger  and  freight 
traffic.  Freight  traffic  is  by  far  the  most  affected,  but  there  are 
at  least  occasional  instances  in  which  the  freight  traffic  is  so 
light  and  so  little  liable  to  grow  that  no  appreciable  value 
whatever  can  be  assigned  to  reduction  of  grades  below  a  cer- 
tain limit.  For,  as  the  whole  objection  to  gradients,  properly 
so  called,  lies  in  their  effect  to  limit  the  length  of  trains,  a  re- 


duction of  their  rate  has  value  only  for  such  trains  as  they  do  ia 
fact  so  limit.  One  train  at  least,  the  "■  way  freight,"  is  very 
often  not  so  limited  on  all  railways,  and  many  minor  railwavs 
are  not  so  fortunate  as  to  run  anything  else  but  way  freights 
over  tlieir  lines. 

730.  Nevertheless,  as  a  rule,  both  the  way  freight  and  all  other 
freight  trains  vary  in  length  directly  with  the  de-facto  gradients, 
and  should  be  assumed  to  do  so.  This  does  not  at  all  assume 
that  all  trains  will  be  fully  loaded,  for  that  is  not  a  practicable 
result,  but  simply  that  the  percentage  of  power  wasted  to 
power  utilized  will  be  sensibly  the  same  for  all  grades  and 
lengths  of  trains,  or  nearly  enough  so  for  all  practical  purposes. 
If  so,  it  necessarily  results  that  the  percentage  of  increase  in 
trains  will  be  much  the  same,  whether  they  are  fully  loaded  or 
not. 

731.  As  respects  passenger  business  (see  par.  %^),  although 
it  is  much  less  directly  and  immediately  affected  by  a  change 
of  grade  than  freight  traffic,  because  of  the  higher  speed,  and 
the    large   surplus   of    motive-power    required  therefor  and   for 
stopping  and   starting,  yet  in  the  long-run,  whenever  the  pas- 
senger business  becomes  considerable  in  volume  or  largely  com- 
petitive, either  the  number  or  the  weight  of  passenger  engines 
must  be  materially  affected  by  the  rate  of  grade.     The  effect   in 
the  case  of  passenger  traffic  is  far  more  irregular,  but  not  there- 
fore the  less  certain.     A  train,  for  example,  might  haul  an  extra 
car  or  two  over  any  given  grades,  or  haul  the  same  cars  over  a 
heavier  grade,  as  well  as  not,  when  the  addition  of  yet  another 
car  to  the  train  of  say  ten  cars  might  require  it  to  be  cut  in  two, 
and  so   immediately  double   the   motive-power  required   by  in- 
creasing the  load  hauled  only  ten  per  cent.     It  is  certain,  more- 
over, that,  whatever  the  margin  of  power  deemed   necessary  for 
emergencies,  if  we  reduce  our  grades  and  train  resistance  by 
any    fixed  amount,    the   weight  of   engines    may  always  be    re- 
duced, or  the  weight  of  train  increased,  in  the  same  proportion, 
and  yet  leave  the  same  margin   for  emergencies  or  anticipated 
growth  of  traffic  as  before,  however  much  or  little  that  may  be. 

37 


578    CHAP,  XV.—TRAIN-LOAD  ON  OPERATING  EXPENSES, 


Hence  a  reduction  of  ruling  grade  has  a  positive  and  present 
cash  value,  even  if  every  passenger  train  on  the  road  will  habit- 
ually run  light  for  an  indefinite  number  of  years. 

732.  But  this  value  will  be  but  small  when  the  passenger 
traffic  will  be  light  during  the  first  few  years  after  construction 
(par.  84)  or  when  the  traffic  is  not  exacting  as  respects  speed,  or 
both,  for  the  reason  that  the  effect  of  any  ordinary  increase  of 
grade,  not  sufficient  to  imply  pushers  for  passenger  as  well  as 
freight  trains,  may  frequently  be  eliminated  by  a  moderate  re- 
duction of  speed  between  stations.  The  limits  within  which 
this  is  certainly  and  readily  possible  may  be  determined  as 
follows  : 

733.  In  Table  180  are  given  the  grades  of  repose  for  various 
passenger  trains  at  various  speeds,  determined  from  the  com- 
puted resistances  in  pounds  per  ton  in  Table  166  by  simply 
dividing  them  by  twenty.  The  limits  of  ordinary  passenger 
trains  are  from  four  to  twelve  cars,  but  the  table  extends  from 
no  cars  at  all  to  sixteen. 

These  so-called  "  grades  of  repose  "  (see  definition  in  par.  384) 
are  grades  equivalent  to  the  addition  which  the  train  resist- 
ance makes  to  the  actual  plus  or  minus  grade  resistance.  Sub- 
tracting them  one  from  another,  as  is  done  in  Table  180  B,  we 

have  THE  AMOUNT  BY  WHICH  THE  GRADE  IS  IN    EFFECT  REDUCED  BY 

REDUCING  SPEED  by  a  Certain  number  of  miles  per  hour.  If, 
then,  it  be  admissible  to  consider  the  speed  of  a  4-car  train  to 
be  reduced  from  thirty  miles  per  hour  to  fifteen  or  twenty  miles, 
we  can  (Table  181)  use  a  grade — 

o.  19  -|-  0.16  -|-o.  13  =  0.48  per  cent, 

or  0.19  +  o«^6  =  0.35  per  cent  higher  than  if  a  speed  of  thirty 
miles  per  hour  were  essential  on  the  grade  as  well  as  elsewhere. 
We  shall  shortly  see  (Table  183)  that  the  loss  of  time  in  so  do- 
ing is  less  than  is  often  supposed.  When  to  this  is  added  the 
relief  gained  by  momentum  if  the  foot  of  the  grade  can  be  ap- 
proached at  thirty  or  forty  or  fifty  miles  per  hour  (Table  118 
and  par.  408)   we  have  considerable  lee-way  in  respect  to  pas- 


CHAP.  XV-TRAm.LOAD  ON  OPERATING  EXPENSES.    579 


Table  180. 

Grades  of  Repose  for  Passenger  Trains  of  Various  Ungths  at 

Various  Speeds. 

[17  X  ^  American  engine,  averaging  .5  ton.  each.    Ac»rfi„g  .0  the  fonnul.  given 

in  Table  i66.]  ^ 


[For 

grades  of  repose  of  freight  trains, 

see  Table  120.] 

Kind  of  Train. 

Weight 
Tons. 

Grades  of  Repose,  Per  Cent,  for  Velocities  in  ] 

VfiLEs  Per  Hour. 

15 

20 

25 

30 

40 

50 

60 

6.03 
3.62 
2.81 

2.12 
1.89 

'•74 

70 

Engine  only 

and  2  cars.. 

"      "     4  cars.. 
"      "     Scars.. 
*•      "  12  cars.. 
"      "  16  cars.. 

56 
112 
168 
280 

39a 
504 

0.60 

0-45 
0.40 
0.36 
0.34 
0-33 

0.88 
0.62 
0.52 
0.46 
0.42 
0.41 

1.24 

0.83 
0.69 
0.58 

053 
0.50 

1.69 
1.08 
0.88 

0-73 
0.65 
0.62 

2.81 

»-74 

1.38 
1. 10 
0.98 
0.91 

4.26 
2.58 
2.02 
1.58 

1-39 
1.28 

8.12 
4.83 

3-74 
2.87 
2.49 
2.28 

Table  tSOB. 
Increase  of  Grade  which  will  be  Compensated  for  i^v  a  p. 

[Deduced  by  subtracting  each  of  the  grades  of  repose  from  the  next  higher.] 


Kind  of  Train 


Reduction  of  Equivalent  Grade  bv  Reducing  Speed  from- 


25  to  20     30  to  25 


£ngine  only 

and  2  cars. 
*'     4  cars. , 
"     8  cars. . 


«( 


12  can. 
16  can. 


0.28 
0.17 
0.13 

O.IO 

0.08 
0.08 


0.46 
0.21 
0.16 
0.12 

O.II 

0.09 


o  45 
0.25 
0.19 
CIS 
0.12 
0.12 


40  to  30 


1.12 
0.66 
0.50 
0.37 
0.33 
0.29 


50  to  40 


60  to  50 


1-45 
0.84 
0.65 
0.48 
0.41 
0.37 


I 


1.77 
1.04 
0.78 

0-54 
0.50 
0.46 


70  to  60 


2.09 
z  21 
0-93 
0-75 
0.60 

054 


*.^uttthr^ttn*:ri^vr^"^.--T— ^^^ 

"early  large  enough  to  fully  .^presertl^e  Zht^fn'     «   ''"  /  "'''^'"  ""*'  "-^^  "«  "<" 
greater  cylinder  and  boiler  ^we^oTt;Venyn:trer1;:r(;^.;;7 


58o   CHAP.  XV.— TRAIN-LOAD   ON  OPERATING  EXPENSES. 


Wife' 

"I 


senger  trains  before  certain  differences  of  grade  may  materially 
affect  them. 

734.  This  assumes  that  there  are  no  stops  made  or  to  be  made  on  the  grade- 
without  ample  reduction  of  grade  at  the  stopping  point,  the  train  which  can  be 
started  promptly  being  for  the  most  part  the  limiting  cause  to  the  length  of 
passenger  trains.  The  ultimate  limits  of  the  possibility  of  eliminating  the  effect 
of  grades  by  reduction  of  speed  must  be  determined  a  little  differently  from  the 
above,  and  may  be  more  appropriately  given  in  Chapter  XX. 

735.  Keeping  all  these  considerations  in  view,  the  effect  of 
change  of  grade  on  passenger  traffic  may  be  summarizes  as  fol- 
lows: 

For  roads  having  considerable  passenger  traffic,  say  over 
four  or  five  trains  per  day  each  way,  the  passenger  trains  will  be 
affected  essentially  as  freight  trains  are,  unless  the  ruliug  grades 
are  short  and  undulating,  and  the  estimated  number  of  each- 
class  of  trains  should  be  added  together. 

For  roads  having  only  one  or  two  light  passenger  trains  per 
day  run  at  no  very  exacting  speed,  the  passenger  traffic  may 
not  be  affected  at  all  by  a  moderate  change  of  grade.  Whether 
it  is  likely  to  be  or  not,  must  be  determined  by  Tables  i8o  and. 

i8i. 

For  such  ordinary  passenger  traffic  as  most  new  American 
roads  look  forward  to  in  the  near  future,  say  from  two  to  five 
trains  per  day,  half  the  estimated  number  of  passenger  trains 
may  be  added  to  the  freight,  for  estimating  the  value  of  reduc- 
ing grade,  for  the  reason  that  at  least  half  the  trains  are  liable 
to  be  affected  by  the  gradients. 

736.  The  tendency  to  increasing  luxury  in  first-class  passenger 
travel  has  been  already  alluded  to  in  par.  712.  An  opposite  ten- 
dency has  begun  to  show  itself,  which  will  tend  to  still  further 
increase  the  effect  of  grades  on  passenger  traflfic — a  kind  of  third- 
class  traffic  carried  at  low  rates  but  in  large  numbers.  It  is 
probable  that  before  many  years  the  mutual  interests  of  the  rail- 
ways and  the  public  will  compel  a  large  extension  of  this  class  of 
traffic,  and  favorable  grades  for  passenger  service  will  then  be  a 
factor  of  great  importance. 

737.  As  an  example  of  the  great  comparative  importance  of 


CHAP.  XV.— RULING   GRADE  AND  MINOR  DETAILS.     58 1 


Jovv  grades,  we  may  now  profitably  refer  back  to  Chap.  X.,  the 
iissumptions  made  in  which  we  have  just  substantiated.  While 
such  estimates  as  are  here  made,  as  has  been  often  stated,  cannot 
be  regarded  as  positive  and  exact,  even  when  carefully  revised  to 
suit  individual  lines,  the  possible  margin  of  error  is  too  small  to 
seriously  modify,  if  corrected,  the  moral  which  they  are  calculated 
to  convey,  which  is  that  wrongly  directed  expenditure  is  at  the 
root  of  much  of  the  financial  difficulties  of  railways. 

In  the  example  referred  to  one  detail  of  occasional  importance 
has  been  neglected,  viz.: 


THE   EFFECT    OF  A    DIFFERENCE    IN    RULING    GRADE  ON   THE    COST    OF 
DISTANCE,   CURVATURE,  AND   RISE  AND   FALL. 

738.  While  we  have  seen  in  Chap.  X.  that  ordinarily,  when  two  lines 
differing  in  ruling  grade  are  to  be  compared,  the  importance  of  the  differ- 
ence in  gradients  and  in  traffic  advantages  combined  will  be  so  great  that 
such  differences  as  may  exist  in  any  or  all  the  minor  details  may  be  neg- 
lected without  affecting  the  decision,  yet  when  the  comparison  between 
two  lines  differing  in  ruling  grade  is  so  close  that  it  is  desirable  to 
determine  accurately  the  effect  of  differences  in  the  minor  details  also, 
the  difference  in  the  rate  of  the  ruling  grades  of  the  two  lines  makes  it 
necessary  to  treat  the  minor  details  somewhat  differently  from  merely 
subtracting  the  amount  of  distance,  curvature,  or  rise  and  fall  on  the  two 
lines  from  each  other,  and  computing  the  value  of  the  difference  only,  as 
we  have  done  heretofore. 

739.  Suppose  the  case  of  two  lines,  each  100  miles  long,  and  with  pre- 
cisely the  same  amount  of  curvature  and  rise  and  fall,  but  with  a  ruling 
grade  on  one  line  of  0.8  per  cent  and  on  the  other  of  1.6  per  cent.     It 
appears  at  first  sight  as  if  in  this  case,  whatever  the  amount  of  curvature 
or  rise  and  fall,  they  might  be  balanced  against  each  other  and  neglected  ; 
but  consideration  shows  this  to  be  so  far  untrue  that,  inasmuch  as  more 
trams  will  be  run  over  one  line  than  the  other,  the  cost  of  each  degree  of 
curvature  and  each  foot  of  distance  or  rise  and  fall  will  be  greater  on  one 
line  than  the  other,  so  that  the  line  having  the  heavier  gradients  will  be 
more  objectionable  in  proportion  to  the  amount  of  curvature  or  rise  and 
fall  which  there  may  be  on  both  lines  alike.     In  other  words,  just  as  there 
«  a  certain  cost  of  operating  each  train-mile  of  distance,  so  there  is  a 


582    CHAP.  XV.-RULING  GRADE  AND  MINOR  DETAILS. 


CHAP.  XV.— RULING  GRADE  AND  MINOR  DETAILS.     583 


1  ! 


certain  cost  of  operating  what  we  may  call  each  train-degree  of  curvature 
and  each  train-foot  of  rise  and  fall. 

If  therefore,  in  such  an  instance  as  that  supposed,  the  two  lines  had 
much  curvature  and  rise  and  fall,  the  money  value  in  favor  of  the  lower 
grade  would  be  considerably  greater  than  if  both  lines  alike  were  nearly 
straight  and  had  very  little  rise  and  fall. 

740.  This  diiference  of  value  should  properly  find  expression  in  a 
different  assumed  cost  per  train-mile;  and  in  estimating  the  value  of  a 
projected  improvement  to  a  line  already  in  operation  it  would  be  so  ex- 
pressed, since  the  curvature  and  rise  and  fall  would  already  have  had  its 
effect,  much  or  little  as  the  case  might  be.  to  increase  the  operating  ex- 
penses  by  which  we  gauge  the  value  of  reducing  grade. 

But  in  the  case  of  a  new  road  we  have  not  this  advantage,  inasmuch 
as  we  cannot  foresee  the  exact  cost  of  each  item  of  operatmg  expense. 
The  most  feasible  method  therefore  for  approximating  to  what  we  really 
desire,  the  difference  in  operating  expenses  per  train-mile  on  the  two 

lines,  is  this:  ,  . 

741.  First.  Estimate  the  cost  per  year  of  all  the  curvature  and  rise 
and  fall  on  the  low-grade  line  for  the  estimated  number  of  daily  trains, 
according  to  Tables  1 1 5  and  1 24.  ^    •  a 

Secondly.  Make  the  same  estimate  for  all  the  curvature  and  rise  and 
fall  on  the  high-grade  line,  for  the  estimated  increased  number  of  trains 
required  to  handle  the  same  traffic,  as  determined  by  Tables  170. 171.  and 

178. 

Thirdly.  Subtract  one  from  the  other  for  the  net  difference. 

Similarly  for  any  difference  of  distance :  If  the  high-grade  line  be  the 

longer,  the  cost  of  operating  the  extra  distance  on  the  high-grade  line 

must  be  estimated  for  the  number  of  trains  on  it;  while  if  the  low-grade 

line  be  the  longer,  by  the  same  amount  the  cost  of  operating  the  extra 

distance  must  be  estimated  for  its  smaller  number  of  trains,  and  hence 

will  be  somewhat  smaller  than  for  a  similar  excess  on  the  high-grade 

line. 

742.  There  is  this  further  caution  :  Inasmuch  as  the  traffic,  and  hence 

number  of  cars  per  day  or  per  year,  is  supposed  to  be  the  same  by  either 

Jine,  the  only  difference  being  that  shorter  trains  and  more  of  them  are 

run  over  the  high  grade,  the  same  cost  per  train-mile  cannot,  strictly 

speaking,  be  assumed  the  same  for  both  lines.    We  have  estimated  in 

Table  176  that  the  cost  of  doubling  the  number  of  trains  for  the  same 

traffic  is  49. 5  cts.  per  extra  train-mile,  or  49.5  per  cent  of  the  average  cost. 

For  a  change  of  grade  so  considerable  as  to  halve  the  number  of  cars  per 


train,  therefore,  the  relative  cost  per  train-mile  in  the  two  lines  would  be 

i.o-fo.48 
as  1. 00  to ,  or  I.  to  0.74,  and  proportionately  for  less  consider- 

able  differences  of  grade.  In  other  words,  whatever  wear  and  tear  results 
from  the  number  of  cars  moved  over  the  line,  as  well  as  the  expense  of 
loading  and  billing  the  freight  in  them,  etc.,  is  unaffected  by  the  change 
of  grades.  Whatever  is  due  to  the  engine  increases  pro  rata  with  the 
number  of  trains. 

743.  For  still  another  reason  than  those  just  mentioned,  it  can 
rarely  be  essential  to  enter  into  minutely  accurate  calculations  as 
to  the  minor  details  to  decide  on  one  line  or  the  other.  When 
the  comparison  between  two  lines  becomes  so  close  that  it  would 
otherwise  be  necessary,  the  possible  effect  of  the  two  lines  on 
volume  of  traffic  ought  alone  to  outweigh  it,  and  the  prudent  rule 
becomes — 

1.  When  the  company  is  or  soon  may  be  poor  (and  it  is  no 
more  than  common  prudence  to  assume  that  it  will  be  embar- 
rassed for  means  at  some  time  in  the  near  future,  when  it  is  not 
backed  by  a  great  system  of  profitable  lines  in  operation),  take  t/ig 
line  of  lo^v est  first  cost. 

2.  When  immunity  from  financial  embarrassment  is  assured, 
take  the  line  which  offers  the  most  promising  conditions  for  future 
growth  of  traffic. 

3.  Only  when  the  two  lines  are  substantially  equal  in  both  these 
respects  enter  into  such  minute  calculations  as  these  just  sug- 
gested, and  virhichever  line  be  selected  no  serious  harm  can  then 
result. 

744.  Having  determined  the  justifiable  expenditure  to  obtain 
low  grades,  we  have  only  taken  the  first  step  toward  their  proper 
adjustment.  Some  of  the  worst  sacrifices  of  gradients  are  made 
without  effecting  any  saving  of  cost  whatever,  simply  from  inat- 
tention to  its  importance,  or  from  attaching  exaggerated  impor- 
tance to  losses  of  distance  or  curvature,  or  from  insufficient  study 
of  the  topography,  leading  to  a  too  hasty  conclusion  that  all  has 
been  done  which  can  be  done,  when  in  fact  a  very  little  study 
would  lead  to  far  better  results.* 


*: 


■ 


It  is  an  invidious  and  unpleasant  thing  to  say,  but  the  importance  of  the 


584    CHAP.  XV.— RULING  GRADE  AND  MINOR  DETAILS. 


This  question  of  how  to  get  tlie  lowest  grade  which  the  region 
admits  of,  at  a  given  cost,  is  discussed  in  Part  V.  and  Appendix  C. 
The  four  following  sub-departments  of  the  general  problem  of 
gradients  yet  remain  to  be  considered: 

1.  The  use  of  assistant  engines  with  high  "bunched"  grades. 

2.  The  balance  of  grades  for  unequal  traffic. 

3.  Limiting  curvature,  and  the  proper  compensation  therefor. 

4.  The  limit  of  maximum  curvature. 

These  questions  we  will  consider  in  their  order. 


caution  thereby  conveyed  seems  to  justify  saying  it:  Out  of  a  hundred  men 
putting  a  line  through  either  easy  or  difficult  country,  but  especially  through  easy 
country,  the  writer's  observation  is  that  all  but  four  or  five  of  them  will  adopt 
rates  of  grade  from  ten  to  fifty  or  even  a  hundred  per  cent  higher  than  the  other 
five  will  obtain  at  the  same  cost;  and  the  same  holds  true  as  to  amount  of  curva- 
ture. 


CHAP.  XVI.— ASSISTANT  ENGINES. 


585 


CHAPTER  XVI. 

ASSISTANT     ENGINES. 

745.  The  general  use  of  assistant  engines,  commonly  called 
PUSHERS,  is  a  comparatively  modern  innovation.  So  recently  as 
1873,  Gen.  Herman  Haupt,*  in  a  paper  on  gradients,  felt  com- 
pelled to  say  that  he  was  making  "an  attempt  to  prove,  contrary 
to  the  generally  received  opinion,"  that  undulating  gradients 
below  the  limits  of  the  maximum  do  not  necessarily  increase  ex- 
penses marerially,  and  "that  the  use  of  higher  gradients  for  part 
of  a  given  distance  will  often  result  in  greater  economy  of  opera- 
tion than  a  lower  and  uniform  gradient  for  the  whole  distance." 

This  statement  has  now  become  a  truism.  Driven  to  econ- 
omy by  the  necessities  of  competition,  the  use  of  assistant  en- 
gines,  even  on  lines  ill  adapted  to  their  most  advantageous  use, 
has  become  very  general  in  recent  years  and  is  constantly  ex- 
tending, although  tliey  are  even  yet  not  used  on  more  than  a 
proportion  of  the  lines  which  might  use  them  with  advantage 
and  economy,  so  that  their  use  is  one  of  the  most  hopeful  direc- 
tions in  which  further  economy  may  be  sought,  especially  on 
low-grade  hues,  where  the  trains  hauled  even  by  one  engine  are 
of  fairly  profitable  length,  but  might  be  readily  increased  by 
nelp  at  a  few  points. 

What  has  been  accomplished,  however,  is  that  whereas  assist- 
ant engines  were  formerly  used  only  in  exceptional  instances  on 
very  heavy  grades,  their  use  has  now  multiplied  many.fold,  and 
the  expediency  of  using  them  when  possible,  even  at  quite  fre- 
quent intervals,  is  universally  admitted  by  skilled  railway  offi- 
cers.  Some  of  our  earliest  and  greatest  engineers,  as  notably 
the  engineers  of  the  Baltimore  &  Ohio,  Pennsylvania,  and  Erie 
[^l^lways,  distinctly  contemplated  the  use  of  pushersand  adapted 

*  See  Railroad  Gazette,  July  5,  1873. 


586 


CHAP.  XVI.— ASSISTANT  ENGINES. 


CHAP.  XVI.— ASSISTANT  ENGINES. 


587 


their  lines  thereto;  no  doubt  in  part  because  of  the  topo-^ 
graphical  conditions  in  passing  the  Alleghanies,  but  in  part  also- 
because  of  the  singular  foresight  and  sagacity  which  the  great 
engineers  who  laid  out  those  lines  showed  in  many  ways.  But 
these  precedents  have  not  been  generally  recognized  as  estab- 
lishing a  general  principle  until  very  recently,  nor  can  it  be  said 
to  be  yet  established  as  fully  as  it  should  be. 

746.  The  presumption  is  strong  in  laying  out  every  line,  that 
advantage  can  be  derived  from  laying  out  the  grades  for  the 
use  of  assistant  engines,  because  of  the  fact  that  topographical 
conditions  always  require  more  or  less  irregularity  of  gradients. 
The  usual  law  is  that  the  grades  will  be  for  long  distances  very 
low  and  easy,  or  can  be  made  so  at  slight  cost,  but  that  for 
much  shorter  distances  much  higher  gradients  will  be  unavoid- 
able. By  adapting  the  line  to  the  use  of  assistant  engines  on. 
these  higher  grades  we  are  enabled  to  utilize  the  full  advantage 
of  the  lower  grades,  by  making  up  our  trains  to  correspond  to 
them,  so  that  long  trains  can  be  handled  over  the  entire  line  by  a 
single  crew,  without  breaking  it  up  into  sections,  and  the  full 
power  of  the  motive-power  actually  in  use  at  all  points  on  the- 
line  be  more  nearly  utilized. 

747.  The  adoption  of  the  opposite  policy,  attempting  to  get  a 
line  of  a  low  uniform  gradient  through  a  country  of  any  diffi- 
culty whatever,  is  very  apt  to  be  enormously  expensive,  and  to- 
be  possible  at  all  only  by  frequent  undulations,  considerable  de- 
tours, and  much  higher  gradients  over  most  of  the  line  than 
than  there  is  any  necessity  for  using.  This  results  from  the  fact 
that  it  sets  at  defiance  one  of  the  broadest  and  most  nearly 
universal  laws  of  physical  geography, — to  which  there  are  few 
and  rare  exceptions  on  the  whole  face  of  the  globe, — that  long 
stretches  of  easy  plains  or  gently  sloping  valleys  penetrate  at 
intervals  to  and  into  the  very  heart  of  even  the  roughest  regions,, 
leaving  short  sections  only  over  which  high  gradients  are  un- 
avoidable. By  following  these  easy  routes  as  long  as  we  can  we 
accomplish  over  most  of  our  line  three  desirable  ends  at  once: 

1.  We  get  the  cheapest  line. 

2.  We  get  the  lowest  through  grades  ;  and, 


3.  More  than  all  else,  we  concentrate  the  resistances  into 
the  remaining  more  difficult  section,  so  that  the  motive-power  on 
it  can  be  accurately  adapted  to  the  work  required  and  kept  fully 
at  work  over  the  distance  where  it  is  used,  thus  making  it  almost 


Fig.  17s 


too   rniims   -  - 


Table  181. 

Comparative  Work  accomplished  by  an  Engine  in  running  100  Miles 
FROM  X10  Y,  Fig.  175,  and  making  a  Rise  of  2640  Feet  thereon  oVer 
THE  Various  Grades  shown. 


Line, 
Fig.  17s. 


A 

O   •  •  •  •  • 

C 

D 

E 


Distance 

Grade  p.c. 

Net 

Miles. 

Net  Load. 
Tons. 

Load. 
Tons. 

100 

05 

II47 

.     50 
50 

Level. 

2675 

I.O 

711 

}    33i 

Level. 

2675 

1-5 

504 

.     75 
25 

Level. 

2675 

2  0 

383 

80 
{    20 

Level. 

2675 

2.5 

304 

Total  Ton-Miles 
Hauled  by  one  Trip 
of  Through  Engine. 


133.700 
35.550 

178.400 
16.800 

200,600 

9.575 
214.000 

6,080 


114,700 
^    169,250 

[    195,200 

[    210,175 

y  220,080 


Total  Enpine- 

Miles  to  Haul 

2675  Tons  100 

Miles. 


233 
Lis    i  ^38 


Per  Cent 
of  Effici- 
ency. 


100. 0 
102.  Z 

104.7 

106.4 

109.9 


The  fifth  column  indicates  that  a  single  through  engine,  vrhich  drops  cars  to  corre- 
spond to  its  hauling  capacity  at  the  foot  of  the  grades  B,  C,  D,  E,  Fig.  175,  will  make 
vastly  more  ton-miles  on  the  high  grades  than  the  low.  This,  however,  is  unfair.  The 
true  test  is  :  //ozv  much  motive-power  ivill  it  take  to  carry  a  whole  train-load^  or  a  thou- 
sand train-loads,  through,  the  typical  train  weighing  by  assumption  above  2675  tons.  The 
two  last  columns  show  that,  from  this  more  correct  point  of  view,  there  is  a  certain  dis- 
advantage in  the  higher  grades,  but  a  most  trifling  one,  so  long  as  the  resistances  are 
concentrated^  so  that  engines  can  be  at  all  times  fully  loaded.  But  if  scattered,  so  that  it 
IS  necessary  to  run  short  trains  from  X  to  K,  because  of  the  occasional  steep  grades,  the 
disadvantage  becomes  enormous. 


588 


CHAP.  XVI.^ASSISTANT  ENGINES. 


CHAP.  XVI,— ASSISTANT  ENGINES. 


589. 


a  matter  of  indifference  what  rate  of  ascent  we  adopt  on  our 
more  difficult  sections — a  fact  which  powerfully  tends  to  still 
further  reduce  the  cost  of  construction  over  those  more  difficult 
sections.  Table  181  and  F'ig.  175  illustrate  fully  how  and  why 
this  advantage  arises,  and  should  be  carefully  studied. 

748.  Even  where  we  are  unable  for  any  reason  to  follow  the 
valley  lines  which  usually  penetrate  far  into  hilly  or  mountainous 
regions,  as  for  instance  when  the  valleys  are  impracticable,  or  are 
less  practicable  than  the  ridges,  it  is  still  true  that  pusher  gradi- 
ents will  almost  invariably  fit  the  country  better.     The  all  but 

universal  law  of  topography 
B^r~>^.  is  that,   when  the  ground  is 

not  a  dead  level,  transitions 
from  one  level  to  another, 
whether  on  a  large  scale  or  on 
a  small  scale,  are  of  the  form 
shown  in  Figs.  176  and  177.  If  on  a  small  scale,  we  may  simply 
adopt  the  dotted  profile  AJB,  and  make  the  fill  at  C  or  cut  at  B.  If 
on  a  larger  scale,  say  for  a  total  rise  of  50  or  60  or  80  feet,  it  be- 
comes impossible  to  do  this,  especially  if  the  necessity  occurs  at 
many  points,  and  we  are  reduced  to  adopting  the  profile  ACB, 
making  BC  the  ruling  grade  of  the  line,  or  else  to  one  of  the  two 
expedients  shown  in  plan  in  Fig.  177— either  to  run  right  over 


Fig.  176. 


/  J^  jki 


"mv^ 


the  obstruction  with  almost  a 
tangent  line,  giving  the  dotted 
profile  AB,  in  Fig.  178,  or  to 
sacrifice  curvature  and  dis- 
tance and  obtain  the  full-line 
profile.  The  first  has  been 
done  to  a  most  unfortunate 
extent  in  the  prairie-lines  of 
the  West  ;  the  last  is  almost 
always  the  proper  course,  if  it 
saves  an  increase  of  ruling 
\  ■*«^..„^^     grade,  even  when  necessary  at 

Fig.  178.  A     many  points  on  the  line, 

749.  But  when  the  rise  to  be  overcome  becomes  more  consid* 


erable,  as  100  or  200  feet,  even  this  course  is  rarely  convenient. 
To  obtain  an  equivalent  for  the  full  line  AB,  Fig.  177,  we  are 
then  compelled,  usually,  to  adopt  a  costly  line  hanging  upon  the 
slopes  of  such  supporting  ground  as  can  be  had  in  order  to  ob- 
tain the  dotted  profile  AB,  Fig.  176,  or  the  solid-line  profile  AB, 
Fig.  178.  When  we  have  got  it— assuming  that  we  can  and  do 
get  it — we  have  even  then,  in  all  probability,  been  compelled  to 
use  a  higher  grade  than  it  is  at  all  necessary  to  use  on  the  re- 
maining and  easier  portions  of  the  line.  If  so,  we  have  not  only 
spent  a  great  deal  of  money  where  we  have  difficulties,  but  have 
injured  our  line  where  we  have  no  difficulties. 

750.  The  alternative  is  to  treat  the  difficult  ground  as  a  sep- 
arate feature  ;  to  maintain  the  lowest  grades  we  can,  on  the 
ground  where  we  have  no  difficulties  ;  to  push  these  low  grades 
as  far  as  possible  to  some  point  C,  Fig.  176,  as  near  as  may  be  to 
the  rise;  and  then  to  adopt  some  entirely  different  and  much 
higher  grade  BC,  conforming  as  closely  as  possible  to  the  natu- 
ral surface,  with  a  view  of  using  auxiliary  power  or  "  pushers"^ 
on  it,  thus  not  only  saving  our  money  on  the  parts  of  the  line 
which  are  naturally  most  costly,  but  retaining  all  our  natural 
advantages  elsewhere  which  cost  us  nothing. 

751.  In  other  words,  the  secret  of  the  vast  economies  which 
may  often  be  realized  by  the  skilful  use  of  assistant  engines  is 
this — that  as  respects  construction  we  work  with  Nature  instead 
of  against  her,  and  that  as  respects  operation  we  gain  a  like  ad- 
vantage by  keeping  every  engine  while  running  fully  at  work, 
the  greater  portion  of  the  hard  work  in  foot-pounds  being  done 
on  a  small  portion  of  the  division,  with  such  favorable  through 
grades,  in  many  cases,  that  there  is  little  more  need  for  an  en- 
gine on  the  remainder  of  it,  than  to  keep  the  longest  trains 
moving  and  under  control.  It  is  a  truth  of  the  first  impor- 
tance, that  the  objection  to  high  gradients  is  not  the  work  which 
engines  have  to  do  on  them  (see  Table  181),  but  it  is  the  work 
which  they  do  not  do  when  they  are  thundering  over  the  track 
With  a  light  train  behind  them,  from  end  to  end  of  a  divi- 
sion, in  order  that  the  needed  power  may  be  at  hand  at  a  few 


S90 


CHAP.  XVI.— ASSISTANT  ENGINES. 


CHAP.  XVI.— ASSISTANT  ENGINES— POWER  OF. 


591 


scattered  points  where  alone  it  is  needed.  But  if  we  may  give 
this  additional  motive-power  its  work  to  do  once  for  all,  and 
have  done  with  it,  high  summits  cost  very  little,  and  an  increase 
of  the  rate  of  grade  costs,  practically,  nothing  whatever.  At  the 
points  of  greatest  difficulty  we  are  independent  of  the  rate  of 
ascent  and  in  a  great  degree  of  the  elevation  attained,  and  are 
therefore  at  liberty  to  concentrate  our  efforts  and  expenditure  on 
the  more  tractable  portions  of  the  line,  where  a  few  feet  per 
mile  reduction  in  grade  (see  Table   170  and  Fig.  169)  may  be  of 

enormous  value. 

752.  in  this  way  it  is  in  every  way  practicable  to  secure  lines 
over  tolerably  high  summits  and  through  difficult  country  which 
shall  approximate  closely  in  operating  value  to  the  most  favor- 
able existing  examples  of  low-grade  lines.  On  the  other  hand, 
BY  SEEKING  FOR  WHAT  WE  DO  NOT  REQUIRE,  by  defying  the  ob- 
stacles of  nature  and  forcing  them  to  conform  throughout  to  the 
Procrustean  standard  of  a  uniform  ruling  gradient,  we  shall 
enormously  increase  the  cost  of  construction,  and  in  the  end  find 
that  we  have  a  far  more  costly  line  to  operate  than  if  we  had 
"stooped  to  conquer"  by  boldly  conforming  to  the  topographical 
conditions  and  then  skilfully  forcing  them  to  serve  our  purpose. 
This  goes  so  far  that  it  is  true  policy  in  very  many  instances  in 
difficult  country  to  make  boldly  for  the  "meeting  of  the  waters" 
at  the  summit,  even  at  the  cost  of  a  higher  summit,  rather  than 
to  zigzag  up  and  down  and  from  side  to  side  in  a  costly  effort  to 
avoid  a  continuous  succession  of  transverse  valleys  and  other 
petty  obstacles,  each  of  which  has  us  at  great  disadvantage. 

753.  The  advantage  of  the  use  of  pusher  grades  are  not  at  all 
confined  to  high  grades,  but  on  the  contrary  are  even  greater 
proportionately  for  low  grades,  provided  only  that  there  be 
business  enough  to  fill  up  the  trains,  and  couplings  good  enough 
to  permit  of  handliiiir  long  trains.  On  roads  of  light  and  irregu- 
lar traffic  there  may  be  no  great  advantage  in  them;  but  many 
roads  having  large  traffic,  which  must  be  hauled  cheaply  because 
it  pays  little,  are  habitually  using  pushers  on  gradients  as  low  as 
0.5  to  0.6  per  cent.     For  example,  freight  pushers  are  used  on  the 


Hudson  River  Railroad,  nearly  95  per  cent  of  which  is  a  dead 
.level,  and  the  remainder  over  summits  a  few  feet  high  on  0.4  to 
^.5  grades. 

THE  POWER  OF  ASSISTANT  ENGINES. 

754.  By  the  use  of  assistant  engines  the  available  motive-power  is  ap- 
proximately doubled  or  trebled  ;  and  it  is  evident  that  economy  in  motive- 
power  requires  that  the  rates  of  these  grades  should  be  proportioned  to 
each  other  as  nearly  as  possible,  in  order  that  neither  grade  may  be  dis- 
portionately  low,  but  that  the  true  ruling  grade  maybe — not  necessarily 
either  the  higher  (pusher)  grade  or  the  lower  grade,  but  that  one  which 
involves  most  difficulty  and  expense  in  reduction. 

With  certain  provisos  which  we  will  shortly  consider,  the  determina- 
tion of  a  practically  exact  balance  of  gradients  for  the  use  of  one  or  more 
assistant  engines  is  a  simple  matter.  If  the  assistant  engine  be  of  the 
same  weight  as  the  through  engine,  the  load  to  be  hauled  by  each  en- 
gine is  reduced  one  half.  If  there  be  two  pushers,  the  load  to  be  hauled 
by  each  engine  is  reduced  to  one  third  of  what  it  was.  If  the  pusher 
have,  say,  10  or  20  per  cent  more  tractive  power  than  the  through  engine, 
the  train  is  in  effect  cut  into  two  unequal  parts,  that  remaining  to  the 

through  engme  bemg  ^  ^  ^  ^  ^^.  or  ^^^  ^ ^ -,  i.e.,  47.6  or  45.5  per  cent 

-of  the  original  weight  of  the  train  behind  tender.  The  grade  on  which 
the  through  engine  can  haul  that  per  cent  of  its  load  on  a  given  through 
grade  will  therefore  be  the  corresponding  pusher  grade  for  pusher  en- 
gines of  such  weight. 

755.  By  the  aid  of  the  long  Table  170,  the  process  of  determining 
such  pusher  grades  for  any  through  grade  is  made  one  of  mere  inspec- 
tion, as  practical  convenience  requires.  For  example,  to  determine  the 
pusher  grades  corresponding  to  through  grades  of  0.5  percent,  we  have — • 


Net  load  behind  tender,  on  0.5  grade... . , 

Half  of  which  is , 

Corresponding  pusher  grades , 

if  of  load,  for  pushers  10  p.  c.  heavier,  is 

Corresponding  pusher  grades 

if  of  load,  for  pushers  20  p.  c.  heavier,  is 

Corresponding  pusher  grades , 

i  of  load,  for  2  pushers  of  equal  weight. . 
Corresponding  pusher  grades , 


Light 
American. 


504  tons. 

252     '• 
.24  per  cent. 

241  tons. 
.31  per  cent. 

229  tons. 
.38  per  cent. 

168  tons. 
.87  per  cent. 


Average 
Consolidation. 


1 147  tons. 

573i  " 
1.30  per  cent. 

550  tons. 
1.36  per  cent. 

522  tons. 
1.44  per  cent. 

382  tons. 
2.00  per  cent. 


592        CHAP.  XVI.— ASSISTANT  ENGINES— POWER  OF. 


CHAP.  XVI.— ASSISTANT  ENGINES— POWER   OF. 


593 


From  these  examples  it  will  be  seen  that  differences  in  type  of  en- 
gine make  no  considerable  difference  in  the  balance  of  grades,  and  we 
shall  hereafter  consider  the  average  Consolidation  type  only. 

756.  If  the  pusher  were  a  tank  engine  having  no  tender,  it  in  effect 
adds  the  weight  of  the  tender  to  the  train  hauled  by  the  pusher ;  so  that 
to  make  the  preceding  calculation  we  should  first  have  to  subtract  the 
weight  of  tender  thus  saved  from  the  total  weight  of  train,  and  then  di- 
vide the  remainder  only  between  the  through  and  pusher  engines,  in  the 
above  proportion,  which  would  increase  the  rate  of  the  admissible 
pusher  grades  materially. 

In  this  manner  Table  182  was  computed,  which  gives  the  proper  bal- 
ance of  grades  for  an  ordinary  Consolidation,  or  practically  for  any  other 
engine,  except  tank  engines,  which  are  separately  noted. 

757.  The  requirements  of  the  passenger  service  naturally  favor  the 
adoption  of  higher  through  grades  rather  than  pusher  grades,  since  un- 
dulating gradients,  however  steep,  have  little  effect  to  impede  hauling 
any  trains  ordinarily  desired,  when  the  rise  on  a  single  grade  is  not  great. 
Owing  to  the  decrease  of  train  resistance  at  slow  speeds  (Table  166) 
and  the  simultaneous  increase  in  the  tractive  power  of  the  cylinders,  the 
limit  at  which  a  high  and  long  grade  can  certainly  be  operated  without 
a  pusher  is  still  further  increased.  The  ultimate  limit  for  the  operation 
of  a  pusher  grade  by  a  single  engine  in  passenger  service,  beyond  which 
pushers  must  be  used  for  passenger  as  well  as  freight  trains,  may  be  de- 
termined as  follows : 

The  most  that  would  be  demanded  of  an  ordinary  17  x  24  passenger 
engine,  weighing  with  tender  56  tons,  more  or  less,  such  as  is  assumed 
in  the  table  of  train  resistance  (Table  166),  is  that  it  should  haul— as  an 
average  of  a  whole  division  and  every  day  in  the  year,  and  not  for  excep- 
tional performances, — 


4  cars,  or  168  tons,  8  cars,  or  280  tons, 
gross  weight  of  train.  gross  weight  of  train. 
At  60  miles  per  hour  maxi-  At  50  miles  per  hour  maxi- 
mum speed  on  a  level.  mum  speed  on  a  level. 


12  cars,  or  392  tons, 
gross  weight  of  train. 
At  35  miles  per  hour  maxi- 
mum speed  on  a  level. 


758.  Now  the  tractive  power  which  such  an  engine  is  capable  of  exert- 
ing in  every-day  practice  at  freight  speeds  of  15  miles  per  hour  would  be 
nearly  if  not  quite  10,000  lbs.,  there  being  from  40.000  to  44,000  lbs.  on 
the  drivers.  Therefore  the  engine  will  be  capable  of  exerting  a  maxi- 
mum tractive  force  on  these  trains,  at  freight  speeds  of  about  15  miles 
per  hour  of  10,000  lbs.  -^  the  weight  in  tons,  or 

59.S  lbs.  per  ton,  35-7  lbs.  per  ton,  25.5  lbs.  per  ton. 


Table  182. 
Balance  of  Grades  for  the  Use  of  Assistant  Engines. 

[Correct  within  an  unimportant  percentage  for  all  classes  of  engines  and  conditions  of 
service,  the  through  and  pusher  engines  having  the  sam*  weight  and  tractive  power.] 


Net  Load 

Grade  up  which  the  same  Train 

CAN  BE  Hauled 

Through-Grade 

(Tons) 

BY  THE  Aid  of— 

WORKED 

for  Average 
Consolidation. 

BY  ONE  Engine. 

One  Pusher. 

Two  Pushers. 

Three  Pushers. 

Level. 

2675 

.38 

.74 

1.08 

.05 

2370 

.47 

.87 

1.25 

.10 

2125 

.57 

1. 00 

i.4r 

>i5 

1936 

.66 

1. 13 

1-57 

.20 

1758 

.75 

1.26 

1.74 

.25 

1618 

.84 

1.39 

1.89 

•30 

1496 

.94 

1.52 

2.05 

.35 

1392 

1.03 

1.64 

2.20 

.40 

1300 

1. 12 

1.76 

2.35 

.45 

1220  — 

1. 21 

1.88 

2.49 

-50 

II47 

1.30 

2.01 

2.64 

.60 

1025 

I  47 

2.24 

2.92 

.70 

925 

1.65 

2.47 

3.20 

.80 

842 

1.82 

2.69 

3.45 

.90 

771 

1.99 

2.91 

370 

1. 00 

711 

2.16 

3-13 

3-95 

1. 10 

658 

2.32 

3-33 

4.20 

1.20 

612 

2.48 

3.55 

4.42 

1.30 

572 

2.64 

3.73 

465 

1.40 

536 

2.81 

3-93 

4.87 

■i-So 

504 

2.96 

4.13 

5-07 

1.60 

475 

313 

4.32 

5-27 

1.80 

425 

3-43 

4.68 

5.68 

2.00 

383 

3.72 

5.03 

6.04 

2.20 

348 

4.01 

5.35 

6.40 

2  40 

318 

4-30 

5.67 

6.73 

2.60 

292 

4-57 

6.00 

7-05 

2.80 

269 

4  86 

6.30 

7.34 

3  00 

249 

5. 10 

6.58 

763 

If  we  assume  \  instead  of  \  adhesion^  we  simply  reduce  the  tractive  power  of  an 
average  Consolidation  (Table  170)  from  10  tons  to  8  tons.  The  ratio  of  the  gross 
weights  of  trains  on  various  grades  remains  unchanged,  and  the  ratio  of  the  weight 
behind  tender  would  remain  so  likewise  if  the  gjoss  weight  of  engine  were  reduced  one 
fifth,  or  by  15  tons.  As  it  is  not,  the  column  headed  8.0  tons  tractive  power  in  Table  170 
should  be  1 1  tons  greater  to  give  the  net  loads,  and  we  find  the  pusher  grades  to  be— » 
33 


flHi 


'■It 


594 


CHAP.  XVI.— ASSISTANT  ENGINES-POWER   OF. 


If  we  allow  8  lbs.  per  ton  for  tractive  friction,  and  divide  the  remainder, 
which  is  admissible  as  grade  resistance,  by  20  (par.  682).  we  have  as  the 
grades  on  which  these  passenger  trains  can  be  handled,  by  reducing 
speed  to  1 5  miles  per  hour, 

2.57  per  cent,  1.38  per  cent,  .875  per  cent. 

On  any  grade  up  to  tTiese  limits,  the  trains  which  such  an  engine 
can  be  expected  to  handle  in  every-day  practice  will  be  readily  handled 
at  the  lower  speed  of  15  miles  per  hour,  if  it  is  possible  to  stand  the  loss 
of  time  thereby.  When  Mogul  or  ten-wheel  engines  are  used,  as  they 
usually  would  have  to  be  for  regular  trains  so  long  as  12  cars,  the  limits 
will  be  considerably  higher;  so  that  we  may  say  in  a  general  way.  that 
grades  up  to  ih  or  li.  or  even  2  per  cent,  are  not  a  serious  obstruction  to 
light  passenger  business,  except  in  loss  of  time.  If  pushers  are  used 
below  the  limits  indicated,  it  is  only  for  urgent  necessity  to  keep  up 
speed,  as  on  fast  through  expresses. 

759.  The  loss  of  time  involved  in  such  checking  of  passenger  speed 
is  much  less  than  is  sometimes  hastily  imagined.  Table  183  gives  its 
exact  limits,  from  which  it  will  be  seen  that  a  reduction  of  speed  from 
40  to  20  miles  per  hour,  for  example,  loses  but  li  minutes  per  mile,  or  15 
minutes  on  an  incline  10  miles  long.     As  the  speed  is  higher  the  loss  of 


Through  grade  for  one  engine. 
Level • 


1.0. 
3.0. 


, Pusher  grades  for  adhesion  of v 

,_^.  1-5.  Difference. 

0.38  0.37  o.oi 

2.16  a. 08  0.08 

3.7a  352  °-~ 


3.0 5.X0  4.75  0-35 

A  lower  rolling-friction  than  8  lbs.  reduces  the  rate  of  pusher  grades  about  0.08  per 
cent  on  a  level  grade,  decreasing  to  0.04  at  a  2  per  cent  grade. 

For  assistant  engines  heavier  than  the  through  engines,  add  the  foUowing  to  the 

above  grades  : 


Through  Gradb. 


One  Assistant  Engine 
heavier  by — 


Level 

I. CO.. 

1.50.. 
2.00.. 


10  p.  c. 


.03 
.07 

.10 

.12 


20  p.  c. 


.07 

■14 
.20 

.24 


30  p.  c. 


.II 

.22 

•  37 


Two  Assistant  Engines 

HEAVIER    BY— 


10  p.  c. 


.07 
•  13 
.17 

.20 


20  p.  c. 


.14 
.26 

.34 

.40 


30  p.  c 


.22 

•39 
.51 
.60 


It  is  rarely  proper  to  assume  that  the  assistant  engines  will  be  of  greater  power  tl^ 
the  through  engines.  Two  pushers  can  only  be  assumed  to  be  used  with  a  large  traffic 
or  very  heavy  grades,  and  three  pushers  only  with  the  very  largest  traffic. 


CHAP.  XVI.— ASSISTANT  ENGINES— POWER   OF. 


595 


time  becomes  very  much  less,  while  the  gain  of  power  becomes  very 
much  greater— a  condition  which  goes  far  to  justify  counting  on  this  re- 
source for  all  classes  of  passenger  trains,  within  reasonable  limits. 

Table  183. 

Loss  OF  Time  in  Minutes  Per  Mile  due  to  a  Decrease  of  Speed  op 

Trains. 
The  table  gives  the  loss  of  time  per  mile  in  minutes  per  mile  in  the  column  headed  by 
the  given  higher  speed  opposite  the  given  lower  speed  to  which  the  speed  is  decreased. 


Lower  Speed. 

Higher  Speeds— Miles  Per  Hour. 

Miles     Minutes 
Per           Per 
Hour.       Mile. 

15 

20 

25 

30 

35 

40 

45 

50 

55 

60 

1                1                1     ■  -■         1 
Time  Lost  Per  Mile  ;   Minutes. 

10             6.0 
15             4.0 
20             3.00 

2.0 

30 

I.O 

3.6 
1.6 
0.6 

4.0 
2.0 
1.0 
0.4 

4.29 
2.29 
1.29 
0.69 
0.29 

4-5 

2-5 

0.9 

0.5 
0.2 

467 
2.67 
1.67 
1.07 
0.67 
0.38 
0.17 

4-83 
2.83 

1.83 

1-23 
0.83 

0  54 

0-33 
0.16 

4.91 
2.91 

1.91 
1.31 
0.91 
0.62 
041 
0.24 
0.08 

50 
3.0 

25             2.4 

3.0 

30                    2.0 

1-4 

35                I-7I 

z.o 

40               1.5 

0.7X 

45               1.33 

0.5 

50               1. 17 

0.33 

55               109 



0.17 
0.09 

It  will  be  seen  that  the  amount  of  time  lost  by  considerable  reductions  of  high  speeds 
is  less  than  by  very  slight  reductions  of  speeds  below  30  miles  per  hour,  while  the  gain  in 
train  resistance  is  very  much  greater  at  high  speeds. 

The  fast  New  York  Central  Limited  Express,  which  makes  the  run  of  970  miles 
between  New  York  and  Chicago  in  24h.  5m.,  with  only  eight  regular  stops,  none  of  them 
for  meals,  loses  55  minutes  in  these  stops  alone.  Including  all  slowing  up  through  towns 
and  yards,  stops  at  crossings,  etc.,  not  less  than  3  hours  of  the  24  are  lost  in  this  way,  or 
about  0.2  minutes  per  mile,  equivalent  to  an  average  reduction  of  5  miles  per  hour  in  speed. 
With  most  fast  trains  the  loss  would  be  more  than  double  this. 


760.  On  the  New  York,  Lake  Erie  &  Western  Railroad,  having  several  long 
■maximum  grades  of  60  feet  per  mile  (1.14  per  cent),  passenger  pushers  are  used 
only  by  the  very  heavy  through  express  trains.  At  Altoona,  on  the  Pennsylva- 
nia Railroad,  at  the  foot  of  the  95-ft.  grade  (1.61  per  cent),  pushers  are  used  for 
nearly  all  passenger  trains,  but  nearly  all  are  heavy  trains.  The  local  accom- 
modation trains,  consisting  of  4  to  6  ordinary  day  coaches  and  baggage  cars, 
use  no  pushers.  About  30  miles  per  hour  is  made  by  the  passenger  trains 
^smg  pushers  up  the  mountains.  Except  for  the  requirement  of  making  this 
«Peed,  many  of  the  passenger  trains  could  dispense  with  pushers,  although  the 


596        CHAP,  XVI.-ASSISTANT  ENGINES^POWER  OF, 


CHAP,  XVI.— ASSISTANT  ENGINES—POWER  OF.  597 


-Ml 


heavier  through  expresses,  consisting  of  6  to  8  cars,  each  averaging  over  25 
tons,  would  find  difficulty  in  ascending  the  mountain  without  an  assistant  en- 
gine even  at  verv  slow  speed. 

On  the  Middle  Division,  having  very  easy  grades,  not  over  16  ft.  per  mile 
at  any  point,  as  manv  as  12  heavy  cars,  but  not  more,  are  hauled  by  a  single 
passenger  engine,  making,  however,  even  with  this  train,  high  average  speeds. 
Similar  trains  are  hauled  over  the  New  York  Central  road  for  the  entire  dis- 
tance from  New  York  to  Buffalo,  except  that  a  pusher  is  used  for  the  grade  of 
about  1.5  per  cent  at  Albany. 

761.  Except  within  the  limits  above  noted,  passenger  trains  as  we^l 
as  freight  must  be  assumed  to  require  pushers.  The  more  certain  it  is 
that  high  speed  will  be  required  at  all  points,  the  moie  likely  they  are 
to  be  required  ;  and  wherever  it  appears  likely  that  the  passenger  traffic 
will  be  important  and  competitive,  it  may.  for  moderately  prosperous 
road  be  giving  no  more  than  due  weight  to  the  great  and  permanent 
value  of  easy  gradients  to  assume  that  all  trains,  both  passenger  and 
freight,  will  probably  require  helping  engines,  especially  as  the  tendency 
to  increase  the  weight  of  passenger  trains  and  cars  is  strong. 

The  assumption  made  as  to  passenger  helpers  will  make  a  consider- 
able difference  in  a  comparison  of  gradients;  for  if  they  be  assumed  to- 
be  used,  the  advantage  of  pusher  gradients  over  moderately  favorable 
through  gradients  will  be  much  less;  while  if  they  be  not  assumed,  the 
disadvantage  for  passenger  service  of  the  higher  rates  of  grade  can  hardly 
be  estimated  at  any  considerable  figure. 

762.  In  laying  out  pusher  grades,  the  effect  of  fluctuations  in  the 
velocity  of  trains  to  modify  the  apparent  relation  of  the  grades  to  each 
other  must  be  carefully  kept  in  mind.    The  effect  of  these  differences 
(fully  considered  in  Chap.  IX.,  par.  397  et  seq)  will  usually  be  that  the 
apparent  maximum  of  the  lower  (single  engine)  grades  will  be  higher 
than  it  really  is,  while  the  actual  maximum  of  the  higher  (pusher)  grades 
will  be  greater  than  the  profile  shows,  so  that  the  latter  will  need  to  be 
reduced  lower  than  an  apparent  balance  requires  in  order  to  give  a  true 
balance.    On  long  steep  ascents  slight  sags  in  the  grade-line  may  be  per- 
missible (par.  414  et  seq.),  but  otherwise  no  excess  of  momentum  can  be 
relied  on  to  carry  trains  over  any  increase  whatever  above  the  normal 
rate-  while  any  stop  on  the  grade,  if  the  latter  be  long,  will  increase  its 
limiting  effect  far  above  the  apparent  maximum,  unless  care  has  been 
used  to  ease  the  grades  for  all  stops  which  can  possibly  be  required. 
Even  if  this  has  been  done,  there  are  always  likely  to  be  occasional  irreg- 
ular stops,  and  the  occasional  operating  inconvenience  therefrom  will  be 
allowed  far  more  than  its  true  weight  in  cutting  down  trains. 


763.  On  the  other  hand,  the  lower  through  grade  will  very  commonly 
be  cut  up  into  such  short  stretches  that  momentum  will,  or  may  be  made 
to.  reduce  its  apparent  rate  very  materially,  and  even  if  not,  moderate 
improvements  in  the  future  will  often  suffice  to  accomplish  this.  More- 
over, it  is  always  comparatively  easy  to  foresee  and  guard  against  limit- 
ing effects  from  stops. 

True  economy  will  ordinarily  dictate,  therefore,  that  the  resistance 

ON  THE   PUSHER  GRADE   SHOULD    BE    AT    LEAST    TEN    PER    CENT    LESS 

THAN  AN  APPARENT  BALANCE  REQUIRES  if  attainable  at  moderate  cost, 
with  the  following  proviso : 

If  the  rate  of  the  pusher  grade  be.  from  its  cost  or  otherwise,  the  fixed 
element  beyond  control,  as  often  happens,  then  the  rate  of  the  lower 
through  grade  should  be  reduced  at  any  reasonable  cost  (it  is  usually 
more  at  the  cost  of  care  than  money)  to  ant/ a  little  below  the  full  extent 
which  an  apparent  balance  requires  ;  in  accordance  with  the  sound  gen- 
eral principle,  that  the  links  in  a  chain  whose  strength  we  cannot  control 
nor  exactly  foresee  should  be  the  weakest,  and  not  those  whose  strength 
we  can  control  and  can  foresee. 

764.  Again,  the  lower  the  rolling- friction  the  greater  the  proportion- 
ate effect  of  gradients  upon  the  total  train  resistance,  and  consequently 
the  lower  must  be  the  rate  of  the  higher  pusher  grade.  As  we  have  as- 
sumed (par.  623  and  Table  170)  8  lbs.  per  ton  rolling-friction,  which  is 
probably  from  2  to  4  lbs.  high  for  the  slower  working  speeds,  the  rate  of 
the  higher  grade  should  be  from  o.i  to  0.2  percent  less  than  theory  would 
otherwise  indicate,  where  possible,  for  this  reason  alone. 

765.  A  variation  in  the  weight  and  power  of  the  assistant  engines 
affords  a  means  of  equalizing  minor  inequalities  in  the  balance  of*gra- 
dients.  should  such  be  discovered,  but  this  should  be  counted  on  with 
caution  in  original  location.  To  count  on  using  pusher  engines  lighter 
than  the  through  engines  would  ordinarily  be  very  bad  practice.  It 
would  be  preferable  to  save  money  and  length  of  pusher  grade  by  using  a 
steeper  rate  of  grade.  To  count  on  using  heavier  pushers  is  open  to  three 
objections:  (i)  The  tendency  is  always  to  use  heavier  and  heavier  through 
engines,  and  a  point  will  then  soon  be  reached  where  corresponding 
increase  in  the  weight  of  pusher  engines  would  be  objectionable  or  im- 
practicable;  (2)  It  imposes  a  greater  tax  upon  the  rails  and  track  at  the 
very  point  where  the  alignment  makes  it  most  objectionable  ;  (3)  Such 
gain  as  is  possible  in  this  respect  is  very  apt  to  be  required  and  used  to 
make  up  for  the  inequalities  in  what  was  supposed  to  be  a  correct  balance 
^  gradients,  the  tendency  always  being  to  get  the  rate  of  the  pusher  grades 


m 


"TWgf— iWI" 


598 


CHAP.  XVI.— ASSISTANT  ENGINES— DUTY  OF. 


CHAP.  XVI.— ASSISTANT  ENGINES— DUTY  OF. 


599 


too  high  for  a  correct  balance  with  the  louver  grades.  In  actual  practice, 
at  the  present  day,  it  will  be  found  that  pusher  engines  usually  are  a 
little  heavier  than  the  through  engines,  and  yet  that  the  pusher  grades 
are  no  higher  in  rate  than  Table  i8i  would  indicate,  the  excess  being 
used,  apparently,  for  the  preceding  and  following  reasons,  and  not  to 
provide  a  true  balance  under  normal  conditions. 

766.  If  the  rate  of  adnesion  be  Ipw,  the  admissible  rates  for  the  higher 
gradients  is  very  materially  decreased,  as  shown  in  Table  183,  for  the 
reason  that  the  percentage  of  effect  lost  in  moving  the  engine  itself  is 
very  materially  greater.  As  on  many  days  in  the  year  the  ratio  of  adhe- 
sion is  unavoidably  low,  on  those  days  the  resulting  inconvenience  will 
be  confined  to  the  pusher  grade,  but  will  be  very  apt  to  lead  to  the  per- 
manent cutting  down  of  trains  on  both  grades. 

The  consequences  of  any  unforeseen  breakdown  or  other  cause  of 
accident  or  delay  are  so  much  more  serious  on  heavy  grades  that  'a  cer- 
tain excess  of  motive-power  is  naturally  sought  for  and  generally  obtained 
in  such  localities,  sometimes  at  the  expense  of  sound  economy. 

The  curvature  on  heavy  gradients  is  usually  very  much  more  severe. 
As  the  speed  is  also,  usually,  very  much  slower,  and  complete  stoppage 
from  lack  of  power  more  frequent,  it  appears  probable  (pars.  308,  335) 
that  the  curve  resistance  per  ton  is  higher,  and  hence  that  either  the  rate 
of  compensation  for  curvature  must  be  made  higher  on  high  pusher 
grades  or  a  lower  average  rate  of  grade  than  a  nominal  balance  requires 
be  adopted. 

THE  DUTY  OF  ASSISTANT  ENGINES. 
767.  Under  the  ordinary  exigencies  of  operation,  with  two  important 
exceptions,  below  noted  (par.  770  et  seg?),  pushing  or  assistant  engine 
service  must  be  rendered  by  separate  engines,  specially  detailed  for  that 
duty  and  available  for  no  other.  It  is  therefore  not  correct  to  assume 
that  the  pushing  service  will  cost  about  the  same  per  mile  run  as  for 
through  engines,  or  that  pushing  engines  will  make  the  same  annual 
mileage.  Rather,  the  safer  basis  is  to  assume  as  nearly  as  may  be  that  a 
certain  number  of  engines  must  be  maintained  for  that  service  alone,  at 
a  certain  cost  per  day  regardless  of  mileage  made,////5  the  extra  cost  due 
to  running  a  certain  number  of  miles,  whether  that  number  be  50  or  100 
or  more  miles  per  day. 

768  As  a  general  and  safe  rule,  the  mileage  of  assistant  engmes  may 
be  taken  at  100  miles  per  day  //  they  will  have  a  chance  to  run  it,  and  as 
at  least  equal  to,  if  not  considerably  in  excess  of.  the  mileage  of  ordinary 
through  engines.     As  much  as  1 30  miles  per  day  is  run  by  pusher  engines 


on  various  roads,  under  favorable  circumstances,  but  experience  does  not 
justify  an  assumption  that  more  than  this  is  practicable.  If,  therefore, 
the  estimated  traffic  will  require  150  miles  per  day  of  pusher  service,  the 
only  safe  basis  is  to  assume  that  two  engines  with  two  crews  will  be  re- 
quired, making  75  miles  per  day  each.  Theoretically,  one  engine  with 
two  crews  might  do  the  work,  but  practically,  if  the  duty  were  too  much 
for  one  engine  and  crew,  convenience  would  almost  certainly  require  and 
justify  keeping  two  engines  in  working  order  with  steam  up  for  at  least 
12  hours  per  day. 

When  the  pushing  service  to  be  performed  is  over  200  miles  per  day 
the  only  safe  basis  is  to  assume  one  engine  for  each  100  miles,  or  frac- 
tion thereof  over  fifty. 

769.  From  one  to  two  months  of  every  year  is  lost  by  engines  while 
in  shop  for  repairs  (see  Table  51),  which  reduces  the  apparent  mileage  per 
engine  per  year  (and  hence  per  day)  by  10  to  16  or  more  per  cent ;  but 
this  loss  need  not  be  considered  in  computing  the  number  of  engines  re- 
quired for  pushing  service  from  the  probable  mileage  to  be  run,  or  its 
cost,  since  the  cost 'of  these  repairs  is  included  in  the  cost  of  the  miles 
actually  run,  and  the  engines  actually  detailed  to  pushing  service  can  and 
will  be  always  in  working  order. 

The  exceptions  to  which  the  preceding  general  rules  do  not  apply  are 
these  ; 

770.  I.  When  traffic  is  very  light,  pusher  grades,  if  not  too  long,  may 
be  operated  by  cutting  trains  in  two,  leaving  half  the  train  at  the  bottom 
of  the  grade,  placing  half  of  it  on  a  siding  at  the  top,  returning  for  the 
other  half,  which  is  preferably  pushed  up,  and  then  proceeding,  after 
coupling  up,  with  the  entire  train  once  more. 

This  is  done  to  only  a  limited  extent  as  a  regular  practice,  although  it  is  a 
resort  in  emergencies  on  nearly  all  roads.  It  might  well  be  done  to  a  much 
greater  extent  than  it  is, if  it  were  only  to  run  a  freight  train  three  times  a  week 
instead  of  daily.  It  is  one  of  those  possibilities  of  economy  which  are  neglected 
until  necessity  compels  them,  because  they  take  some  trouble  and  some  devia- 
tion from  ordinary  routine  in  management. 

Convenience  requires  that  there  should  be  a  siding  at  least  half  a  train  long 
(preferably,  of  course,  a  full  train  long)  at  both  top  and  bottom  of  the  grade,  the 
lack  of  which  is  no  doubt  one  great  reason  why  this  expedient  is  not  oftener  re- 
sorted to, 

'71.  2.  At  short  pusher  grades  near  stations,  yard  or  switching  engines 
can  often  perform  a  part  or  all  of  the  required  pushing  service  at  very 
moderate  cost— or,  what  amounts  to  the  same  thing,  the  pushing  engines 
can  be  so  utilized  for  switching  service  as  to  greatly  reduce  the  cost  and 
inconvenience  of  using  pushers. 


6oo 


CHAP.  XVI.— ASSISTANT  ENGINES— DUTY  OF. 


CHAP.  XVI.— ASSISTANT  ENGINES— COST  OF, 


6oi 


The  instances  are  many  where  yard  engines  are  utilized  in  this  way,  if 
only  to  help  trains  tlirough  yards  at  which  there  would  be  no  difficulty, 
except  for  the  fact  that  it  is  a  yard,  because,  for  obvious  topographical 
and  commercial  reasons,  it  is  very  common  to  find  large  yards  near  short 
stretches  of  objectionable  gradients.  When  the  yard  is  very  large,  so 
that  several  yard  engines  are  constantly  employed,  the  pushing  service 
cannot  be  assumed  to  be  added  without  adding  its  full  pro  raid  to  the 
number  of  engines,  but  in  all  cases  the  cost  and  inconvenience  of  the 
service  will  be  decreased,  and  so,  indirectly,  the  number  of  engines  which 
will  probably  be  required  for  the  joint  service,  to  the  extent  perhaps  of 
15  or  20  per  cent  of  the  whole  number  of  engines.  Switching  engines  of 
the  ordinary  type,  having  all  their  weight  on  drivers  are  not  well  adapted 
for  pushing  service,  on  runs  of  over  a  mile  or  two,  nor  much  used  there- 
for, since  they  are  ill  adapted  for  high  speed,  which  is  often  desirable  in 
returning  down  hill. 

772.  The  convenience  of  the  service  must  be  considered  as  well  as  the 
theoretical  requirements  in  estimating  both  the  probable  duty  and  prob- 
able cost  of  the  assistant-engine  service,  as  also  of  course  in  laying  out 
the  grades.  Unless  a  station  be  situated  immediately  at  the  foot  or  top 
of  the  grade,  the  service  must  be  assumed  to  begin  at  the  nearest  consid- 
erable station,  if  there  be  one  within  three  to  five  miles  of  either  point, 
because  that  is  where  convenience  will  require  that  it  should  begin  in 
practice. 

Unless  two  successive  pusher  grades  are  more  than  five  or  perhaps 
even  eight  miles  apart,  they  may  more  prudently  be  taken  as  one  and  the 
same  grade,  because  in  practice  that  is  the  way  in  which  they  will  be 
likely  to  be  operated.  The  tendency  is  always  to  consider  convenience 
in  such  matters,  even  at  the  expense  of  economy;  and  it  may  be  questioned 
if  there  is  even  a  theoretical  economy  in  breaking  up  a  pusher  run  into  two 
for  less  than  a  five-mile  interval,  or  even  under  special  circumstances,  with 
thin  traffic,  for  considerably  more.  The  inconveniences  of  stopping  and 
starting  and  of  maintaining  the  double  service  and  the  loss  of  time  are  too 
great.  No  stop  is  required  at  the  top  of  the  grade  for  uncoupling  the 
pusher,  but  for  coupling  on  a  stop  is  necessary,  and  a  single  stop  of  a 
heavy  tram  costs  more  than  a  five-  or  even  ten-mile  run  of  a  light  engine, 
which  would  otherwise  be  standing  idle  with  steam  up. 

773.  In  considering  the  question  of  the  probable  duty  of  assistant  en- 
gines it  is  further  to  be  remembered  that  trains  do  not  come  at  equal  in- 
tervals of  time  apart,  but  some  are  likely  to  come  so  near  together  that 
two  or  more  engines  will  be  almost  indispensable  at  certain  times  of  the 


day,  and  some  so  far  apart  that  much  time  will  be  lost  while  under  steam. 
On  the  other  hand,  good  time  can  generally  be  made  down  hill ;  and  the 
systems  of  automatic  and  other  block  signals  have  now  been  brought  so 
near  perfection  that  short  sections  at  least  can  be  so  protected  that  little 
time  need  be  lost  between  trains  for  the  sake  of  allowing  a  margin  of 
safety  in  time. 

American  railways  are  but  beginning  to  avail  themselves  of  these  in- 
terlocking and  signal  devices,  the  use  of  which  may  be  expected  to  ma- 
terially increase  hereafter.  For  sections  on  which  pushers  are  used  they 
are  particularly  well  adapted.  At  such  points  the  number  of  trains  is 
practically  doubled,  and  it  may  well  be  a  question  between  such  signals 
and  a  double  track. 

For  any  considerable  traffic  a  telegraph  station  at  top  and  bottom  of 
the  grade  is  all  but  indispensable. 

THE    COST    OF    ASSISTANT    ENGINES. 

774i  This  may  be  divided  into  three  elements; 

1.  Interest  charge  on  the  original  cost,  special  to  the  use  of  pushers,  in- 
cluding extra  engines,  engine-houses,  if  any;  sidings;  block  signals,  if  any; 
etc. 

2.  Cost  per  day  for  wages  and  a  certain  portion  of  the  fuel  and  repair 
charge;  all  of  it  independent  of  the  mileage  run  per  day,  as  is  also  the  cost 
of  maintclning  block  signals,  if  any. 

3.  Cost  per  mile  run  for  fuel  and  repairs,  and  for  wear  and  tear  of 
road-bed,  track,  and  sidings. 

775.  When,  as  will  usually  happen,  an  approximately  fair  mileage  can 
be  obtained  from  the  assistant  engines,  say  80  to  100  miles  per  day,  it  is 
unnecessary  to  separate  these  items  from  each  other,  but  the  whole  cost 
per  mile  run,  exclusive  of  maintenance  of  way  and  interest  charges,  may 
be  assum.ed  not  to  vary  materially  from  that  of  ordinary  through  engines, 
unless  there  is  some  considerable  difference  in  weight. 

The  experience  of  the  Philadelphia  &  Reading  Railroad  indicates  that 
*hj  intermittent  service  of  pushing  engines  does  not  add  materially  to 
€Xf)er.ses,  and  much  other  evidence  to  the  same  effect  might  be  given,  as 
^Iso  for  the  fact  that  assistant  engines  will  realize  a  somewhat  higher 
yearly  service  than  through  engines,  owing  to  the  nature  of  their  service, 
which  facilitates  care  and  prompt  repairs.  At  least  the  difference  in  cost, 
il  any  exist,  must  in  general  be  trifling.  Assuming  there  were  none  at  all, 
the  DIRECT  RUNNING  EXPENSES  for  fuel,  oil,  and  water,  repairs  and  engine- 


6o2 


CHAP.  XVL— ASSISTANT  ENGINES— COST  OF. 


wages  would  average,  as  per  Table  80,  page  179  (see  Chap.  V.  for  further 
details),  20.8  cents  per  mile. 

776.  The  maintenance-of-way  expenses  must  also  be  estimated  at 
a  considerable  figure.  There  is  a  peculiar  temptation  in  this  case  to  fall 
into  the  error  discussed  in  par.  125.  and  assume  that,  except  in  the  one 
Item  of  wear  of  rails,  there  will  be  little  additional  expense  for  mainte- 
nance of  way ;  but  partly  for  the  indirect  causes  discussed  in  par.  125 — the 
necessity  of  maintaining  a  higher  standard  as  trains  increase,  as  well  as 
of  keeping  up  to  the  same  standard— the  cost  of  maintenance  of  way  will 
certainly  be  materially  increased.  For  reasons  which  may  be  readily  de- 
duced from  pars.  717-18,  it  will  certainly  not  be  excessive,  and  probably  as 
nearly  fair  as  is  possible,  to  assume  that  the  whole  cost  per  train-mile  of 
maintenance  of  way,  excluding  maintenance  of  bridges  and  buildings,  is 
increased  about  50  per  cent  by  the  pusher,  i.e.,  is  as  much  for  the  pusher 
alone  passing  up  and  down  as  for  the  whole  train  passing  one  way. 

777.  The  total  cost  of  pusher  service  (including  the  return  light  down 
grade)  per  mile  of  incline  (on  the  basis  of  $1.00  per  train-mile  average 
cost)  will  then  be  as  follows : 

Direct  running  expenses,  fuel,  water,  oil,  repairs,  and  wages 

per  mile  of  round  trip 41.6  cents 

Maintenance  of  way  expenses  per  mile  of  round  trip  17.5  cents 

(Table  80)  x  2 35,0      " 

Total  cost  per  mile  of  incline  per  round  trip 76.6     " 

Or  per  year  per  daily  train  per  mile  of  incline,  $0,766  x  365  =  $280.00. 

778.  The  introduction  of  steel  rails  and  the  general  cheapening  of  all  railway 
supplies  has  greatly  reduced  within  recent  years  the  cost  of  such  service,  especi- 
ally for  maintenance  of  way.  In  the  former  edition  of  this  work  this  expense 
per  mile  of  round  trip  was  estimated  at  94  cents,  of  which  54  cents  were  for  lo- 
comotive expenses  and  40  cents  for  maintenance. 

779.  This  estimate  assumes  that  the  pushing  engines  are  kept  fairly 
busy,  so  as  to  make  something  like  80  to  100  miles  per  day  average  mile- 
age. If  this  seem  impossible  or  doubtful,  it  will  require  to  be  increased 
correspondingly.  All  that  the  engine  falls  below  100  miles  per  day,  i.e., 
all  potential  mileage  not  actually  run,  may  be  assunied  to  cost  i  to  i  as 
much  per  mile  as  if  it  had  been  run,  and  is  so  much  added  to  the  cost  of 
what  is  run. 

780.  This  results  from  the  following  estimate;  Comparing  the  cost 
per  mile  run  of  an  engine  in  actual  service,  as  per  Table  80,  and  the  cost 


CHAP.  XVI.— ASSISTANT  ENGINES— COST  OF.  605 

of  an  engine  standing  still  in  the  yard  with  steam  up  for  an  equal  period 
of  time,  we  have,  approximately,  the  following: 

Average  in  service,  Standing  in  yard. 

cts.  or  p.  c.  Per  cent.    Am't,  cts.  or  p.  c. 

Fuel 7.6  10                  0.8 

Oil  and  water, 1.2  o. 

Repairs 5.6  10                    .6 

Wages 6.4  100                  6.4 

Maintenance  of  way,      .    .  17.5  o 

38.3  7.8 

781.  The  chief  loss  from  standing  still  is  in  engine-wages.  Fuel  is 
not  necessarily  wasted  to  any  such  extent  as  to  make  it  an  item  of  im- 
portance. The  total  consumption  per  hour  of  an  engine  standing  in  the 
yard  to  simply  make  good  the  loss  from  radiation  has  been  determined 
by  experiment  not  to  exceed  necessarily  24  to  35  lbs.  of  coal,  or  about  the 
quantity  burned  in  service  in  running  one  halt-mile.  This  would  indi- 
cate that  the  consumption  of  an  engine  standing  idle  in  a  yard  for  a 
whole  day  with  steam  up  would  only  be  one  or  two  per  cent  of  what  it 
would  be  in  service;  but  an  engine  standing  idle  only  between  intermit- 
tent periods  of  service  would,  by  carrying  a  larger  fire  and  the  cooling  off 
of  the  machine,  as  well  as  by  blowing  oflf  through  the  safety-valve  and 
other  effects  of  careless  firing,  waste  much  more  than  this  proportion ;  so 
that  the  allowance  made  above  (10  per  cent)  is  hardly  too  high. 

782.  The  effect  on  cost  of  repairs  per  mile  run  of  intermittent 
work  is  likewise  slight.  There  is  no  doubt  some  bad  effect  from  the 
intermittent  and  irregular  nature  of  pusher  service,  but  the  mere  fact 
that  an  engine,  between  its  trips,  stood  idle  with  steam  up  for  an  hour, 
more  or  less,  instead  of  immediately  starting  off  on  another  trip,  would 
of  itself  add  little  to  the  cost  of  repairs  per  mile  actually  run.  Deterio- 
ration would  no  doubt  be  going  on,  but  all  the  great  causes  of  deteriora- 
tion— wear  and  tear  of  running  gear  and  machinery,  from  stopping  and 
starting,  brakes  and  running  over  the  track,  injury  to  boiler  and  boiler- 
tubes  by  cooling  off,  by  the  fierce  heat  of  the  fire  and  by  the  mechanical 
action  of  the  coal  drawn  through  the  tubes,  etc.,  etc. — are  absent.  The 
above  allowance  is  therefore  ample,  and  probably  excessive,  leading  to 
'^he  resulting  conclusion,  that  the  cost  of  an  engine  per  hour  standing  in 
the  yard  with  steam  up  is  little  more  than  one  fifth  as  much  as  if  in  mo- 
tion at  15  or  20  miles  per  hour. 

The  correctness  of  this  conclusion  might  be  indicated  in  another  way 


^ 


6o4   CH.  XVI,— ASSISTANT  ENGINES  AND  THROUGH  GRADES.      J 

by  comparison  with  experience  with  switch  engines,  but  more  detailed      ' 
comparison  would  lead  us  too  far. 

783.  The  interest  charge  on  pusher  engines  is  fairly  chargeable  to  the 
cost  of  the  service  as  well  as  the  running  expenses,  for  the  same  reason 
that  the  interest  charge  in  the  extra  engines  required  to  operate  a  heavier 
grade  must  fairly  be  added  to  the  other  expenses  entailed  by  the  grade, 
as  specified  in  par.  721.  Properly  speaking,  the  first  cost  of  these  extra 
engines  is  a  part  of  the  cost  of  constructing  the  line  of  those  grades,  as 
much  as  the  bridges  or  track  thereon,  and  it  should  be  included  in  the 
estimate  of  the  cost  of  construction  unless  the  interest  charge  is  added 
to  the  operating  expenses. 

784.  To  accurately  estimate  the  cost  of  pusher  service,  then,  we  must 
determine — 

First.  The  length  of  pusher  run  in  miles  (par.  'J6^). 

Secondly.  The  probable  number  of  daily  trips  per  engine,  and  hence 
the  number  of  engines  required  for  the  given  traffic.  * 

Thirdly.  Determine  the  annual  interest  on  their  first  cost. 

Fourthly.  Compute  the  cost  of  the  mileage  made,  according  to  pars. 
777  and  780. 

The  sum  of  the  last  two  items  will  be  the  total  cost  of  the  pusher  ser- 
vice. 

COMPARISON   OF   PUSHER-GRADE     LINES   WITH    UNIFORM    GRADIENTS. 

785.  Ordinarily,  when  pusher  grades  are  used,  they  will  not  be  per- 
iectly  balanced  with  the  through  grades,  but  either  one  or  the  other, 

whichever  opposes  most  difficulties  of  con- 
struction to  obtaining  low  grades,  will  be 
the  true  limiting  gradient.  The  other 
must  then  be  assumed,  in  order  to  give  a 
fair  comparison  with  a  uniform  gradient 
line,  to  be  of  such  rate  as  to  give  a  per- 
fect balance  (Table  182),  although  the  fact 
that  it  is  really  lower  will  not  therefore  be  a 
wholly  valueless  advantage,  even  for  freight 
purposes.  In  Fig.  179.  for  example,  the  0.7  through  grade  and  the  1.75 
pusher  grade  are  not  perfectly  balanced.  The  pusher  grade  should  either 
be  reduced  to  1.65  or  the  through  grade  be  assumed  to  be  equivalent  to 
•0.75.  unless  the  circumstances  make  it  proper  to  assume  the  use  of 
heavier  pusher  engines  than  through  engines,  which  is  rarely  the  case 
<par.  763  et  seg.). 


Fig.  179. 


CH.  XVI.— ASSISTANT  ENGINES  AND  THROUGH  GRADES.    605. 

786.  If,  then,  we  have  two  alternate  locations,  AB  and  AA'B,  Fig. 
179,  one  of  which,  AB,  is  on  a  lower  through  grade  (say  of  1.25  per 
cent),  which  it  has  appeared  practicable  to  operate  without  assistant 
power,  and  the  other,  A'B,  is  the  lowest  through  grade  which  it  has 
been  or  will  be  practicable  to  secure  apart  from  the  incline  AA',  which 
it  is  expected  to  work  with  assistant  power,  BY  adopting  the  LINE 
WITH  ASSISTANT   POWER — 

First.  We  gain  what  is  equivalent  to  a  reduction  in  the  ruling  grade, 
from  the  rate  AB,  which  in  the  diagram  is  1.25  per  cent,  to  the  rdit^  A'B, 
whatever  it  may  be.  The  amount  of  this  gain  will  depend  upon  the  skill 
and  good  fortune  with  which  the  grades  have  been  adjusted,  but  it  wilL 
ordinarily  be  a  very  considerable  difference. 

Second.  We  lose  the  cost  of  assistant  power  on  the  incline,  as  esti- 
mated according  to  pars.  'JTJ~']%\. 

787.  The  problem  being  thus  stated,  the  values  previously  deter-^ 
mined  give  us  a  ready  and  simple  method  of  solving  it.  Thus  if,  in  Fig. 
179,  we  have  estimated  the  probable  number  of  daily  trains  required  on 
the  pusher-grade  line  A'B,  which  is  actually  a  0.7  maximum,  but  is  virtu- 
ally m^de  0.75  by  the  effect  of  the  imperfect  balance  of  the  pusher 
grades,  then,  by  adopting  the  line  having  a  uniform  maximum  gradient 
of  1.25  per  cent,  we  have  in  effect  increased  the  ruling  grade  0.50  per 
cent.  Now,  assuming  the  pusher  line  to  be  100  miles  long  with  a  pusher 
grade  of  10  miles  length  on  it,  and  the  other  line  to  be  105  miles  long, 
the  estimated  difference  in  the  operating  values  of  the  two  alignments- 
would  be  as  follows,  allowing  the  rate  of  interest  on  capital  to  be  5  per 
cent. 

In  favor  of  the  pusher  line  A  A'B,  per  daily  train  : 

Difference  in  ruling  grade — a  saving  of  0.50  per  cent  increase 

above  a  0.7  per  cent  grade  :  Value  by  Table  178,  $3,541  -> 

0.05  X   5  =  $354,000  for  a  division  100  miles  long.     For  a 

division  105  miles  long  we  have  (par.  740),  $354,000  x  105  =  $371,700 

In  favor  of  the  uniform  gradient  AB  : 

10  miles   saved   of    assistant-engine   service,  cost  by  par.  "jyj 

$2,800,  which,  capitalized  at  5  per  cent,  = $56,000 

Net  difference  in  operating  value  due  to  difference  in  gradients 

only,  in  favor  of  line  ^^'^ $315,700 

Value  of  5  milesof  distance  in  favor  of  line  ^y^'^  possibly  noth- 

^200 
ing,  and  possibly  by  par.  196,  — -—  x  5  =        $29,000 

Total  difference  in  operating  value,  per  daily  train,  in  favor  of 

low-grade  (pusher)  line $344,700 


€ 


6o6   CH.  ItVL— ASSISTANT  ENGINES  AND  THROUGH  GRADES, 


To  this  is  to  be  added  an  allowance  for  any  difference  in  the  probable 
traffic,  for  any  loss  of  time  of  assistant  engines,  and  for  any  difterence  in 
the  probable  capital  expenditure  for  locomotives,  which  will  naturally 
be  least  on  the  line  which  shows  the  highest  operating  value. 

788.  By  computing  various  examples  of  this  kind  it  will  be  seen  how 
very  large  an  economy  almost  invariably  results  from  using  pushers,  but 
the  condition  that  the  pusliers  must  be  kept  busy  and  be  always  on  hand 
to  have  them  economical  must  be  remembered.  The  larger  the  trartic 
of  the  road  the  more  easily  can  this  be  assured,  and  consequently  the 
more  frequently  can  pushers  be  used.  They  are  sometimes  used  as 
often  as  three  or  four  times  on  a  division,  but  with  a  light  traffic  this 
would  be  inexpedient. 

All  the  preceding,  however,  applies  to  freight  business  only.  The 
use  of  pushers  in  passenger  service  is  far  less  general  (par.  757). 

789.  Whether  for  passenger  or  freight  service,  perhaps  the  most  ad- 
vantageous and  satisfactory  basis  of  comparison  of  all  for  comparing 
alternate  systems  of  gradients,  as  it  certainly  is  the  simplest,  is  to  deter- 
mine the  number  of  engine-miles  which  must  be  run  per  through  car  (or 
ton) — i.e.,  per  car  or  ton — moved  over  the  line  for  the  entire  distance 
between  termini. 

A  "car"  has  become  in  recent  years  such  a  very  indeterminate  thing, 
owing  to  the  rapid  increase  in  weights  carried,  that  the  ton  is  the  best 
limit  to  use,  as  in  Table  170,  giving  the  capacity  of  engines  on  various 
grades. 

By  this  process  the  effect  of  differences  of  distance  as  well  as  grad- 
ients is  included  in  the  same  estimate,  and  having  assumed  a  reasonable 
price  (see  Table  143)  for  the  cost  of  the  additional  motive-power  and 
train-service  required,  the  estimate  is  very  readily  completed. 

790.  Thus  the  example  already  given  (par.  787  and  Fig.  179)  may  be 
compared  as  follows : 

\J\nt^  AA' B  iox  pushers:  105  miles;  10  miles,  1.25  per  cent  (79.2  ft. 
per  mile),  90  miles,  actually  0.7  per  cent,  but  in  effect  0.75  per  cent. 
Regular  load  for  through  engine  with  11  tons  on  drivers  (Table  170),  881 
tons. 

Line  AB^  uniform  gradient :  100  miles,  1.25  per  cent  (52.8  ft.  per 
mile).     Engine  load  (Table  170),  592  tons. 

We  then  have  this  comparison  : 

Line  AA'B^  881  tons  x  105  miles  =  92,505  ton-miles  hauled  by  100  + 
10  miles  run  by  engine  (in  one  direction),  or  841  ton-miles  per  engine- 
mile,  or  -^  =  8.0  through  tons  per  engine-mile. 
105 


CH  XVI.— ASSISTANT  ENGINES  AND  THROUGH  GRADES,   607 

• , 

Line  AB,  592   tons,  through  load,  no  pusher  service,  or  i^-  =  5.92 

through  tons  per  engine-mile. 

8  00 
We   have   then   -- —  =  35.14  per  cent  excess  of  engine-mileage  on 

592 
line  AB  for  the  same  through  traffic,  whatever  it  may  be  ;  and  estimating 

the  cost  of  this  extra  engine-mileage  at  about  half  the  average  cost  of  a 
train-mile,  as  in  par.  720  (which  is  not  quite  correct,  because  the  excess 
of  /r«/«-mileage  on  line  AB  is  even  greater  than  the  excess  of  engine- 
mileage)  the  freight  operating  expenses  over  the  two  lines  will  be  to 
each  other  about  as  100  to  1 17.6.  Estimating  then,  however  rudely,  the 
operating  expenses  over  either  line,  we  have  a  tolerably  close  indication 
of  the  difference  in  value  between  them,  which  will  lead  to  almost  exactly 
the  same  total  as  in  par.  787. 

791.  With  reference  to  the  passenger  business  on  this  particular  line, 
if  only  a  moderate  through  traffic  is  to  be  handled,  the  difference  in  the 
gradients  will  be,  with  well  arranged  stations,  a  matter  of  little  conse- 
quence. If  only  a  little  heavy  passenger  traffic  is  to  be  handled,  under 
otherwise  favorable  conditions,  the  uniform  gradient  of  1.25  per  cent 
will  have  a  certain  advantage ;  but  if  any  really  heavy  passenger  traffic  is 
to  be  handled,  the  pusher  line  will  have  much  the  same  advantage  for 
it,  and  for  much  the  same  reasons  as  it  has  for  the  freight  traffic.  It  is 
a  much  more  indeterminate  problem,  but  the  financial  importance  of 
high  passenger  speeds  at  all  points  and  the  effect  upon  it  of  low  gradients 
and  easy  curvature  is  generally  over-estimated  (pars.  757-9)* 


6oS    CH.  XVII.— BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC, 


i!i 


CHAPTER  XVII. 

THE    BALANCE   OF    GRADES    FOR    UNEQUAL    TRAFFIC. 

792.  An  engine  which  has  carried  a  full  load  in  one  directioa 
must  return  at  nearly  the  same  expense,  whether  the  train  be- 
hind it  be  fully  loaded  or  not.     There  must,  of  course,  be  the 
same  number  of  cars  in  each  direction,  in  the  long-run,  or  very 
nearly  so  (there  being  some  lines  over  which  considerable  num- 
bers of  cars  run  only  in  one  direction,  returning  by  other  routes), 
and    of  course  there  is  always  precisely  the  same  amount  of 
motive-power  available.     If,  therefore,  the  movement  of  traffic 
is   permanently  heavier  in   one  direction  than   in   the  other,  or 
there  is  good  reason  to  expect  that  it  will  be,  the  grade  opposed 
to  the  lighter  returning  traffic  may  be  made  heavier  than  that  in 
the  opposite  direction   by  an  amount  sufficient  to  make  the  re- 
sistance of  trains,  and  hence  the  requisite  motive-power,  the  same 
in  both  directions.     No  advantage  whatever  results  from  reduc- 
ing  the    return    grades  below   this,   beyond   the   small  amount 
which  represents  its  value  for  occasional  emergencies  when  the 
usual   balance   of  traffic  is  temporarily  disturbed,  and   the  still 
smaller  amount  which  represents  the  value  of  reducing  the  rate 
of  any  grade,  as  pointed  out  in  par.  462;  and  hence  great  economy 
may  sometimes   be  effected  in   construction   by  utilizing  to  the 
full  such  increase  in  grade  as  is  legitimately  made  possible  by 
the  difference  in  resistance  due  to  the  lighter  load  in  one  direc- 
tion. 

793.  The  determination  of  the  proper  balance  of  grades, 
under  any  assumed  difference  of  traffic,  is  a  simple  matter.  The 
determination  of  the  basis  of  fact  upon  which  the  adjustment 
must  rest  is  not  so  simple,  but  rather  one  of  great  uncertainty, 
except  in  some  cases  of  roads  built  for  carrying  minerals  or 


CH,  XVII.-BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC   609 

Other  special  traffic.  For  roads  of  a  large  and  mixed  traffic  as 
even  our  through  East  and  West  trunk  lines,  the  problem  is  much 
complicated  by  the  fact  that  changes  of  importance,  especially 
in  the  transportation  of  minerals  or  from  the  construction  of  new 
hnes,  are  liable  to  occur  at  any  time.  Thus  the  growino-  an- 
thracite coal  trade  to  the  West  has  produced  and  is  producing 
great  changes  in  the  ratio  of  the  tonnage  East  and  West;  and  not 
unfrequently  on  different  parts  of  the  same  line  the  burden  of 
traffic  IS  m  opposite  directions— perhaps  from  causes  entirely  be- 
yond foresight  when  the  road  was  first  built.  Nearly  always  the 
ratio  of  preponderance  varies  considerably  from  point  to  point. 

794.  On  the  Pennsylvania  Railroad  the  balance  of  traffic  is 
Widely  different  at  different  points,  the  westward  preponderating 
greatly  at  the  western  end,  and  the  eastward  at  the  eastern  end, 
as  shown  in  Table  184,  which   is  well  worthy  of  study.     Table 

Table  184. 

Comparative  Volume  of  the  Traffic  East  and  Traffic  West  at  Various 
Points  on  the  Main  Line  of  the  Pennsylvania  Railroad,  between 
New  York  and  Pittsburg.     1885. 


Jersey  City. 

Trenton 

Philadelphia 
Columbia. . . 
Harrisburg . . 

Mifflin 

Altoona 

Conemaugh. 

Derry 

Pittsburg. . . . 


Miles  from 
New  York. 


I 

57 

91 
171 

196 

245 
327 
364 
398 
444 


Comparative  Volume  of 
Traffic  (Phila.  =  i.oo). 


Eastward. 


0.51 
0.74 
1.00 
1.06 
1. 17 
0.98 
0.77 
0.72 
0.56 

o.3oi 


Westward. 


1. 15 
1. 13 
I.OO 

0.92 

0.94 

o.8r 
1. 10 
1.05 

0.73 
1.27 


Ratio  of  Loaded  Cars.* 
East  to  West. 


I  to  1.47 
I  to  2. 13 
I  to  3.26 
I  to  3.76 
I  to  4.09 
I  to  3.97 
I  to  2.25 

I    to    2.22 

I  to  2.49 
I  to  0.78 


^L^^T^'T"'^  '"  '^'  """'  "^^  '^"  '°"^*=''  '^^•^  ^*^«^  ^'■^  '»'>'•«  J'&htly  loaded  than  those 
East,  so  that  the  actual  excess  of  east-bound  over  west-bound  was  greater  than  this  tabl^ 

it'wT';  ^^^'"^'"^^;  -^^-  ^^^  -«^-^-"^  -"  were  presu  Jbly  the  heav.es"     tI 
average  drsproportton  over  the  •u>hole  road,  in  ton-miles,  may  be  deduced  from  Table  98  to  be 

in  d^ff/'^"''''"^  '°  "^f "  '^  "  '^'■"  ^'  ^'"  '^^'  '^^  ^^"^^'°"  '"  the  disproportion  is  as  lawless 
•n  different  years  as  the  above  table  shows  it  to  be  on  different  parts  of  the  same  line 

39 


6lO   CH.  XVII.— BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC. 


flu 


! 


^ 


i 


98,  pages  232-3,  shows  the  revolutionary  way  in  which  this  dis- 
proportion has  varied  during  the  past  forty-five  years,  or  during 
the  entire  liistory  of  the  road.  Neither  the  extent  nor  the  nature 
of  these  changes  could  well  have  been  anticipated  when  the  road 
was  first  constructed;  but  from  our  present  stock  of  knowledge, 
actual  or  potential,  as  to  the  course  of  such  matters  in  the  past, 
we  may  make  a  reasonable  and  safe  approximation  at  least  to 
tlie  future  probabilities  in  this  respect,  by  investigating  the  facts 
as  to  neighboring  or  rival  lines.  The  proper  manner  of  doing 
this  we  will  shortly  consider.  A  large  body  of  further  statistics 
of  the  same  kind  as  to  other  roads  might  be  presented,  but  not 
enough  to  serve  any  more  useful  purpose  for  any  particular  line 
than  the  approximate  figures  given  in  this  chapter,  without  an 
inadmissible  amount  of  them. 

795.  Assuming  the  ratio  of  the  tonnage  in  each  direction  to  be 
known  or  assumed,  the  admissible  difference  of  gradients  to  correspond 
may  be  very  quickly  determined  by  the  aid  of  the  long  Table  170,  by  de- 
termining the  total  load  in  tons  behind  the  tender  which  must  be  hauled 
on  the  return  trip,  for  a  given  disproportion  of  tonnage.  The  total  load 
can  at  once  be  divided  into  paying  load  (freight)  and  dead  load  (cars),  if 
we  know  or  assume  the  average  load  and  weight  per  car.  By  1890,  with 
the  prevailing  tendency  to  increase  average  load,  it  is  probable  that  the 
total  load  hauled  in  the  direction  of  heaviest  traffic  might  fairly  be 
divided  as  follows : 


General  Traffic,  . 

Total  weight 

per  car  or 

train. 

.      .           1.00 

Live  weight 

per  car  or 

train. 

0.60 

Dead  weight 

per  car  or 

train. 

0.40 

Mineral  Traflic,  . 

.      .           1. 00 

0.72 

0.28 

At  present  this  is  a  little  too  favorable ;  not  as  respects  the  nominal 
loads,  but  as  respects  the  loads  actually  hauled,  although  some  of  our 
best  roads  approach  it.  For  example,  the  average  load  0/  loaded  cars  on 
the  Pennsylvania  Railroad  is  now  14  tons,  and  of  East-bound  only  15^ 
tons.  The  average  weight  of  the  empty  cars  is  probably  in  the  neighbor- 
hood of  lo^  tons.     See  Table  154.  p.  486. 

Then  if  the  return  tonnage  be  only  half  as  great,  the  total  weight  of 

return  trains  will  be  only  0.60  -f-  -—  =  80  per  cent  as  heavy  in  tons;  and 
having  computed  this  weight  in  tons  (making  also  an  allowance  which 


Cff.  XVII.-BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC.   6ll 

we  shall  consider  in  a  moment)  we  find  at  once  from  Table  170  the  cor 
respondmg  grade.  'luic  170  tne  cor- 

give?sufficient'  dr'to'"""^?  ""f '  "'  ''^'°"  "'^^  <=°™P"'«'^-  »'>-'' 
ZL  cond  Hon,  ^K  f}^  *''^  P™P"^  '''''^"«  ""der  almost  any 

there  are  a  good  L.y  ::^CSi:X  1^0^^  ^^mlsTat  ^^ 
wh,ch  ,s  probably  the  reason  why  in  not  a  few  instances  oactua  pic 
tice  errors  of  importance  have  been  made  in  it  *  ^ 

plicltld  rrtrfonr""  °'  *''^/'--""=-'  ta-ance  of  gradients  is  com- 
I.  The  journal  friction  of  empty  cars  is  at  least  2  lbs  per  ton  (-  o  r 

,r.ffi!  "'^°'^«"';f  balance  of  grade  to  that  extent  in  favor  of  the  liehtest 
I  ptv'"Tti:  hlr  "h'""  '""^'^-  ^""^  P-PO^io-tely  if  a  par^  fetum 
tZLeHi'es  '°"  '"  *=°'"P"'"«  '^^'^'^  '«5.  as  indicated  by  the 

orcars''i=ert;iT;^.^^^^^ 

cent,  win  go  empty  even  i„\he  dt^  ion  of    he '  eavTsf  traffif  Th'" 
cars  serve  to  increase  by  so  much  the  proportion  o    t  e    ead  t  thi'": 
load  of  trams,  and  by  so  much  diminish  the  admissible  d^^erence  in  j  I 
dients,  and  so  also  will  the  fact  that  even  loaded  drs  do  nn,   K  ^ 
means  average  their  full  nominal  caoacitv      Roth  of  ?J      ,  ^  ^"^ 

^n/f  ®"  ^'  ^''^  ^'^P^oportion  of  traffic  varies  not  only  from  year  to  vear 


Eg.,    a   prominent  text- book  gives  extrart«  frr»r«  ^«;  •  1 

-i..rcouMr.aXrr:stm:;L:Hr„r'''"'' "  "^  --'-■ ''- 


6l2    CH.  XVII.— BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC, 

Table  185, 

Proper  Adjustment  of  Ruling  Grades  for  an   Unequal  Volume  of 

Traffic  in  Opposite  Directions. 

[Correct  within  an  inconsiderable  percentage  for  all  classes  of  engines  and  conditions. 
of  service.  Computed  for  an  average  Consolidation  engine  from  Table  170,  as  explained 
in  par.  795.  Rolling-friction  of  empty  cars  assumed  to  be  2  lbs.  per  ton  greater  than  that 
of  loaded  cars.] 


Opposing 

RETURN  GRADES 
;  AN  Equal  Resistance  to  the  Power  of  the  Engine  if  the 
Gross  Weight  of  Cars  and  Load  returning  is— 
(Weight  in  direction  of  heaviest  traffic  =  i.oo) 

Gradb  opposed 

TO  Heaviest 

Traffic. 

.88 

.76 

.64 

.52 

.40 

.28 

Pet  Cent. 

Ratio  of  Return  Freight  only  to  that  in 
Direction  of  Heaviest  Traffic. 

Freight 

Cars 

Returning 

Empty. 

Coal  Cars 

Returning 

Empty. 

(See  par.  802.) 

0.8 

0.6 

0.4 

0.2 

Level 

.03 

.08 

.15 

.29 

.46 

0.84 

.1 
.2 

•3 

.4 
.5 
.6 

.7 
.8 

•9 

.14 
.26 

•37 

.48 
.60 

•71 

.82 

93 
1.04 

.21 
.34 
.47 

.60 
.72 

.85 

•97 
1. 10 
1.22 

•30 
.46 
.61 

.75 
.90 

1.04 

1. 19 

1.33 
1.48 

•45 

.63 

.81 

.98 
1. 16 

1.33 

1.50 
1.66 
1.83 

.69 

.92 

1. 14 

1.35 
1.56 

1.77 

1.98 
2.17 

2.37 

1. 14 

1.44 
1.73 

2.00 
2.27 
2.54 

2.79 
304 
3-28 

I.O 

1.15 

1.35 

1.62 

1.99 

2.56 

3-52 

1.2 

1.4 

I         1.6 

1.8 
2.0 
2.2 

2.4 
2.6 

2.8 

1-37 

1-59 
1. 81 

2.03 
2.24 
2.46 

2.68 
2.89 
3." 

1.60 
1.84 
2.08 

2.33 

2.57 
2.80 

3.03 
3.26 

350 

1.90 
2.17 
2.44 

2.71 
2.98 

324 

3.49 
3-74 
3-99 

2.32 
2.63 
2.94 

3-24 

3-54 
3.82 

4.10 

4-37 
4.64 

2.94 
3.31 
3.65 

3.98 
4.32 
4-65 

4.97 
5.20 

5.52 

396 
4.40 
4.80 

5-17 

5.55 
5.88 

6.21 

6.53 
6.83 

3.0 

3.32 

3-74 

4.23 

4.91 

5.80 

7.10 

3.5 
4.0 

3.86 
4.38 

4-30 
4.86 

4.84 
5-44 

5-54 
6.16 

6.46 
7.10 

7.87 
8.47 

Excess  rolling- 
friction  from 
empty  cars, . 

r            ^ 
.  0.4  1  0.8 

[0.02    0.04 

!  lbs.  per  ton 

1     1.2       1     1.6       1     2.0 

grade  per  cent 

0.06          0.08          O.IO 

2.0 

O.IO 

CH.  XVII.— BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC,   613 

missible  rate  of  return  grades  by  about  0.2  per  cent  in  the  "  north-east  comer"  of  the 
table,  Its  effect  decreasing  very  rapidly  from  that  point  in  each  direction. 

A  LOWER  RATIO  OF  ADHESION  (than  ^)  will  also  REDUCE  the  admissible  rate  of 
return  grade,  its  effect  being  very  important  in  the  "south-east  corner"  of  the  table  but 
decreasing  still  more  rapidly  in  each  direction  therefrom. 

The  use  of  tank  engines  will  very  materially  increase  the  admissible  rate  of 
return  grades,  having  a  directly  contrar>'  effect  to  a  lower  ratio  of  adhesion.  The  same 
IS  true  in  less  degree  as  the  proportion  of  weight  on  drivers  or  ratio  of  adhesion  is  increased 

None  of  these  changes  being  proper  ones  to  assume,  it  is  not  deemed  necessary  to  eive 
■exact  figures.  ** 


A  lower  assumed  rolling-friction  (than  8  lbs.  per  ton)  will  reduce  the  ad- 


moved  at  once;  and  since  there  must  be  more  or  less  irregular  fluctua- 
tions in  the  volume  of  all  traffic,  it  may  well  happen,  and  not  unfrequently 
does  happen,  that  for  the  time  being  the  burden  of  traffic  shall  be  in  the 
opposite  direction  to  the  normal  one.  Thus  on  the  leading  East  and 
West  lines  of  the  United  States,  especially  those  of  the  second  gfade.  it 
is  not  uncommon  to  see  engines  running  East  light  to  handle  an  lin- 
usual  quantity  of  West-bound  traffic,  although  there  is  normally  a  very 
heavy  excess  of  east-bound  traffic  on  nearly  all  of  them. 

When    this    occurs    favorable    west-bound    grades    are    a    decided 
economy,  although  ordinarily  they  may  be  unimportant. 

Nevertheless,  the  importance  of  this  cause  should  not  be  exaggerated 
Marked  irregularities  of  this  kind  are  exceptional  and  short-lived! 
and  would  justify  but  very  small  expense  to  reduce  grades  on  their 
account  below  what  the  average  requires.  Irregularities  of  5  or  10  per 
cent  may  be  expected  to  exist  for  nearly  half  the  time,  and  hence  to  jus- 
tify about  half  the  expense  for  reducing  the  grades  correspondingly  that 
would  be  incurred  to  provide  for  the  average  condition  of  the  whole 
traffic.  There  is  also  a  certain  small  economy  in  being  able  to  send 
back  some  of  the  surplus  engines  and  train  crews  light,  as  passenger 
extras. 

4-  For  passenger  traffic  equally  balanced  grades  are  always  desirable, 
as  noted  more  fully  in  par.  807  et  seq. 

799.  It  is  noticeable  that  all  four  of  these  limiting  provisos  tend  to 
diminish  the  admissible  variation  in  opposing  rates  of  grade.  In  the 
aggregate  they  indicate  that  a  reduction  of  the  grades  against  the  light- 
est traffic  by  something  like  0.2  to  0.3  per  cent  (10  to  16  ft.  per  mile)  be- 
low what  the  assumed  average  disproportion  in  weight  of  trains  seems  to 
require,  is  worth  nearly  half  as  much  as  if  required  by  the  average  con- 
ditions themselves.  When,  in  addition  to  these  reasons  for  approximat- 
ing more  closely  to  an  even  balance  in  spite  of  a  known  disproportion  of 
traffic,  the  very  existence  of  the  assumed  disproportion  appears  doubtful, 


I? 

!      4 


•     ( 


» '1 


11 


ti 


614   CH.  XVII.— BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC. 

Still  greater  caution  should  be  used  in  assuming  that  anything  will  be 
unobjectionable,  but  an  exact  balance  of  resistances,  which  latter  is  of 
course  the  safest  assumption  to  make  when  the  future  is  for  any  reason 
very  doubtful. 

Nevertheless,  although  the  estimates  of  the  probable  future  dispro- 
portion should  always,  for  the  reasons  given,  be  exceedingly  conserva- 
tive, it  may  on  many  if  not  on  most  lines  be  determined  with  practical 
certainty  that  a  certain  minimum  disproportion  at  least  will  exist  for  the 
decade  or  so  ahead,  which  is  as  long  (par.  78  et  seg.)  as  the  engineer  is 
financially  warranted  in  looking  ahead. 

800i  It  is  to  be  remembered  also  that  the  same  assumed  balance  of 
grades  which  permits  the  grade  in  one  direction  to  be  made  higher  re- 
quires the  grade  in  the  other  to  be  made  lower,  if  possible,  so  that  the 
assumption  of  a  certain  preponderance  of  traffic  in  one  direction  does 
not  warrant  any  relaxation  of  effort  to  obtain  low  grades,  but  merely 
gives  it  a  little  different  direction.  If  there  be  merely  a  probability  that 
the  traffic  in  one  direction  will  be  slightly  heavier  than  in  the  other, 
with  a  possibility  that  it  may  be  either  considerably  heavier  or  evenly 
balanced,  and  the  same  expenditure  will  substitute  grades  of  0.65  one 
way,  and  0.55  the  other,  in  place  of  0.6  grades  both  ways,  it  is  good  en- 
gineering to  do  this,  for  we  can  only  strike  an  average  between  the 
maximum  and  minimum  possibilities  and  act  in  accordance  with  the 
mean.  It  is  demonstrable  mathematically,  as  well  as  clear  to  the  reason, 
that  this  course  is  as  binding  upon  us  as  if  we  had  positive  knowledge 
that  the  mean  of  our  estimates  (if  they  really  are  such,  and  not  guesses) 
was  the  exact  truth. 

Topographical  considerations  often  make  it  impossible  to  even  at- 
tempt a  balance  of  gradients,  at  least  m  the  way  of  favoring  the  heaviest 
traffic.  It  is,  however,  nearly  always  possible  to  favor  the  expense  ac- 
count in  such  cases,  somewhat  at  least,  by  not  showing  unnecessary 
favors  to  the  lighter  traffic. 

801.  For  an  exclusively  mineral  traffic  the  expediency  of  ad- 
justing the  grades  for  the  full  theoretical  difference  can  rarely  be  ques- 
tioned, and  it  is  of  course  for  this  traffic  that  the  greatest  difference  is 
required.  At  the  present  time  the  ratio  of  load  to  weight  of  car  is  con- 
siderably over  2  to  I,  so  that  less  than  ^  of  the  weight  of  a  full  train 
is  cars  and  over  |  paying  load.  Consequently,  the  return  trains  of 
empty  cars  with  less  than  ^  as  much  as  the  full  trains,  and  the  proper 
balance  of  grades  shows  a  wide  contrast  in  them,  as  will  be  seen  in 
Table  185. 


CH.  XVII.— BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC.   615 

802.  An  important  fact  to  remember  in  considering  an  almost  exclu- 
sively mineral  traffic  is  that  whatever  general  freight  business  there  may 
be  will  probably  be  against  the  main  traffic  almost  exclusively,  and  that 
the  consumption  of  supplies  per  inhabitant  is  large  in  mining  regions, 
and  almost  wholly  imported.  The  traffic  per  inhabitant  of  mining  re- 
gions, including  shipments  of  machinery,  etc.,  as  also  the  outpur  per 
miner  (about  |  to  Vtt  of  the  total  inhabitants),  may  be  readily  estimated 
by  a  little  investigation.  The  figures  vary  too  greatly  to  attempt  any 
general  analysis. 

803.  For  general  freight  business  no  such  difference  as  with  mineral 
traffic  ever  exists,  but  something  closely  approaching  to  it  exists  at  times 
on  the  leading  East  and  West  trunk  lines,  on  which  the  normal  average 
is  only  from  3  to  4  tons  West  to  10  East.  It  is  probable  that  there 
will  always  continue  to  be  a  heavy  preponderance  of  East-bound  traffic 
in  the  United  States,  although  whether  it  will  continue  to  be  as  heavy 
in  the  future  as  in  the  past  is  a  far  more  doubtful  matter.  The  propor- 
tion of  export  traffic  will  become  relatively  less  as  the  population  of  this 
continent  increases,  and  this  traffic  has  now  a  great  influence  in  causing 
the  disproportion  of  traffic  which  at  present  exists.  If  the  East  were  to 
continue  to  be  the  manufacturing  region  par  excellence  this  loss  would 
be  compensated  for,  but  that  this  will  be  the  case  seems  very  doubtful. 

804.  An  enormous  West-bound  anthracite  coal-traffic,  moreover,  has 
sprung  up  within  the  last  few  years  which  is  reducing  and  will  still  more 
largely  reduce  the  existing  disproportion.  The  rise  and  growth  of  this 
traffic  is  a  good  illustration  of  the  great  changes  which  may  come  with 
time,  but  which  are  for  the  moment  not  considered.  It  is  the  chief  cause 
for  the  very  remarkable  reversal  of  the  current  of  local  traffic  shown  in 
Table  98. 

The  only  definite  fact  seems  to  be  that  the  burden  of  traffic  will  al- 
ways be  heavily  toward  a  manufacturing  or  mining  region  and  away 
from  the  shippers  of  the  heavier  cereals.  Thus  it  is  about  three  to  one 
from  West  to  East,  and  about  two  to  one  from  the  Northern  to  the 
Southern  States. 

805.  The  latter  fact  shows  that  it  is  not  safe  to  say  broadly  that  the 
burden  of  traffic  is  from  an  agricultural  to  a  manufacturing  region  ;  for 
the  South,  which  is  chiefly  agricultural,  ships  to  the  North,  as  yet.  much 
ess  m  weight  than  it  receives  ;  the  reason  being  that  its  exports  are 
largely  cotton,  and  that  the  current  of  its  commercial  business  follows  a 
kmd  of  triangular*  course— from  the  South  to  New  York  or  Europe, 
thence  to  the  interior  of  the  United   States,  and  thence  to  the   South 


I'M! 


6l6   en.  XVII.—BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC. 

again.     But  the  rapid  development  of  the  mineral  resources  of  the  South 
is  bringing  about  a  change  in  this  respect. 

806.  The  possibility  of  some  such  roundabout  process  of  exchange 
as  this,  especially  on  a  small  scale,  is  one  which  must  be  very  frequently 
remembered  if  a  reasonable  estimate  of  probabilities  is  to  be  made. 
Thus,  when  the  Mexican  system  of  railways  was  projected  it  became  at 
once  important  and  difficult  to  determine  in  which  direction  would  be 
the  largest  freight  movement.  The  central  plateau  is  a  region  of  great 
and  largely  undeveloped  grazing  and  agricultural  possibilities,  but  on 
the  other  hand  is  a  great  and  largely  undeveloped  mining  region,  hav- 
ing no  workable  coal  as  yet  known.  Bearing  in  mind  the  character  of 
the  regions  of  the  United  States  to  the  north,  the  writer  concluded  that 
the  traffic  would  not  probably  be  very  unequal,  but  that  the  tonnage 
would  be  the  heaviest  northward.  This  expectation  has  not  yet  (1885) 
been  fulfilled,  but  the  direct  contrary  is  the  case,  the  preponderance 
being  very  heavily  into  the  City  of  Mexico,  and  largely  on  account  of 
the  triangular  process  of  exchange  referred  to.  The  products  exported 
are  on  the  coast  or  seek  the  coast,  and  thence  by  very  indirect  channels 
pay  for  the  shipments  (as  yet  small)  which  go  to  Mexico  in  return  by 
rail.  Whether  or  not  this  tendency  will  continue  is  doubtful.  Proba- 
bly it  will  not.  but  the  burden  of  traffic  will  be  out  of  Mexico  when  a 
fuller  development  has  come.  In  any  case  it  illustrates  the  necessity  of 
looking  beyond  the  superficial  and  immediate  possibilities,  and  remem- 
bering that  great  changes  may  come  with  time. 

807.  For  passenger  service  grades  should  in  all  cases  be  equally 
balanced,  because  whether  passenger  cars  be  loaded  or  unloaded  makes 
but  an  inconsiderable  difference  (par.  606)  in  the  weight  of  trains,  even 
if  it  were  not  certain  that  passenger  travel  must  be,  in  the  long-run, 
equal  in  each  direction,  in  spite  of  a  temporary  preponderance  in  one 
direction,  due  to  emigration.  Therefore,  in  proportion  as  the  passen- 
ger traffic  is  a  larger  and  mineral  traffic  a  smaller  element,  and  in  pro- 
portion as  the  preponderance  of  freight  tonnage  is  doubtful,  the  expedi- 
ency of  seeking  uniform  grades  in  each  direction  increases. 

808.  It  follows  also,  that  when  an  unequal  freight  or  mineral  traffic 
exists,  combined  with  a  considerable  passenger  traffic,  there  is  always  a 
certain  advantage,  and  hence  a  certain  justifiable  expenditure,  in  reduc- 
ing the  rate  of  grade  in  either  direction,  although  the  other  be  left  un- 
changed. The  passenger  service  is  always  benefited  by  reducing  the 
higher  rate  of  grade,  whichever  it  may  be  (provided  ft  is,  for  passenger 
service,  a  de-facto  limiting  grade,  as  explained  in  par.  407) ;  and  after 


CH.  XVII.—BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC.   617 

this  has  been  done  there  is  a  certain  advantage  to  the  freight  traffic  only 
m  reducing  the  grades  against  the  heaviest  traffic.  The  admissible  ex- 
penditure for  doing  this  is  only  that  appertaining  to  the  particular 
traffic  benefited. 

809.  For  example,  suppose  the  grades  on  any  line  to  be  i.oo  and 
1.20  per  cent  (52.8  and  63  ft.  per  mile),  and  the  ratio  of  the  weight  of 
freight  in  each  direction  to  be  about  as  on  the  Pennsylvania  Railroads, 
viz  ;  as  i.o  to  0.3: 

IVell-adjusted  grades  for  freight  service  would  be  Percent 

_      (Table  185) 0.6  and  1.2 

Well-adjusted  grades  for  passenger  service  would  be 1.0  and  i.o 

We  can  properly  expend,  therefore,  to  reduce  the  grade  which  limits 
the  freight  traffic  (1.0  per  cent)  to  0.6  per  cent,  as  much  as  the  freight 
traffic  alone  justifies ;  and  to  reduce  the  grade  which  is  heaviest  for  pas- 
senger service  (1.2  per  cent)  to  1.0  per  cent  only  as  much  as  the  passen- 
ger service  alone  justifies,  which,  in  case  of  a  light  local  passenger  busi- 
ness, will  not  be  much  (par.  732). 

810.  Even  if  the  business  of  a  road  consists  of  three  distinct  classes 
of  traffic,  passenger,  freight,  and  mineral,  each  one  of  which  would  re- 
<iuire  a  different  balance  of  ruling  grades,  this  difference  need  introduce 
no  confusion  in  the  estimations  of  the  value  of  reducing  grades,  for  we 
have  only  to  determine  from  Table  185  to  what  class  or  classes  of  traffic 
any  proposed  reduction  of  grade  will  be  valuable  or  worthless  to,  and 
the  justifiable  expenditure  to  reduce  it  may  be  determined  for  that 
traffic  only  by  the  methods  of  Chap.  XV..  par.  726  et  seq. 

811.  It  may  also  be  noted  that  a  mineral  traffic  should  in  general  be 
considered  simply  as  a  part  of  the  general  freight  traffic.  It  is  only 
under  peculiar  circumstances,  as  when  the  haul  is  short  or  the  mineral 
traffic  is  very  large,  that  they  should  be  separately  considered,  and  never 
when  their  separate  conduct  would  involve  a  large  wastage  of  motive- 
power  or  of  empty  car-mileage,  in  either  direction,  since  the  two  can 
always  be  combined  together,  light  freight  trains  being  filled  up  with 
coal  cars  or  vice  versd,  as  is  now  done  on  the  trunk  lines.  It  has  even 
come  about  that  empty  grain  cars  returning  West  are  filled  up  with  coal  so 
as  to  go  loaded  in  both  directions,  and  this  tendency  may  be  expected 
to  increase  or  prevail  whenever  it  will  save  a  considerable  movement  of 
cars  in  opposite  directions,  since  it  effects  a  very  large  economy. 

812.  A  heavy  tonnage  goes  into  all  cities,  since  they  consume  much 
and  produce  nothing  except  in  the  form  of  manufactures,  which  for  the 


)i 


6l8    CH,  XVII.— BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC^ 


CH,  XVII.— BALANCE  OF  GRADES  FOR  UNEQUAL  TRAFFIC.   619^ 


most  part  weigh  much  less  Calthough  they  pay  much  more)  than  the  raw- 
materials  which  are  shipped  for  producing  them. 

813.  The  exact  balance  of  grades  for  the  traffic  becomes  easy  in  the 
case  of  a  line  already  in  operation,  and  this  should  be  the  first  step  in 
studying  contemplated  improvements,  since  it  may  save  the  necessity  of 
improving  the  grades  in  one  direction,  or  at  least  some  of  them. 

814.  The  lines  of  few  existing  railways  have  been  studied  during  construc- 
tion wiih  this  end  in  view.  Some  of  the  earlier  lines  come  the  nearest  to  it; 
for  example,  we  may  take  three  of  the  most  sagaciously  located  lines  in  the 
United  Slates— the  Baltimore  &  Ohio,  the  Pennsylvania,  and  the  Erie.  The 
Baltimore  &  Ohio  mountain  grades  have  been  laid  out  to  some  extent  with  this 
end  in  view,  since  they  have  2.2  per  cent  grades  (for  t6  miles)  opposed  to  West- 
bound traffic  and  only  2.0  per  cent  opposed  to  East-bound,  but  this  difference  is 
far  less  than  the  disproportion  in  traffic  would  warrant,  the  balance  for  2.0  per 
cent  with  a  disproportion  similar  to  that  of  the  Pennsylvania  road  (Table  185) 
being  about  3.2  per  cent.  This,  however,  is  the  less  important  on  such  a  line, 
because  the  heavy  grades  are  so  long  that  the  trains  and  motive-power  can  be 
adapted  quite  accurately  to  each  other,  as  they  are  in  fact,  on  each  separate 
grade.  Using  two  pushers  on  the  2.0  per  cent  grade,  and  only  one  on  the  2.2 
per  cent,  moreover,  would  about  equalize  them  for  such  a  disproportion, 
although  it  is  only  on  grades  of  some  length  that  two  pushers  can  be  advan- 
tageously used.  The  gradients  of  the  Baltimore  &  Ohio,  considered  as  a  whole, 
are  admirably  adapted  for  cheap  working,  in  spite  of  their  heavy  rates,  from 
the  fact  that  they  are  all  "bunched"  in  one  locality.  At  Piedmont  is  one  of 
the  largest  yards  in  the  world,  and  all  trains  are  made  up  anew  there. 

815.  The  Pennsylvania  road  has  i  per  cent  grades  opposed  to  East-bound' 
traffic.  The  weight  of  cars  and  freight  westward  being  by  Table  184  about 
I  to  0.4  in  the  neighborhood  of  Altoona,  a  correct  balance  of  grades  would  be 
by  Table  185  about  1.6  per  cent.  Actually  it  is  t.8  per  cent,  and  the  traffic  is- 
worked  with  one  pusher  eastward  and  two  pushers  westward. 

816.  The  Erie  is  at  two  or  three  of  its  leading  summits  a  good  instance  of 
well-balanced  grades,  which  is  not  the  least  of  the  striking  merits  of  the  line. 
Even  without  allowing  for  the  early  date  at  which  it  was  built,  the  consummate 
engineering  skill  with  which  it  was  carried  through  the  mountains  and  the  pri- 
meval forest,  without  the  aid  of  maps  and  without  a  single  tunnel  on  its  line  (as 
it  then  was;  one  has  since  been  built  at  Jersey  City),  with  very  low  grades,  and 
on  very  nearly  the  best  line  which  could  now  be  selected,  must  ever  excite  ad- 
miration. Nevertheless,  the  Erie  and  its  branches  afford  several  examples  of 
ill-adjusted  grades,  but  it  will  be  more  profitable,  as  well  as  more  just,  to  con- 
sider the  instances  on  its  main  line  where  they  have  been  carefully  adjusted. 

817.  The  Delaware  Division  ascends  eastward  out  of  the  Susquehanna 
Valley  on  a  60-ft.  (1.14  per  cent)  grade   for  8  miles,   thence   descends  on  a 


57  ft.  (1.08)  and  49-ft.  (0.93)  grade  for  about  7  miles  to  Deposit,  and  thence 
follows  an  unbroken  descending  grade  of  10  to  15  ft.  per  mile  to  Port 
Jervis.  The  curvature  probably  increases  the  equivalent  grade  to  about  0.35 
per  cent.  Now,  in  descending  eastwardly  from  the  summit  the  low  rate  at- 
tained is  attained  only  by  following  down  the  hill-side  at  an  elevation  of  40  or 
50  ft.  above  the  bottom  of  the  valley  for  nearly  the  whole  distance,  with  much 
curvature — about  one  mile  more  of  distance  and  at  least  twice  the  cost  for  con- 
struction which  would  have  been  necessary  for  a  line  located  in  the  bottom  of 
the  valley  on  a  grade  of  1.2  or  1.3  per  cent.  It  would  have  been  most  natural, 
therefore,  under  all  the  circumstances,  to  have  chosen  the  light  line;  but  let 
us  consider  the  consequences  to  the  light  trains  returning.  As  the  grades 
are  now,  a  single  pusher  engine  will  just  suffice  to  pass  a  fully  loaded  west- 
bound train  over  the  hill,  the  balance  being  (Table  185)  0.35  and  1.03.  Had 
the  grade  been  any  higher,  the  capacity  of  West-bound  engines  over  the  whole 
division  would  have  been  cut  down  in  proportion.  It  was  plainly  the  intent  of 
the  engineer,  therefore, — for  it  is  but  just  to  give  him  credit  for  the  foresight 
which  his  work  indicates, — that  East-bound  trains  should  be  taken  to  the  sum- 
mit from  Susquehanna  as  a  separate  matter,  leaving  all  the  remainder  of  the 
division,  for  trains  in  both  directions,  exceedingly  favorable.  As  a  matter  of 
fact,  trains  are  taken  up  from  Susquehanna  with  two  pushers. 

818.  On  the  Eastern  Division,  at  Port  Jervis,  a  different  adjustment  has 
been  used,  the  grades  against  East  bound  trains  being  46  ft.  and  against  West- 
bound 60  ft.,  which  is  approximately  a  correct  adjustment  for  enabling  trains 
with  pushers  to  run  over  the  hill  with  equal  loads  each  way.  The  remainder 
of  the  division  is  not  a  very  good  specimen  of  location.  Some  improvements 
in  recent  years  have  been  made  in  it,  but  it  is  questionable  if  a  radical  re- 
construction of  the  entire  division  would  not  prove  immensely  profitable.  On. 
the  Buffalo  and  Western  divisions  also,  and  on  many  of  the  branches,  ruling 
grades  were  made  the  same  each  way  at  considerable  expense  without  any 
adequate  compensating  advantage. 

819.  Examples  of  badly  adjusted  grades  on  other  lines  might  be  multiplied 
almost  indefinitely,  but  it  would  be  to  little  purpose  to  do  so.  When  the 
grades  are  long,  considerable  leeway  in  rate  may  be  taken  by  assuming  that  the 
grade  will  be  separately  operated,  but  with  short  grades  of  4  to  6  or  7  miles  this 
is  not  expedient. 


\\\ 


'620 


CHAP.  XVIIL^UMITING  CURVATURE, 


CHAP.  XVIII.-^LIMITING  CURVATURE. 


621 


curves  and  grade  together  make  the  equivalent  grade  a  succession  of  i.o 
and  0.5  per  cent  grades,  as  represented  by  the  dotted  line  of  Fig.  180. 

Such  conditions  have  precisely  the  same  deleterious  effect,  no  more 
and  no  less,  that  a  long  tangent  grade-line  would  have  if  broken  up  in. 
similar  fashion. 


I 

■ 


1 


CHAPTER   XVIII. 

LIMITING    CURVATURE    AND    COMPENSATION    THEREFOR. 

820.  Under  three  different  conditions  curvature  may  come  in, 
in  advance  of  gradients,  as  a  limiting  agent  to  fix  the  weight  of 
trains: 

1.  When  curves  are  introduced  on  a  maximum  grade  without 
reducing  the  rate  of  the  latter  by  wliat  is  called  the  compensa- 
tion FOR  curvature,  SO  as  to  keep  the  aggregate  resistance  con- 
stant on  both  curves  and  tangents. 

2.  When  a  line  is  nearly  or  quite  level,  and  yet  runs  through 
a  region  requiring  much  curvature  which  (as  is  very  apt  to  hap- 
pen on  such  lines)  cannot  be  "compensated"  because  there  are 
no  grades,  or  no  sufficiently  high  grades  to  reduce,  in  order  to 

•eliminate  their  additional  resistance. 

3.  When  on  lines  of  the  latter  (or  any  other)  class  curvature 
•of  such  short  radius  is  used  as  to  limit  the  length  of  trains  more 
than  would  the  same  amount  of  curvature  with  longer  radii. 

These  causes  are  more  or  less  interrelated  with  each  other, 
but  we  will  consider  them  separately,  so  far  as  may  be,  in  the 
order  mentioned,  summarizing  our  conclusions  at  the  end  of  this 
chapter  (page  632). 

821.  We  have  seen  (par.  335)  that  curve  resistance  varies  from  less 
than  0.5  lb.  per  ton  to  perhaps  2.0  or  even  more  lbs.  per  ton  per  degree 
of  curve,  according  to  circumstances ;  which  at  2  lbs.  per  ton  for  each 
tenth  of  grade  (par.  382)  is  equivalent  to  from  0.025  to  o.io  per  cent  of 
grade  per  degree.  Assuming,  therefore,  a  "straight"  (uncompensated) 
0.5  per  cent  grade.  Fig.  180,  with  alternate  equal  lengths  of  tangent  and 
10°  curves  succeeding  each  other,  and  assuming  that  the  curve  resistance 
is  (see  par.  834  below)  at  the  rate  of  i  lb.  per  ton,  the  effect  of  the  curve 
resistance  is  in  effect  to  double  the  grade  on  the  curves,  so  that  the 


^^^ 


id®         0:^-.?« 


'>^ 


/I' 


^^  ^ 


Fig.  180.— Effect  of  Unreduced  Curvature  to  reduce  Grades. 

822.  An  immense  portion  of  the  heavy  grade-mileage  of  the  world- 
has  been  constructed  in  precisely  this  way,  the  grade  being  carried 
through  at  a  uniform  rate  over  curves  and  tangents  alike.  Until  within 
recent  years  nearly  all  American  railways  were  so  constructed,  and  when 
the  curves  were  compensated  at  all,  low  rates  of  compensation  (0.02  and 
0.03  per  cent  per  degree)  were  and  still  are  chiefly  used,  for  which  indeed 
much  can  be  said  (par.  834  below),  although  in  general  a  less  rate  than 
0.05  cannot  be  regarded  as  good  practice. 

823.  The  practice  of  reducing  grades  on  curves  appears  to  have  been 
first  introduced  on  the  Continent.  American  engineers  soon  followed. 
English  engineers  have  neglected  and  still  do  neglect  it  very  generally. 
In  no  part  of  the  world  is  it  universal,  many  prominent  roads  in  this 
country  having  neglected  it  wholly ;  as.  for  instance,  the  Erie,  Boston  & 
Albany,  Baltimore  &  Ohio  (for  the  most  part),  Pennsylvania  (for  the 
most  part),  and  in  recent  years  such  lines  as  the  Cincinnati  Southern, 
Chesapeake  &  Ohio,  most  of  the  Denver  &  Rio  Grande,  and  a  host  ot 
other  lines. 

824.  The  argument  by  which  a  neglect  to  reduce  grades  on  curves 
has  been  justified,  when  any  attempt  at  all  has  been  made  to  justify  it,  is 
that  the  resistance  is  averaged  by  momentum  so  that  the  broken 
grade-line  of  Fig.  180  is  reduced  by  the  equalizing  effect  of  slight  fluctu- 


622 


CHAP.   XVIII.— LIMITING  CURVATURE. 


CHAP.   XVIII.— LIMIT ING   CURVATURE. 


623 


ations  of  velocity  to  the  continuous  0.75  grade-line  shown  below  it.  The 
general  principle  upon  which  this  argument  is  based  is  a  sound  one,  to 
the  extent  that  under  favorable  conditions  precisely  that  effect  may 
result,  either  on  actual  irregularities  of  grade,  or  on  equivalent  ones 
caused  by  unreduced  curvature.  It  is  not  true  at  all  that  any  injurious 
effect  upon  the  train,  or  any  increase  of  virtual  gradient,  necessarily  re- 
sults from  the  gradient  like  the  broken  line  in  Fig.  180  in  place  of  the 
straight  0.75  grades,  under  certain  and  proper  conditions.  Why  and  how 
this  is  so,  and  under  what  conditions,  has  been  so  fully  discerned  in 
Chap.  IX.  (par.  397  et  seq.)  that  it  need  not  be  repeated,  further  than  to 
say  that  a  curve  may  be  considered  as  adding  simply  so  much  to  the 
grade,  and  the  two  cases  be  treated  alike. 

825.  But  conditions  justifying  the  assumption  that  unreduced  curva- 
ture can  thus  be  made  harmless  by  the  effect  of  momentum  cannot  exist 
on  any  actual  maximum  grade,  unless  by  some  rare  accident,  and  conse- 
•quently  it  is  a  rule  which  should  be  regarded  as  of  universal  application, 
and  rigidly  adhered  to,  that  unreduced  curvature  should  under  no 
circumstances  be  permitted  on  the  maximum  grade,  and  that  the  reduc- 
tion should  in  general  be  ample,  especially  near  stations  and  where  there 
is  an  excessive  resistance.     The  reasons  for  this  are  three,  as  follows : 

I.  The  distribution  of  curvature  even  on  a  grade-line  only  a  few  miles 
long  naturally  tends  to  become  unequal.  Instead  of  being  equally  dis- 
tributed, as  assumed  for  merely  illustrative  purposes  in  Fig.  180,  it  is  far 
more  likely  to  be  concentrated  in  masses  of  perhaps  several  hundred 
degrees  of  almost  continuous  curvature,  with  long  intermediate  stretches 
of  much  better  alignment,  giving,  if  such  curvature  is  not  reduced,  an 
equivalent  profile  more  like  Fig.  185,  from  which  it  is  far  more  difficult 
to  obtain  a  straight  "  virtual  "  profile  (par.  398)  by  fluctuations  of  velocity 
than  with  a  more  even  distribution  of  curvature;  and  when  such  excess 
of  curvature  comes  well  up  toward  the  top  of  a  long  grade  it  becomes 
under  most  circumstances  practically  impossible  to  do  so. 

826.  2.  Even  if  the  curvature  be  tolerably  evenly  distributed,  the 
speed  on  maximum  grades  is,  with  the  full  train  which  good  operating 
management  presupposes,  necessarily  slow.  With  extra  heavy  car-loads 
or  in  unfavorable  weather — wet,  frosty,  misty,  very  cold,  or  windy — it  is 
necessarily  very  slow.  At  what  point  on  the  line  the  most  unfavorable 
conditions  will  be  encountered  (for  there  are  always  slight  variations, 
from  wind  or  differences  of  track  if  nothing  more)  cannot  be  exactly 
anticipated,  but  on  the  top  of  long  grades,  especially,  it  can  be  antici- 
pated with  confidence  that  a  very  slow  speed,  not  exceeding  10  or  12 


miles  per  hour,  will  be  rather  the  rule  than  the  exception.  At  such 
speeds,  and  especially  at  still  lower  speeds,  there  is  every  reason  to  be- 
lieve that  the  curve  resistance  is  greater  (pars.  308,  335),  while  there  is 
no  available  momentum  to  overcome  it.  A  train  moving  at  10  miles 
per  hour  (Table  118)  has  only  3.55  ft.  of  "  velocity-head."  At  a  compen- 
sation of  0.05  per  degree  (i  lb.  per  ton)  70°  of  curvature  will  destroy  this 
head  completely,  since  at  that  rate  of  compensation  each  20°  of  central 
angle  destroys  one  foot  of  vertical  head.  In  other  words,  a  train  mov- 
ing at  10  miles  per  hour,  which  could  just  continue  that  speed  on  a 
tangent,  would  be  stalled  at  once  by  seven  stations  of  10°  curve,  or,  if  by 
good  luck  not  stalled,  its  speed  would  be  reduced  so  low  that  additional 
journal-friction  (par.  640  and  Appendix  B)  as  well  as  (probably)  addi- 
tional curve-friction  would  come  in  and  ensure  stalling  on  any  closely 
following  curve. 

827.  3.  Stopping  of  trains  on  grades  from  accident  or  otherwise  is  not 
un frequently  necessary,  and  then  it  is  entirely  clear  that  a  stoppage  on  a 
long  unreduced  curve  is  a  disastrous  disadvantage,  especially  if  it  be  on 
a  long  succession  of  curves  so  as  to  forbid  the  expedient  of  backing  down 
off  the  curve  to  get  a  fair  start.  It  is  then  strictly  true  that  it  is  the 
grade  at  that  one  particular  point  which  is  the  limiting  gradient,  and 
that  we  cannot  strike  an  average  with  lower  tangent  grades  before  and 
behind,  and  assume  it  is  the  same  thing  as  if  we  actually  had  a  uniform 
average  resistance  at  all  points. 

828.  The  rule  that  a  grade-line  should  be  unbroken  by  unreduced 
curvature  is  still  sound,  in  spite  of  the  fact  that  there  are  certain  circum- 
stances under  which  slight  and  short  sags  below  the  grade-line  may 
be  introduced  to  save  expense  of  construction,  especially  where  economy 
in  first  cost  is  a  great  object,  as  it  is  so  much  more  often  than  is  realized 
during  the  period  of  construction.  A  sag  below  a  grade-line  and  a  rise 
above  it — which  is  what  an  uncompensated  curve  in  effect  introduces — 
are  two  entirely  different  matters. 

Thus,  if  we  have  a  1.25  per  cent 
maximum  grade,  up  which  a  train 
can  just  make  its  way  at  a  uniform 
speed  of  10  miles  per  hour,  a  rise  of 
3.55  feet  above  the  grade-line  will,  as 
we  have  just  seen,  stall  the  train.  On 
the  other  hand,  a  sag  in  a  grade-line 
-of  an  equal  amount,  as  at  C  in  the 
grade-line  AB,  Fig.  181,  not  only  does  not  endanger  a  stall,  but  actually 


Fig.  x8i. 


\\ 


f  > 

!   I 


\    % 


624 


CHAP.   XVIII.— LIMITING  CURVATURE. 


CHAP.   XVIII— LIMITING  CURVATURE. 


625 


increases  the  velocity  of  passing  from  A  to  B.     For  by  assumption  we 
have  at 

A,  velocity  of  ten  miles  per  hour  =  (Table  118)  vel.  head  of  3.55  ft. 

^'        "  "  "  =  "  "  3.55  ft. 

C,  vel.  head  of  3.55  +  3-55  =  7- 10  ft.  =  (Table  118)  a  velocity  of  14.14 
miles  per  hour. 

829.  Then  by  the  laws  of  accelerated  and  retarded  motion  (see  par. 
371   or  any  text-book  on  physics)  the  average  speed  between  A  and  C 

and  C  and  i5as  well,  and  hence  between  A  and  B  =  ^QQo  X  HH  _  ,2  07 

2 
miles  per  hour— a  gain  in  average  speed  of  2.07  miles  per  hour,  or  about 

3  ft.  per  second  in  passing  over  the  sag  shown  in  Fig.  181,  the  compara- 
tive times  being  about  2  m.  o  sec.  and  i  m.  40  sec. 

This  gain  of  time  is  for  the  same  reason  that  a  body  descending  from 
A  to  B,  Fig.  182,  over  the  different  paths  a,  d,  c,  d,  although  acted  on  by 

the  same  force  (gravity  acting  through 
CB),  takes  a  very  different  time  for  de- 
scending to  B,  the  cycloid  d  being  the 
"curve  of  quickest  descent."  The  re- 
sulting velocity  at  B  is  in  all  cases  the 
same,  barring  loss  by  friction,  but  the 
time  consumed  in  reaching  B  is  widely 
different. 

830.  Therefore,  while  compensation  for  curvature  should  never  be 
omitted,  it  may  still  be  admissible,  in  certain  exceptional  cases  (as  to 

temporarily  save  large 
fills  or  otherwise  reduce 
works),  to  introduce  a 
sag  below  a  grade-line, 
which  is  never  the  case 
with  a  rise  above  a  grade- 
line.  Thus  the  dotted 
profile,  bbbb.  Fig.  183.  can 
certainly  be  operated  un- 
der any  and  all  circum- 
stances (if  the  sag  be  not 
too  great,  par.  435  and 
Table  121)  as  a  virtual  grade  of  the  same  rate  as  the  average  actual 
grade  ;  but  with  the  grade-line  aaaa  this  is  not  possible,  unless  the  initial 
speed  be  very  high  or  the  points  aa  rise  but  little  above  the  average 
grade-line. 


Fig. 183. 


FxG.  183. 


831.  The  principle  is  the  same  as  the  one  so  familiar  to  hydraulic  engineers 
known  as  the  "hydraulic  grade-line."  If  water  is  to  be  conveyed  from  a  high 
reservoir  to  a  lower  point  of  delivery,  it  is  an  axiom  in  hydraulics  that  any  lib- 
erties whatever  can  be  taken  with  the  grade  of  the  pipes  without  affecting  the 
discharge  in  the  least,  more  than  the  same  increase  of  length  and  curvature 
would  do  in  a  pipe  laid  to  a  uniform  grade,  provided  the  pipe  at  no  point  rises 
above  a  straight  line  connecting  the  points  of  supply  and  delivery,  which  is 
known  as  the  "hydraulic  grade-line,"  as  on  the  line  bbbh.  Fig.  183.  If,  how- 
ever, the  pipe  rises  above  this  line,  by  however  little,  as  at  the  highest  a,  Fig. 
183,  the  discharge  will  immediately  be  reduced  to  correspond  with  the  new 
hydraulic  grade-line  passing  through  the  point  of  supply  and  tangent  to  the  now 
highest  point  on  the  pipe. 

In  theory  a  lo-mile  grade  of  50  ft.  per  mile  might  be  broken  up  into  (i)  5 
miles  of  level  and  (2)  5  miles  of  100  ft.  per  mile,  without  increasing  the  de-facto 
ruling  grade  above  50  ft.  per  mile;  but  we  cannot  reverse  the  orders  of  these 
gradients,  making  the  first  last  and  the  last  first,  without  a  theoretical  as  well  as 
practical  increase  of  the  gradient  to  100  ft.  per  mile.  Even  in  the  former  case, 
the  velocity  at  the  end  of  the  first  five  miles  of  level  would  have  to  be  87^  miles 
per  hour,  assuming  an  initial  velocity  of  15  miles  per  hour.  This  is  hardly  a 
practicable  speed  for  freight  trains;  and  it  therefore  should  not  be  understood 
that  any  considerable  sags  below  a  grade-line  are  admissible.  The  only  asser- 
tion made  is  that,  assuming  such  speed  to  be  practicable,  even  250-ft.  sags 
below  a  grade-line  would  do  no  harm,  whereas  any  rise  whatever  above  it 
would  destroy  it,  theoretically  as  well  as  practically. 


Fig.  184. 

832.  A  remarkable  instance  of  the  advantage  thus  to  be  gained  at 
times  occurred  in  tHe  writer's  practice,  and  is  shown  in  Fig.  184.     Near 
40 


626 


CHAP,   XVIII.— LIMITING  CURVATURE. 


i 


the  middle  of  a  long  grade-line  which  it  was  very  desirable  to  keep  down 
to  the  lowest  limits,  occurred  a  saddle  between  two  hills,  where  support- 
ing ground  was  wholly  lost.    Consequently,  although  there  was  no  ma- 
terial difference  in  the  profile  at  any  other  point,  both  being  side-hill,  at 
this  point  any  lift  of  the  grade-line  meant  so  much  addition  to  the  fill. 
To  bring  the  grade-line  down  to  within  a  few  feet  of  the  surface  meant 
an  increase  of  the  pusher  grade  from  1.15  to  1.25,  equivalent  to  an  increase 
of  ruling  grade  on  a  long  d'vi.^on  from  0.4  to  0.5.    To  obtain  the  lower 
grade  required  a  very  long  fill,  containing  some  190.000  cubic  yards  when 
fully  made  (estimated  to  cost  20  cts.  per  yard);  but  by  introducing  a  sag  in 
the  grade-line  of  some  25  feet  (shown  by  dotted  lines  on  Fig.  184),  as- 
sumed as  about  the  extreme  depth  of  sag  which  it  would  be  proper  to  at- 
tempt to  operate  as  a  continuous  virtual  profile,  even  temporarily,*  the 
fill  could  be  reduced  to  some  30,000  cubic  yards,  leaving  the  track  to  be 
gradually  raised  up  to  the   straight  grade-line  when  and  if  necessity 
should  appear  and  convenience  serve.    To  make  the  fill  in  the  beginning 
was  not  justified  by  the  financial  status  of  the  company,  nor  by  the  time 
at  its  disposal,  nor  could  material  be  obtained  at  reasonable  cost  except 
by  train. 

833.  There  were  then  three  possibilities,  besides  that  of  making  the 
fill  complete : 

1.  That  the  grade  would  continue  to  be  operated  indefinitely  as  a  vir- 
tual straight  grade  by  the  aid  of  momentum,  tolerating  the  necessary 
velocity  of  30^  miles  per  hour  in  the  bottom  of  the  sag. 

2.  That  the  fill  would  be  raised  somewhat  from  time  to  time,  so  as  to 
reduce  the  necessary  fluctuation  of  velocity  to  less  objectionable  limits. 

3.  That  the  traffic  of  the  line  would  prove  so  thin  (it  was  very  doubt- 
ful) that  the  trains  would  for  the  most  part  be  light  and  the  necessity  for 
either  expedient  not  be  great. 

In  this  way  it  was  possible  to  have  one's  cake  and  eat  it  too;  to  econ- 
omize  as  much  as  was  otherwise  possible  against  the  contingency  of 
future  poverty,  and  to  lose  nothing  (but  rather  gain  the  interest  on  the 
cost  of  the  fill)  in  case  the  future  should  prove  prosperous ;  for  at  the 
worst  the  1.15  line  could  certainly  be  operated  as  a  virtual  1.25. 

So  pronounced  an  instance  of  the  legitimate  use  of  sags  in  grade-lines 
will  rarely  occur,  but  the  same  principle  may  be  availed  of  often  on  a 


CHAP.    XVIII.— LIMITING  CURVATURE. 


»  Velocity-head  due  to  speed  of  15  miles  per  hour  (Table  118) 7- 99  ft. 

Add  for  depth  of  sag  below  virtual  profile [  35  00  " 

Velocity-head  in  bottom  of  sag  (giving  speed  of  30J  miles  per  hour),  32.99  ft 


627 


smaller  scale,  if  only  to  introduce  a  little  extra  compensation  in  a  long 
curve  on  a  high  fill,  returning  to  the  original  grade-line  by  a  slightly 
steeper  grade  beyond.  ^ 

834.  It  will  naturally  follow  from  what  has  preceded  that  THE  proper 

RATE   OF    COMPENSATION    IS    NOT  A   FIXED  QUANTITY,   but    may  under 

varying  circumstances  vary  within  somewhat  wide  limits.  The  more 
usual  rates  are  from  0.03  to  0.05  per  cent  per  degree  of  curvature,  corre- 
sponding to  0.6  to  i.o  lbs.  per  ton  per  degree.  If  the  precise  amount  of 
curve  resistance  were  known,  and  if  it  were  always  the  same,  of  course 
but  one  rate  of  compensation  would  be  proper,  but  as  its  precise  rate  is 
not  known,  and  as  there  is  strong  reason  to  believe  (Appendix  A)  that 
in  startmg  a  train  it  may  possibly  amount  to  as  much  as  2.0  lbs.  per  ton 
a  compensation  sufficient  to  equalize  curve  resistance  in  ordinary  circum^ 
stances  cannot  be  assumed  to  be  certainly  sufficient  at  points  where 
speed  may  be  expected  to  be  very  slow,  as  toward  the  top  of  long  grades 
and  occasionally  at  other  points. 

835.  Under  these  circumstances,  prudence  would  indicate  that  wher- 
ever there  is  NO  physical  limit  to  the  possible  reduction  of  grade  on 
curves,  .t  should  be  made  ample,  so  that  the  curves  should  certainJy  offer 
no  greater  resistance  than  the  adjacent  tangents.  At  stations  this  rule 
would  require  a  grade  reduction  of  o.i  per  cent  per  degree 

On  the  other  hand,  when  we  are  merely  trying  to  equalize  the  tangent 
and  curve  resistance  on  a  long  ascent;  and  whatever  is  taken  off  the 
curves  must  be  added  on  to  the  tangents  and  vice  versa,  no  such  practice 
|s  proper  A  chain  is  only  equal  to  the  strength  of  its  weakest  link,  and 
n  avails  httle  to  know  which  is  the  weakest  link  if  we  cannot  strengthen 
It.  If  we  come  as  near  to  an  exact  equality  as  we  can,  in  compensating 
for  curvature,  it  is  of  no  importance  whether  our  compensation  is  a  little 
too  great  or  a  little  too  small.  In  the  one  case  trains  will  stall  on  the 
tangents  and  in  the  other  on  the  curves-that  is  all.  Our  object  is  simply 
to  guard  against  a  certainty  of  stalling  on  either.  Nothing  more  than 
this  IS  important. 

836.  Hence  it  may  well  be  that  on  a  long  and  crooked  ascent,  where 
the  curvature  greatly  exceeds  the  tangents,  yet  where  there  are  one  or 
two  considerable  tangents,  prudence  will  require  the  assumption  of  a  very 
low  rate  of  compensation  ;  for  otherwise  a  very  slight  loss  of  elevation 

ZZ^  '"""•■  '""'*;P"^.'^,''y  -"^"y  -""e^.  will  prevent  our  attaining  the 
^es  red  summit  at  all  without  a  considerable  increase  of  the  normal  tan- 

this  m^H^'      1  "'    r'  ^"''''''  '"^'"  "^  '°  'he  real  curve  resistance, 
th.s  may  do  no  harm,  but  on  the  other  hand,  if  we  have  guessed  wrongly 


' 


iwpv^pv 


628 


CHAP.   XVII I. -^LIMITING  CURVATURE. 


4H 


and  exaggerated  the  probable  curve  resistance,  we  shall  have  unneces- 
sarily increased  our  tangent  grade.  Hence,  by  assuring  a  low  rate  of 
curve  resistance  in  such  a  case,  we  can  hardly  in  any  case  lose  anything 
appreciable,  and  may  save  a  needless  loss  of  grade.  A  compensation 
rate  of  0.03  per  degree  of  curvature  may  then  be  proper,  below  which  the 
rate  of  compensation  should  never  fall. 

837,  For  the  same  reasons,  it  may  well  happen  that  at  different  points 
on  the  same  line  different  rates  of  compensation  may  be  proper.  Where 
the  loss  of  elevation  by  a  high  rate  of  compensation  is  a  very  serious  mat- 
ter, because  of  a  great  amount  of  curvature,  it  may  be  taken  at  a  mini- 
mum. At  other  points,  where  there  is  less  curvature  to  be  compensated 
and  a  higher  compensation  can  be  had  at  little  or  no  cost,  it  should  there- 
be  used.  The  effect  will  be  to  make  most  of  the  maximum  grade  scat- 
tered over  the  division  a  little  easier  to  handle  trains  on  than  the  longest. 
or  worst  grade.  This  may  well  result  in  handling  a  car  or  two  more  than 
would  be  deemed  possible  were  the  resistance  as  great  at  two  or  three 
points  as  it  is  at  one. 

It  has  been  elsewhere  said  (see  Table  1 24)  that  it  is  always  worth  while 
to  keep  a  little  below  the  maximum  where  possible,  at  moderate  cost. 
This  is  only  another  application  of  the  same  principle,  but,  owing  to  the 
uncertainty  which  hangs  about  the  question  of  curve  resistance,  it  is  a 
wiser  way  of  attaining  the  same  end  than  to  reduce  the  nominal  tangent 
grade,  especially  in  the  vicinity  of  stations. 

838.  To  illustrate  the  importance  of  sometimes  varying  the  rate  of 
compensation  to  suit  circumstances,  assume  a  1.5  percent  average  grade^ 
Fig.  185,  nearly  ten  miles  long  (500  stations — taking  a  "  mile"  at  5000  ft.. 
for  convenience  of  computation),  subdivided  as  follows  in  respect  to» 
amount  of  curvature : 


Top, 


Middle. 


■■\ 


(( 


*« 


150  stations  with  about  50**  per  mile  =  continuous  1°  curve 

(with  f  of  the  line  tangent). 
100  stations  with  about  300°  per  mile  = 
100        "  "        "       400**    "      "     =s 

(with  J  of  the  line  tangent). 
Lcrwer         X  ^5°  stations  with  about  8)"  per  mile  = 

(with  f  of  the  line  tangent) 

Assume  also  a  stoppmg- place  near  B;  at  the  foot  of  the  grade,  so  that 
no  assistance  from  velocity  can  be  counted  on : 

This  is  in  no  respect  an  unreasonably  or  improbably  irregular  distri- 
bution of  curvature  on  such  a  line,  nor  an  unusually  large  amount  of 
curvature  for  a  cheap  line  in  rough  country.  In  all  there  will  be  150°-^ 
6oo'*  +  8oo°  +  22q°=i775°  of  curvature  on  the  ascent. 


CHAP,  XVIIL^LIMITING  CURVATURE. 


629 


At  various  rates  of  compensation  for  curvature  the  grades  required 
on  tangents  for  various  rates  of  compensation  would  be  as.  follows,  as 


!                             { 
-J. «P. I ???. 


Fig.  185. 


the  student  will  do  well  to  determine  for  himself  by  a  brief  comou- 
tation ;  *  ^ 

At  0.03^  per  degree,  1.50  -j-  .1065  =  1.6065  per  cent. 
"0.05      "        "        1.50 +  .1775  =  1.6775    "      " 
"  0.10     ••        ••        1.50 +  .355    =  1.855      "      " 

839.  If  the  topography  were  such  that  we  had  just  500  stations  in 
which  to  rise  750  feet,  this  would  mean,  if  we  adopted  a  compensation 
of  o.io  per  degree  instead  of  0.03.  that  our  tangent  grade  (which  would 
then  certainly  be  the  governing  one.  because  we  have  adopted  a  compen- 
sation which  will  CERTAINLY  bring  the  resistance  on  curves  below  that 
on  tangents)  will  be  greater  by  0.25  per  cent,  or  5  lbs.  per  ton,  than  with 
the  lower  rate  of  compensation.  In  other  words,  in  order  to  secure  the 
wholly,  or  almost  wholly,  worthless  end  that  trains,  when  and  if  they 
stall,  shall  stall  always  on  tangents  and  never  on  curves,  we  have  greatly 
increased  the  chances  of  their  stalling  on  tangents,  on  the  top  or  bottom 
sections  of  the  grades  at  least,  where  the  tangents  are  the  lonrresf— 
a  plain  act  of  folly.  ^ 

840.  But  this  is  but  one  side  of  the  question.    The  total  rise  in  feet 
and  the  elevation  of  intermediate  points  would,  under  the  various  as- 

♦  Knowing  approximately  the  total  degrees  of  central  angle  on  any  grade 
we  have  only  to  multiply  the  total  by  the  assumed  rate  of  compensation  to  find 
how  much  total  elevation  will  be  lost  by  the  compensation.     The  elevation 
divided  by  the  length  of  the  grade,  will  give  the  rate  by  which  the  tangeni 
maximum  must  be  increased  to  introduce  the  compensation. 


:  :i 


^  J 


ii^ 


I 


i 


630 


CHAP.   XVIII.— LIMITING  CURVATURE. 


CHAP.   XVIII.— LIMITING  CURVATURE. 


631 


sumed  rates  of  compensation,  have  to  be  as  shown  in  Table  186;  and  it 
will  be  seen  that  the  middle  point  c  of  the  entire  grade  comes  at  about 
the  same  elevation  with  either  rate  of  compensation,  but  that  there  is  a 
material  difference  in  the  height  of  the  grade-line  at  the  beginning  and 
end  of  the  middle  sections  C  and  A  or  at  the  "  quarter  points"  of  the 
grade.  While  the  through  uncompensated  grade-line  falls  as  shown  by 
the  dotted  line,  the  effect  of  introducing  the  curve  compensation,  by 
whatever  rate,  is  to  give  a  profile  like  the  solid  line,  the  point  C  being 
from  I  li  to  38  feet  higher  than  before,  and  the  point  D  from  9  to  31  feet 
lower,  according  to  the  rate  of  compensation. 

Table  186. 

Illustrating  the  Effect  of  Different  Rates  of  Curve  Compensation 
TO  Modify  the  Elevation  of  Intermediate  Points  on  Long  Grade- 

Lines 

[Based  on  the  data  of  par.  838  and  Fig.  185.] 


B 
C. 


(Foot  of 
Grade.) 


D 

E  (summit) 


1-5 
Straight. 
No  compensa- 
tion. 


Rise. 

325 

150 

150 
935 


Eleva- 
tion, 
o. 

335. 

375- 

525- 

750- 


1.6065 
Tangent  Grade. 
.03  compensation. 


Rise. 

336.48 
143.65 
136.65 
334.33 


Eleva- 
tion. 
0.00 

336.48 

379- »3 
515-78 
750- 


1.6775 
Gi 


Tangent  Grade. 
.05  compensation. 


Rise. 

•  •  •  •  •  • 

844.13 

137-75 
127.75 
340.38 


Eleva- 
tion. 
0.00 

344.13 

381.87 

509-62 

750. 


1-855 
Tangent  Grade. 
.10  compensation. 


Rise. 

363.35 
125.50 
105.50 
255-75 


Eleva- 
tion. 
0.00 

363.25 
388.75 
494-24 
750. 


Difference  in  Resulting  Elevations  at  Various  Points  on  the  Grade,  from  the 

Straight  Tangent  Grade. 


B  (foot  of  grade) 

C 

c 

D 

E  (summit) 


Constant 

11.48  ft.  higher 

413"        " 
9;22  "    lower. 

Constant 


38.25  ft.  higher. 

13-75"        " 
30.76"    lower. 


■  Topographical  conditions  will  sometimes  permit,  but  will  more 
usually  forbid  assuming  that  we  have  such  leeway  in  the  necessary  posi- 
tion of  the  grade,  thus  depriving  us  in  a  measure  of  the  privilege  of  free 

choice. 

841.  Now  suppose,  on  such  a  grade,  that  the  middle  300  stations  or 
about  4  miles,  on  which  most  of  the  curvature  is  bunched,  was  so  situ- 


ated as  to  make  it  essential  to  rise  only  some  230  feet,  unless  consider- 
able extra  expense  were  to  be  incurred,  while  at  the  same  time  the 
character  of  the  line  elsewhere  was  not  such  as  to  admit  of  a  lower 
maximum  tangent  grade.  Under  these  circumstances,  which  may  fre- 
quently occur,  it  would  be  a  great  error  not  to  reduce  grade  on  curves  by 
the  full  amount  which  the  topographical  conditions  made  possible  with- 
out loss  up  to  even  o.  10  per  cent  per  degree  of  curve,  in  the  existing 
state  of  our  knowledge,  even  if  at  other  points  we  used  less.  In  that 
case,  if  we  have  overestimated  the  probable  or  possible  resistance  on 
curves,  it  is  not  likely  to  do  harm,  because  the  large  amount  of  curva- 
ture and  small  amount  of  tangents  will  enable  any  excess  of  resistance 
in  the  latter  to  be  equalized  by  momentum,  whereas  if  we  have  under- 
estimated the  curve  resistance  a  similar  effect  is  not  possible,  or  at  least 
not  as  fully  possible,  on  account  of  the  greater  length  of  curves. 

On  the  upper  and  lower  sections,  where  tangents  prevail  and  curves 
are  the  exception,  the  opposite  principle  prevails.  If  the  curve  compen- 
sation be  too  little  it  will  be  equalized  easily  enough  by  momentum  on 
short  and  infrequent  curves,  so  that  the  result  will  be  the  same  in  effect 
as  if  the  balance  were  exact. 

842.  Under  the  circumstances  of  the  example  just  considered,  as- 
suming the  middle  part  of  the  grade  to  be  fixed  as  just  assumed,  the 
proper  course  to  pursue  with  the  lower  part  of  the  grade  would  be  to 
ease  its  rate  a  little,  if  circumstances  permitted  doing  so  at  little  or  no 
expense;  otherwise,  to  reduce  its  virtual  rate  by  the  simple  expedient 
of  removing  the  stopping  point  at  the  foot  of  the  grade  some  distance 
from  it,  so  as  to  ensure  gaining  something  by  momentum.  A  speed  of 
25  miles  per  hour  at  the  foot  of  the  grade  reduced  to  10  miles  per  hour 
at  Cwill  (Table  118)  ensure  a  gain  from  surrendered  energy  of  22.20  — 
3.55  =  18.65  vertical  feet  fsee  Fig.  185),  which  will  reduce  the  grade  on 

the  first  150  stations  by  — —  =0.124  per  cent,  and  so  secure  an  equality 

with  the  virtual  grade  of  the  next  section  above,  even  with  the  lowest 
possible  rate  of  curve  resistance.  The  curve  compensation  on  this  lower 
section  should  in  any  case  be  small,  whatever  it  may  be  on  the  middle 
section  just  above. 

843.  On  the  upper  section  DE,  assuming  the  lower  and  middle  sec- 
tion to  have  be^  fixed  as  above,  an  effort  will  naturally  be  made  to 
lengthen  the  line  a  little  at  the  upper  end  at  the  expense  of  a  moderate 
amount  of  distance  and  curvature,  so  as  to  give  a  gradient  DF  instead 
of  DE,  Fig.  185  ;  but  if  this  be  not  possible,  the  disadvantage  will  not  be 
very  serious.     Our  case  will  be  this :   By  virtue  of  an  excess  in  rate  of 


'  ■  1 


6],2 


CHAP.   XVIII.— LIMITING  CURVATURE. 


curve  compensation  we  have  the  broken  virtual  gradient  ACDE  in- 
stead of  the  straight  grade  BE,  which  is  of  course  preferable.  The  dis- 
advantage at  the  lower  end,  which  would  naturally  be  the  most  serious 
(par.  828),  since  it  carries  our  virtual  gradient  above  the  grade-line  BE, 
which  we  desire,  we  have  neutralized  by  momentum.*  The  disadvan- 
tage at  the  upper  end,  since  it  merely  carries  our  profile  a  little  below 
the  grade-line,  will  in  great  measure,  if  not  entirely,  neutralize  itself  by 
momentum. 

In  this  way  we  have  done  the  best  which  can  be  done  to  avail  ourselves 
of  every  chance  in  our  favor,  whereas  by  assuming  any  hard-and-fast  rule 
whatever,  and  then  following  it  blindly  (as  we  might  be  justified  in  doihg 
if  we  knew  it  was  correct),  we  are  certain  to  lose  something,  and  may  lose 
a  good  deal. 

844.  Our  practical  conclusions  as  to  rate  of  curve  compensa- 
tion, therefore,  may  be  summarized  as  follows: 

1.  With  short  grades  or  under  favoring  topographical  condi- 
tions compensate  as  liberally  as  possible  up  to  a  maximum  at 
special  points  of  o.io  per  cent  per  degree. 

2.  Where  speed  may  sometimes  be  very  low,  and  hence  in- 
variably on  or  very  near  to  known  stopping-places,  this  maxi- 
mum rate  appears,  with  our  present  knowledge,  none  too  much. 
In  general,  however,  0.05  per  cent  per  degree  (=  i  lb.  per  ton) 
is  an  ample  equivalent  for  curve  resistance,  and  for  fast  trains 
alone  probably  0.02  to  0.03  per  cent  (=  0.4  to  0.6  lb.  per  ton) 
is  sufficient  to  balance  the  resistance. 

3.  On  sections  where  curves  largely  predominate  over  tan- 
gents it  is  particularly  desirable  to  have  ample  compensation,  and 
if  excessive  it  will  do  least  harm.     On  the  contrary, 

4.  On  sections  where  the  amount  of  curvature  is  small  it  is  less 
important  to  have  full  compensation,  and  if  excessive  it  will  do 
most  harm. 

5.  When  the  rate  of  compensation  can  only  be  increased  at  the 
CERTAIN  cost  of  a  Corresponding  increase  in  the  rate  of  tangent 
grades  (making  very  sure  that  it  is  certain,  and  no*t  an  over-hasty 


*  The  word  *'  momentum"  here  and  elsewhere  is  used  in  a  somewhat  un- 
scientific way,  to  correspond  with  the  popular  use  of  the  word.  The  scientist 
will  not  be  confused  thereby,  while  the  average  reader  is  assisted. 


CflAP.   XVIII.— LIMITING  CURVATURE, 


633 


conclusion  from  inexperience  or  lack  of  care),  no  larger  rate  than 
vi-e  feel  practically  certain  will  be  required  to  balance  the  curve 
resistance  (0.03  to  0.04)  should  be  chosen. 

Otherwise,  we  are  committing  the  folly  of  making  a  certain 
addition  to  the  grade  in  one  place,  to  avoid  one  in  another  place 
which  is  merely  problematical. 

6.  On  any  minor  gradients  where  the  curvature  is  not  suffi- 
cient to  bring  the  virtual  profile  up  to  the  maximum  it  is  not 
important  to  compensate  for  curvature  at  all,  although  it  is  gen- 
erally as  well  to  do  so,  especially  at  points  where  to  do  so  will 
slightly  reduce  the  cost  of  construction,  as  is  very  apt  to  be  the 
•case  on  long  curves. 

When  not  compensated,  the  curvature  merely  has  an  equiva- 
lent effect  to  a  slight  undulation  of  gradient  (Class  A  of  rise  and 
fall,  par.  438)  which  produces  no  shock  to  the  train  and  so  is 
not  a  measurable  disadvantage. 

7.  It  is  not  in  the  least  essential  or  important  to  precisely 
-adapt  the  compensation  to  the  exact  length  of  each  curve.  The 
reduced  rate  may  as  well  as  not  begin  and  end  at  the  nearest  even 
station,  and  may  be  made  a  little  less  on  one  curve  and  a  little 
more  on  one  immediately  above  if  a  horizontal  slice  of  a  foot  or 
more  may  thereby  be  taken  off  a  high  fill  on  the  tangent  connect- 
ing them,  but  never  so  as  to  cause  the  grade  to  rise  above  the  uniform 
grade-iine. 

8.  Curves  immediately  below  a  known  stopping-place  for  all 
trains  need  not  and  should  not  be  compensated  at  all. 

9.  The  rate  of  compensation  should  be  uniform  per  degree 
for  all  degrees  of  curvature,  or  in  no  case  made  greater  for  the 
sharper  curves.  It  may  even  be  made  less  for  curves  of  over  10° 
[par.  335  (9)]-  If  the  rate  be  reduced  one  half  for  the  excess 
over  10°,  making  the  compensation  for  a  16°  curve  thirteen  times 
that  for  a  1°  curve,  it  will  certainly  lead  to  no  bad  results,  although 
a  rather  rough  rule. 

This  is  directly  contrary  to  the  usual  practice,  which  is  to  increase  the  rate 
of  compensation  with  the  sharpness  of  the  curve,  if  anything;  but  this  oractice 
Tests  upon  the  assumption  which  we  have  seen  to  be  the  direct  contrary  of  the 
<ruth  (par.  321  et  al.),  that  the  curve  resistance  increases  with  the  degree  of  the 


634 


CHAP.  XVIII.— LIMITING  CURVATURE. 


If> 


iiil 


HI 


lif 

5*1 


curve.  The  results  of  experience  on  the  New  York  elevated  lines  and 
numerous  others  with  very  sharp  curves,  both  of  standard  and  narrow  gau^e  is. 
enough  to  disprove  this,  confirmed  as  it  is  very  directly  by  the  indications 'of 

lo.  Since  we  have  seen  in  Chap.  VIII.  (par,  330-335)  that 
there  is  no  reason  to  believe  that  curve  resistance  increases  per 
ton  with  the  length  of  the  train,  or  even  (appreciably)  with  the 
type  of  engine  (par.  285  et  seq.)  there  is  no  reason  for  varying  the 
compensation  because  of  the  grades  or  length  of  train,  except  for 
this—that  It  is  usually  easier  to  spare  the  elevation  for  a  liberal 
rate  of  compensation  with  low  grades  than  with  high  ones.  It 
is  therefore  proper  to  do  so. 


CHAP.   XIX. -THE  LIMIT  OF  MAXIMUM  CURVATURE.   635 


CHAPTER   XIX. 

THE    LIMIT    OF    MAXIMUM    CURVATURE. 

845.  Although  badly  adjusted  grades  have  a  more  serious 
effect  on  operating  expenses,  there  is  no  detail  connected  with 
location  which  has  so  great  an  effect  on  the  cost  of  construction 
as  that  which  we  are  about  to  consider-nor  any  in  which  the  ten- 
dency is  so  notable  to  go  to  one  extreme  or  the  other,  without 
any  very  definite  or  defensible  reasons.  It  is  evident  that,  while 
circumstances  will  often  justify  and  require  the  use  of  very  sharp 
curvature  or  of  very  easy  curvature,  they  will  in  no  case  either 
justify  or  require  that  conclusions  should  be  jumped  at  in  some 
such  manner  as  that  sketched  in  par.  245. 

846.  Moreover,  it  may  be  again  repeated,  and  cannot  be  too 
fully  recognized  and  clearly  borne  in  mind,  that  both  the  amount 
and  radius  of  curvature,  like  the  amount  and  rate  of  grades  is 
even  more  dependent  upon  study,  care,  and  skill  than  on  topog- 
raphy. There  exists,  too,  a  most  dangerous  tendency  to  use 
more  and  sharper  curvature  than  is  at  all  necessary  in  country 
of  some  difficulty,  and  less  and  easier  curvature  than  is  at  all 
expedient  in  country  of  no  difficulty,  or  in  countrv  whose  only 
difficulty  comes  from  trying  to  hold  close  to  an  air-line  (Chap. 
XX.).  Errors  of  this  kind,  resulting  merely  from  lack  of  care 
or  skill,  are  especially  apt  to  lead  to  the  use  of  absurdly  sharp 
curvature  if  one  has  imbibed  the  notion  that  easy  radii  are  unim- 
portant. 

847.   Recognizing   these  dangers,   we  proceed  to  analyze,  as 
nearly  as  may  be,  the  causes  which   fix  the  advisable   limit'  of 
maximum  curvature  and  the  cost  of  exceeding  it.      We  have* 
seen  (par.  343)  that  these  causes  may  all  be  separated  under  the 
two  following  heads,  sharply  defined  from  each  other: 


-036  CHAP.  XIX.—  l^HE  LIMIT  OF  MAXIMUM  CURVATURE. 


First.  The  inherently  greater  co?>Ti.m^ss^  not  of  curvature 
measured  by  degrees,  but  of  sharp  curvature  instead  of  easy 
CURVATURE /£?/-  approximately  the  safue  number  of  degrees.  In  other 
words,  the  greater  wear  and  tear  of  track  and  rolling-stock,  con- 
sumption of  fuel,  danger  of  accident,  loss  by  decreased  speed, 
etc.,  which  results  from  using  loo  feet  of  io°  curvature  instead 
of  looo  feet  of  i°  curvature  for  deflecting  the  line  through  a  cen- 
tral angle  of  io°,  or  from  using  900  feet  of  10°,  and  550  feet  of 
tangent  at  each  end,  for  deflecting  through  an  angle  of  90°,  as  in 


4 


■so'lan.   " 

Fig.  186. 


Fig.  187. 


•[There  is  a  certain  loss  of  distance,  aa,  in  using  the  sharper  instead  of  easier  curve  which  is 

not  reierred  to  in  the  text.    See  par.  859.]  ' 

Fig.  187,  instead  of  using  1800  feet  of  5°  curve  and  only  50  feet 
of  tangent,  as  in  Fig.  186. 

Secondly.  The  limiting  effect  of  sharp  curvature  on  the 
weight  and  length  of  trains,  provided  it  be  sharp  enough  to  have 
such  effect.     Some  is,  and  some  is  not. 

848.  In  other  words,  we  are  here  met,  upon  the  threshold  of 
the  subject,  with  a  distinction  precisely  analogous  to  that  which 
we  have  already  found  (par.  361)  to  exist  in  the  case  of  gradients. 
All  grades,  without  distinction  and  wherever  situated,  entail  a 
certain  additional  expense  per  train  passing  over  them;  and  in 
addition  to  this  the  highest  rate  of  grade  entails  a  certain  and 
much  greater  expense  which  does  not  appear  at  all  in  the  ex- 
penses per  train-mile  (except  as  it  may  tend  to  decrease  them  by 
shortening  trains),  but  solely  in  an  increase  in  the  number  of 
trains.  In  like  manner,  all  curves,  without  distinction,  entail  a 
certain  additional  expense  per  train  passing  over  them  for  every 


CHAP.  XIX.— THE  LIMIT  OF  MAXIMUM  CURVATURE.  63/ 

degree  of  the  curve,  and  this  cost,  it  may  be,~or  may  not  be- 
increases  rapidly  with  the  sharpness  of  the  curve;  but  in  addi- 
tion  to  this,  the  sharpest  curve  (or  curves)  on  the  line  //  //  be 
sharp  enough,  will  have  the  further  effect  of  limiting  the  weight 
and  length  of  trains.  In  fact,  if  made  sharp  enough,  it  will  so 
severely  limit  the  weight  of  trains  as  to  make  it  impossible  to 
run  any  trains  at  all. 

At  a  certain  definite  radius,  therefore,  the  expense  and  loss 
arising  from  short  radii  take  a  sudden  jump.  The  inherent 
cost  per  train-mile  per  degree  of  sharp  instead  of  easy  CMxyj2.Un-^ 
continues  on  as  before,  and,  in  addition  thereto,  there  is  tlie 
large  additional  expense  caused  by  the  limiting  effect  of  any 
shorter  radius  upon  the  weight  of  trains. 

849.  It  is  plain  that  the  point  at  which  this  sudden  jump  will 
or  may  occur  is  intimately  connected  with  and  depends  upon 
the  rate  of  the  maximum  grade,  because  the  higher  the  grade 
the  greater  the  resistance  on  a  tangent,  and  hence  the  sharper 
the  curve  which  may  be  used  (i.e.,  which  it  is  possible  to  use)  on. 
levels  or  minor  gradients  without  any  limiting  effect  on  trains 
Hence  the  shorter  the  trains  which  can  be  hauled  independent 
of  the  sharpest  curve,  the  shorter  the  radius  which  may  be  freely 
used  on  levels  or  minor  gradients  without  affecting  the  number 
of  trains  required  for  a  given  business. 

850.  Now,  just  as  in  the  case  of  gradients,  this  distinction 
between  these  diverse  sources  of  expense  is  one  which  must  be 
carefully  kept  in  mind  if  any  correct  and  intelligent  decision  as- 
to  the  limit  of  maximum  curvature  is  to  be  reached. 

In  the  first  place,  it  needs  no  great  effort  of  mind  to  perceive 
that  the  first  item  mentioned  above,  the  inherent  costliness  of 
sharp  curvature,— that  portion  which  is  visible  in  increased  wear 
and  tear  and  expenses  per  train-mile,— affords  no  ground  for  the 
fixing  of  any  arbitrary  and  inflexible  standard  or  limit,  nor 
should  it  be  considered  or  allowed  to  have  any  weight  what- 
ever in  ascertaining  at  what  radius  to  fix  that  limit.  For,  mak- 
ing  for  a  moment  the  exaggerated  estimate  that  the  cost  of 
curvature  per  degree  increases  as  the  square  of  the  degree  of 


f  t 


m 


638  CHAP.  XIX.— THE  LIMIT  OF  MAXIMUM   CURVATURE. 


CHAP.   XIX.^THE   COST  OF  SHARP   CURVATURE.       639 


the  curve,  it  may  easily  be,  and  often  is  the  case  at  certain 
points,  that  the  cost  of  construction  will  vary  as  the  cube  of  the 
radius,  and  hence  a  sudden  sharp  ravine  or  rocky  spur  might 
justify  and  require  a  12°  or  15°  curve  for  this  account  alone, 
although  3°  or  4°  curves  were  the  maximum  on  all  the  rest  of 
the  line.  But  what  we  then  require  to  determine  is:  Will  any 
such  curve  have  the  further  effect  of  limiting  the  weight  of  trains 
over  the  whole  line,  or  injuriously  restricting  speed  ?  For  in 
that  case,  plainly,  a  large  additional  expenditure  will  be  justifi- 
able to  increase  its  radius. 

851.  This  latter  expenditure  does  not  vary  with  the  number 
of  curves,  as  does  the  wear  and  tear,  but  is  a  certain  fixed 
amount,  which  can  alone  be  used  to  take  out  such  curves,  how- 
ever many  or  few  they  may  be,  and  must  be  distributed  to  one 
curve  or  to  fifty,  according  to  their  number.  This  fact  alone  is 
sufficient  to  show  the  essential  dissimilarity  between  it  and  the 
sum  which  represents  the  direct  or  inherent  disadvantage  of 
using  short  instead  of  long  radii.  As  the  latter  is  always  so 
much  per  sharp  curve,  or  per  degree  of  sharp  curvature,  it  always 
has  its  effect — much  or  little,  as  the  case  may  be— on  the  justifi- 
able expense  to  increase  the  radius  of  each  particular  curve,  for 
it  is  to  be  added  in  each  case  to  the  proportion  for  that  curve  of 
the  estimated  value  of  avoiding  any  limiting  effect  from  its 
radius;  but  it  does  not  form  an  element  in  fixing  the  point  at 
which  limiting  effect  begins,  and  hence  should  be  allowed  no 
weight  whatever  in  ascertaining  that  limit. 

All  this  seems  clear  enough  when  the  attention  is  specially 
directed  to  it,  but,  as  with  many  other  problems  which  advance 
from  simple  premises,  it  requires  a  constant  effort  of  the  mind 
to  keep  it  always  in  view.  Hence,  although  it  has  no  real  or 
necessary  connection  with  our  present  subject,  we  may  first 
briefly  consider 

THE    INHERENT    COSTLINESS    OF    SHARP    CURVATURE. 

852.  For  the  consideration  of  this  question  all  actual  or  possible  lim- 
iting effect  from  curvature  on  the  length  or  speed  or  easy  riding  of  trains. 
or  the  use  of  any  desired  type  of  locomotive,  must  be  disregarded.    Such 


injurious  effect  as  the  sharpest  curves  may  have  on  these  details,  if  any, 
IS  another  matter.  The  question  is  simply— as  between  the  two  methods 
shown  in  Figs.  186,  187— of  turning  an  angle  of  90"  within  a  distance 
of  1900  feet  of  track  :  Which  adds  the  most  to  the  operating  expenses 
per  train  due  to  that  1900  feet— the  method  of  Fig.  186,  showing  1800 
feet  of  5°  curve  and  50  feet  of  tangent  at  each  end,  or  that  of  Fig.  187, 
with  900  feet  of  10°  curve  and  500  feet  of  tangent  at  each  end  } 

853.  Rigorously  excluding  all   thought  of  possible   limiting  effect 
from  the  mind,  it  is  very  difficult  to  see  reasons  why  the  inherent  cost  of 
curvature,  per  train-mile  per  degree,  should  be  in  the  least  increased  by 
using  short  instead  of  long  radii,  i.e.,  by  using  100  ft.  of  10°  curve  instead 
of  1000  ft.  of  1°  curve,  to  cover  the  same  central  angle.     The  wear  and 
cost  of  rails  appear  from  superficial  investigations  (the  writer's  among 
others:  see  par.  317)  to  indicate  that  rail  wear  increases  faster  than— or 
even  (as  the  writer  once  suggested)  as  the  square  of— the  degree  of 
curvature ;  but  this  is  a  purely  deceptive  appearance,  due  to  the  fact  that 
the  rate  of  wear  increases  as  the  rails  become  worn  to  "  fit  the  flange" 
(par.  338),  and  thus  expose  a  greater  area  to  rubbing  friction.    It  is  plain 
that  at  any  given  date  in  a  large  lot  of  rails  laid  at  the  same  time  those 
•on  the  sharper  curves  will  have  fulfilled  a  greater  proportion  of  their  total 
life,  and  hence  will  have  begun  earlier  to  wear  more  rapidly.     From  a 
more  correct  comparison  of  all  the  data  it  appears  rather  as  if  both  curve 
resistance  and  rail  wear  (and  hence  fuel  consumption)  increased  more 
slowly  instead  of  faster  than  the  degree  of  the  curve  (par.  311).     If  so, 
the  total  RAIL  WEAR  caused  by  10°  of  central  angle  will  be  less,  rather 
than  more,  on  a  10°  curve  than  on  a  1°  curve.    While  this  cannot  as  yet 
be  positively  asserted,  it  may  be  regarded  as  certain  that  the  balance  is 
at  least  even. 

864.  It  may  with  far  more  certainty  be  claimed  that  the  cost  of  main- 
tenance OF  ROAD-BED  AND  TRACK  is  Considerably  decreased,  per  de- 
gree of  central  angle,  by  the  use  of  short  radii,  because  a  good  portion  of 
It  IS  nearly  constant  per  100  feet  of  curve,  regardless  of  radius,  such  as 
the  extra  cost  of  lining,  maintaining  uniform  and  proper  elevation,  and 
the  shorter  life  of  ties,  in  order  that  they  may  be  capable  of  sustaining 
the  lateral  reaction  of  the  rails,  which  latter  is  theoretically  (although 
probably  not  quite  practically)  the  same  on  all  curves  (par.  311). 

It  would  be  a  most  liberal  estimate  to  assume  that  the  additional  cost 
per  station  for  maintaining  road-bed  and  track  due  to  curvature  increases 
as  the  square  root  of  the  degree  of  curvature,  making  it  3.16  times  as 
much  per  100  ft.  of  line  on  a  10°  curve  as  on  a  1°  curve,  or  making 


i  si 


■  ( 


i 


•  I 


640       CHAP.  XIX.— THE   COST  OF  SHARP   CURVATURE. 


the  additional  cost  due  to  A"  of  central  angle  compare  as  10  on  a  i'*^ 
curve  to  3.16  on  a  10°  curve.  This  entire  item  is  a  small  one,  but  so  far 
us  it  goes  it  is  distinctly  favorable  to  the  use  of  sharp  instead  of  easy- 
curvature. 

855.  Figs.  186,  187  are  literal  copies  of  diagrams  which  the  writer 


^ 


-^CL 


a 


v^ 


.<^ 


\ 


Fig.  187. 


submitted  to  two  or  three  of  the  most  thoughtful  practical  road-masters 
of  his  acquaintance  for  an  opinion  as  to  probable  comparative  main- 
tenance expenses.     The  reply  of  one  of  them  was  as  follows : 

•*  Assuming  a  tie  to  last  8  years  on  tangent  it  will  last  about  6  years  on  a  10° 
curve,  so  as  to  keep  gauge  safe,  and  we  will  say  7  years  on  the  5°  curve.  Then— 
I'or  10"  line— Cost  of  ties  for  eight  years  on  looo-ft.  tangent, 

500  lies  at  50  cts. $25000 

450  ties  on  900  ft.  of  10°  curve  at  50  cts.  =  $225  for  6  years, 

=  for  8  years, 300  00-I550  00 

For  5°  line— Cost  of  ties  for  8  years  on  looft.  tangent,  50 

ties  at  50  cts., 25  00 

900  ties  for  1800  ft.  of  5'  curve,  at  50  cts.  =  I450  for  7  years 

=  for  8  years SU  30-|539  3© 

••  Therefore  there  is  a  saving  of  I10.70  at  the  end  of  8  years  in  favor  of  the 
5"  line,  and  we  may  conclude  that  the  maintenance  of  line  and  surface  will  bear 
the  same  proportion  as  ties. 

"According  to  this  figuring  there  is  a  saving  of  about  2  per  cent  in  main- 
tenance in  taking  the  5°  line.  This  is  small,  and  in  looking  at  the  two  lines  in 
all  their  bearings  I  believe  the  10°  line  is  the  preferable  one  for  maintenance,  as 
on  it  we  get  more  tangent  than  curve,  while  the  5°  for  ihe  same  distance  is 
nearly  all  curve  and  very  little  tangent." 

The  fallacy  in  the  first  part  of  this  estimate,  which  was  perceived  but 
not  located,  lies  in  assuming  that  a  5°  curve  will  only  dimmish  the  hfe 
of  a  tie  half  as  much  as  a  10°  curve:  which  is  hardly  so,  the  flange  pres- 
sure being  the  same  on  both.     Moreover,  the  extra  work  of  Iminc  and 


CHAP.  XIX.— DISTANCE  AND   SHARP  CURVATURE.      64I 

surfacing  is,  still  more  nearly,  so  much  per  lineal  foot  of  curve,  regardless 
of  the  radius. 

856.  The  wear  and  tear  of  wheels  and  running  gear  of  rolling- 
stock  will  naturally  follow  the  same  general  law  as  the  rail  wear,  so  that 
it  may  be  considered  to  vary  directly  as  the  degree  of  curvature,  remain- 
ing constant  per  degree  of  central  angle. 

857.  Moreover,  tlie  total  cost  of  repairs  of  rolling-stock  and  track,  for 
those  items  which  are  at  all  liable  to  be  affected  by  the  wear  and  tear 
and  loss  of  power  on  curves,  is  very  small,  as  thus  : 

Per  cent  of 
total  expenses. 
Engines,  19  per  cent  only  of  the  total  cost  of  repairs  appears  to 
vary  with  curvature  and  grades  (Table  85);  19  per  cent  of  5.6 

per  cent  (Table  80) _       j  q- 

Cars  (Table  86),  23  per  cent  appears  to  vary  as  above;  23  per  cent 

of  lo.o  per  cent  (Table  80), _       ^  ^ 

Rails,  say  50  per  cent  of  2.0  per  cent, =       j  qo 

/'k^/,  say  10  per  cent  of  7.6  per  cent, =       0.76 

A  total  per  cent  of  only 5.13 

Thus  only  about  5  per  cent  of  the  total  operating  expenses  is  likely  to 
be  affected  at  all  by  curvature,  and  a  good  part  of  that  only  slightly,  and 
a  good  part  of  what  remains  by  sharp  and  easy  curvature  of  equal 
amount  nearly  equally. 

858.  It  is  also  to  be  remembered  that  sharp  curves  lengthen  short 
tangents,  as  is  clearly  brought  out  by  Figs.  186,  187— an  advantage 
which  facilitates  what  would  otherwise  be  impossible,  the  use  of  easy 
transition  curves  (see  Index),  and  hence  may  be  made  to  greatly  decrease 
the  unavoidable  shock  in  entering  and  leaving  curves. 

859.  The  effect  of  a  change  of  radius  on  the  total  length  of  the 
LINE,  although  apparently  pertinent,  has  no  real  bearing  on  this  ques- 
tion. The  use  of  sharp  curvature  always  increases  the  length  of  the  line 
between  the  same  tangents  by  the  amount  aa.  Fig.  187,  and  has  besides 
a  marked  further  tendency  both  to  increase  the  length  of  the  line  and  to 
increase  the  degrees  of  central  angle,  because  of  the  differences  of  loca- 
tion which  naturally  result.  But  the  disadvantage  of  this  extra  length 
and  curvature  is  a  matter  for  separate  estimation,  because  it  is  not  an 
essential  and  unavoidable  feature  of  a  mere  change  of  radius,  and  hence 
does  not  directly,  although  it  commonly  will  indirectly,  affect  the  deci- 
sion in  favor  of  using  easy  curvature.  In  fact,  although  it  rarely  occur* 
in  practice,  it  is  not  in  the  nature  of  things  impossible,  that  the  use  of  a 

41 


'  1 


'If 


-^:^ 


642      CHAP.  XIX.— DISTANCE  AND   SHARP   CURVATURE, 


shorter  radius  should  result  in  a  decrease  of  both  distance  and  degrees 
of  central  anoxic.  On  a  small  scale  it  very  frequently  does  so,  in  the  man- 
ner outlined  in  Fig.  188. 


Fig.  188. 

860.  On  the  other  hand,  it  may  well  happen  that  the  adoption  of  a 
location  adapted  to  short  radii  would  double  the  amount  of  curvature, 
and  that  the  estimated  cost  of  this  would  be  more  than  the  estimated 
saving  on  construction.  In  that  case  the  short  radii  would  not  be  used, 
but  they  would  be  abandoned,  not  because  of  the  sharpness  of  the  curv- 
ature, but  because  there  was  so  much  of  it. 


Fig.  189. 

861.  The  loss  or  gain  in  distance  by  connecting  any  two  given  tangents  with 
one  curve  instead  of  another,  Fig.  189,  may  be  very  simply  determined  as 
follows: 

To  DETERMINE  THE  DIFFERENCE  IN  LENGTH  OF  LINE  via  ANY  TWO 
CURVES   OF   DIFFERENT   RADII,  CONNECTING  THE   SAME   TANGENTS: 

Let  /  =  length  of  longer  curve,  of  D" ,  with  tangents  T\ 


/'  = 


(« 


shorter 


«<  j)> 


T\ 


CHAP,  XIX.— DISTANCE  AND   SHARP  CURVATURE.      643 


Then  geometrically  77  =  ~  =  ~.  if  we  assume,  as  for  all  practical  pur- 
poses  we  may,-if  curves  of  over  8°  or  10°  are  run  in  with  50-foot  chords  -that 
the  degree  of  curvature  is  directly  as  the  radius. 


Then/'=|,/and7-  =  |,7', 


'-r'  =  (] 


D 
D' 


)r. 


Letting  Z  _  the  length  via  any  one  of  the  sharper  curves  shown  in  Fig   i8q 
from  tangent-point  to  tangent-point  of  any  curve  of  longer  radius  (from  T  to 
2  )  we  have 


Z-.  =  ..(.--)_(,_-), 


=  {2T-l) 


D-D 
D' 


But  the  value  of  2  7^  -  /  for  a  Z>°  curve  is  to  its  value  for  a  i»  curve  as  --. 
Consequently,  tabulating  {2T  -  i)  for  a  1°  curve,  we  have  as  the  differencf in 
ilie  length  of  the  line  via  any  two  curves  of  D  and  D'  degrees,  connecting  the  same 
•tangents  : 

=  tabular  number  X  —  X  — — — 

D  D' 

D'  —  D 

=  tabular  number  X 

D'D 

.  u  1  ,  difference 

=  tabular  number  X  -~;^^  of  the  two  degrees  of  curvature, 

862.  Table  187  gives  such  a  tabulation  for  angles  differing  by  1°  up  to  130". 
The  ••  tabular  number"  is  simply  the  difference  between  the  length  of  a  i' 
curve  of  any  given  central  angle  and  the  lengths  of  its  tangents.  It  is  there- 
iore  given  for  any  angle  whatever  by  the  formula 

7^=  tan  i/X  5730  X  2  -  ioo7; 

'"  ^h'ch  T-  tabular  number  for  Table  187, 

/  =  intersection  angle  in  degrees. 

The  problem  is  rarely  one  of  practical  importance,  since  two  curves  of  con- 
siderable difference  in  radius  rarely  connect  the  same  tangents,  but  is  some- 
times convenient  for  determining  the  effect  of  minute  changes.  For  the  two 
curves  shown  in  Figs.  186,  187,  we  have— 

Tab.  no.  for  90"  (Table  iS;)  =  2459.3  x  A  (~4)  =  246  feet  loss  of  distance 
ty  the  :o°  curve.  '«)X5' 


644  CHAP.  XIX.—  THE  LIMIT  OF  MAXIMUM  CURVATURE. 

Table  187. 

Difference    in    Length    of    Line  vid    any    Two   Curves   of   Different 

Radii,  connecting  the  same  Tangents. 

[To  determine  the  required  difference,  multiply  the  tabular  number  below,  corresponding 

difference 


to  the  given  central  angle  by  the 


product 


of  the  two  degrees  of  curvature.] 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

o» 

0.00 

0.00 

0.02 

0.08 

0.16 

0.32 

0.56 

0.88 

1.32 

1.86 

io» 

2.56 

3-40 

442 

5-62 

7.02 

8.64 

10.50 

12.60 

14.98 

17. 6a 

20» 

20.6 

23.8 

27-4 

3«-4 

35-8 

40.4 

45-6 

5x2 

57-2 

63.6 

30' 

70.6 

78.0 

86  0 

94.2 

103.4 

113.2 

123.4 

134-2 

145-8 

158.0 

40« 

170.8 

184.4 

198.8 

214.0 

229.8 

246.6 

264.2 

282.6 

302.0 

322.4 

5o» 

343-6 

365-8 

389.0 

4x3-4 

438.8 

465 -4 

493-0 

521.8 

552.0 

583-4 

60° 

616.0 

650.0 

685.4 

722.2 

760.6 

800.4 

841.8 

884.8 

929.4 

975-8 

7o« 

1023 . 8 

1073.8 

1125.6 

1179.4 

1235.2 

1293.0 

»353-o 

1415-2 

1479.6 

1546  4 

8o» 

1615.4 

1687.2 

1761.4 

1838.4 

1918.0 

2006.0 

2086.0 

2174.4 

2266.2 

2361.0 

9o<> 

2459-4 

2561.0 

2666.4 

2775-6 

2888.6 

3005.6 

3126.8 

3252.4 

3382.4 

3517.3 

loo» 

3656-4 

3801.2 

3951-0 

4106.4 

4267.2 

4434-0 

4607.0 

4786.4 

4972.4 

5165.4 

no" 

5365-6 

5573-4 

5789.2 

6013.2 

6245.8 

6487.6 

6738.8 

6999.8 

7271.4 

7554  0 

iao» 

7848.0 

This  table  is  not  correct  to  the  nearest  tenth,  but  only  to  the  nearest  even  two-tenths. 
As  a  certain  small  fraction  only  of  the  tabular  number  is  to  be  taken,  the  error  was  not 
deemed  of  enough  moment  to  require  recomputation.  The  table  gives  merely  the  differ- 
ence between  the  length  of  the  two  tangents  to  a  i»  Curve  and  the  length  of  its  arc,  for 
any  given  central  angle. 

863i  Precisely  this  same  method  of  analysis  will  enable  us  to  determine  at 
once  the  difference  between  the  radius,  long  chord,  middle  ordinate,  tangent, 
or  any  other  function  of  any  two  similar  curves  if  we  know  the  value  of  the 
same  function  for  a  similar  1°  curve.  Thus  the  difference  between  the  radii  of 
a  5"  and  10°  curve  is 

10-5 


5730  X 


and  between  a  7"  and  8°, 


5730  X 


10  X  5 

8-7 


=  573.0  feet; 


T_  _  5730 

8X7"    56 


=  102.3  feet. 


864.  From  all  the  considerations  which  have  been  suggested 
together  we  may  perhaps  assume  that  the  inherent  cost  of  curv- 
ature per  train-mile  is  independent  of  the  radius,  or  at  least  does 
not  increase  appreciably  with  the  sharpness  of  the  curve,  and  this- 


CHAP.   XIX.— LIMITING  EFFECT  OF  CURVATURE.       645 

view  simplifies  a  decision  as  to  the  limit  of  radius.  But  whether 
this  view  be  entirely, correct  or  not  is  a  matter  of  perfect  indiffer- 
ence for  deciding  the  problem  immediately  before  us,  as  it  is 
hoped  has  been  made  perfectly  clear. 

Dismissing,  therefore,  from  our  minds  this  confusing  and  irrel- 
evant question,  we  will  now  confine  our  attention  exclusively  to 
the  LIMITING  EFFECT  of  cuivature  as  the  only  cause  which  justi- 
fies  the  fixing  of  any  arbitrary  limit  whatever  to  the  sharpness 
of  curves. 

THE    LIMITING    EFFECT    OF    CURVATURE. 

865.  Curvature  may  have  a  limiting  effect  in  three  ways  : 

1.  It  may  forbid  the  use  of  certain  types  or  weights  of  en- 
gines, or  so  impede  it  as  to  make  it  practically  inexpedient  The 
extent  to  which  this  cause  does  or  may  operate  has  been  already 
considered  (par.  285  et  seq.)  and  found  to  be  small. 

2.  It  may  impede  the  running  of  trains  at  high  speeds  by  the 
necessity  of  frequently  checking  speed  or  maintaining  a  low  rate 
of  speed  for  considerable  distances  when  the  intervals  between 
the  sharper  curves  are  small. 

3.  It  may  compel  the  hauling  of  shorter  trains  by  its  addition 
to  curve  resistance. 

The  second  cause  has  been  already  considered  from  the  me- 
chanical side  (in  par.  268  et  seq.)  and  found  to  appreciably  affect 
passenger  trains  alone. 

866.  As  a  business  question,  the  effect  which  we  there  saw 
sharp  curves  to  have  on  tiie  safe  speed  shows  their  use  to  be  on 
many  roads  of  heavy  passenger  traffic  a  consideration  of  extreme 
importance,  justifying  and  requiring  an  extremelv  low  limit  of 
curvature.  Nevertheless,  under  average  conditions,  the  same 
tacts  show  it  to  be  one  of  minor  importance. 

867.  It  depends  chiefly  on  a  road  of  any  given  character  on  the 
amount  and  disposition  of  the  sharp  curvature.    Thus  on  the  ele- 
vated railways  of  New  York,  with,  perhaps,  the  heaviest  passen- 
ger traffic  in  the  world,  a  few  excessively  sharp  curves  are  used 
such  as  those  shown  in  Figs.  189,  190,  191.     These  are  not  found 


'  ■»' 


CHAP.   XIX.—LIMITING  EFFECT  OF  CURVATURE. 


HI 


Fig.  189.-RHVERSED  Curves  of  90  Feet  Minimum  Radius  for  Turning  Right  Angles  ok 

Manhattan  Railway,  Sixth  Ave.  Line. 

There  are  four  rig:ht-ang:led  turns  on  the  Sixth  Avenue  line  similar  in  substance  to 
Fig.  189.  In  order  to  be  able  to  turn  within  the  stfeet  limits  short  reversed  curves  were 
introduced,  making  the  total  of  the  central  angles  134°  34',  or  44»  34'  over  the  necessary 
right  angle.  The  dotted  curve  of  200  feet  radius  (or  about  29°  instead  of  63°),  shows 
with  how  little  encroachment  on  private  property  the  radius  could  be  more  than  doubled. 
In  Fig.  190  the  dotted  alignment  would  save  212°  30'  -  i44»  =  68°  30',  besides  nearly- 
doubling  the  radius.  About  800  trains  per  day  pass  around  these  curves.  The  shortest 
interval  or  "  headway"  between  trains  is  only  9i  minute  on  the  Third  Avenue  line  and  \\^ 
minutes  on  the  Sixth  Avenue  line,  during  the  busiest  hours.  Counting  both  curves  to- 
gether, more  than  one  third  as  many  passengers  pass  over  them  per  year  as  ther?  are  who 
enter  all  the  trains  of  all  the  125,000  miles  of  railway  in  the  United  States.  The  gross 
earnings /i-r  mile  mount  up  to  $230,000,  and  the  operating  expenses  to  $125,000. 

The  property  on  the  corners  which  is  cut  by  the  dotted  curves  is  in  no  case  particularly 
valuable,  and  $20,000  or  $30,000  would  have  been  the  greatest  net  loss  which  would  be 
likely  to  result  from  substituting  any  one  of  the  dotted  curves  for  the  constructed  curve. 
No  accidents  of  any  kind  have  happened  on  any  of  these  sharp  curves  since  the  roads  were 
opened  in  1878. 

The  curves  are  of  standard  gauge,  and  the  cars  are  about  48  feet  long.  Their  draw- 
bars  go  from  truck  to  truck,  and  not  between  the  car-bodies. 


CHAP.   XIX.~LIMITING  EFFECT  OF  CURVATURE.      647 


:    H 


J] 


Fig.  X90.-REVERSED  Curves  of  no  Feet  Radius  on  Manhattan  Eletated  Railway 

Third  Ave.  Line.  """'f 


Line  oF  Unifor/n  Speed. 
y_ 


1.414. i^  !>.  ?^_  _  Pi^T/f /fiL'^i 

—Speedl  — , . i— -^<^^^t^gfo' 

-  I  I 

Slowinffhp 


I      Increasinrr  Speed, 


Fig.    Xgi.-lLLUSTRATING  THE   EFFECT  OF   LONGER   RaDIUS  ON   COMPARATIVE  SpBED. 


.i^. 


648       CHAP.   XIX.— LIMITING  EFFECT  OF  CURVATURE, 

to  be  a  measurable  disadvantage  as  respects  limiting  speed  (for 
if  they  were,  a  few  thousand  dollars  would  take  them  out),  be- 
cause, although  every  moment  of  lost  time  is  of  great  import- 
ance, the  speed  between  tlie  frequent  stops  is  slow  (not  over  30 
miles  per  hour)  and  the  motive-power  between  stations  (because 
of  the  frequency  of  stops)  abundant.  Therefore  the  speed  is 
checked  to  a  safe  limit  almost  instantaneously  on  approaching 
the  curve,  and  resumed  again  on  passing  it  almost  as  quickly,  and 
the  total  loss  per  curve  does  not  exceed  20  to  30  seconds  for  each 

curve;  only  a  small  of  part  which  (     .—  or   39.    3    per   cent,    on 

curve  and  ^  or  50  per  cent  in  approaching  and  leaving  the  curve, 
as  a  brief  analysis,  which  the  student  should  make,  will  show) 
could  be  saved  by  doubling  the  radius  of  curvature.  Fig.  192 
and  Table  107,  page  273,  will  indicate  the  method  of  determin- 
ing this. 

868.  If,  however,  there  were  many  of  these  curves,  the  loss  of 
time  would  not  only  increase  pari  passu^  but,  by  frittering  away 
the  time  and  nervous  energy  of  the  engineman,  obstructing  his 
view  ahead,  and  similar  indirect  causes,  cause  a  still  further  de- 
crease in  the  practicable  speed,  and  likewise  decrease  the  admis- 
sible frequency  of  trains,  thus  causing  an  unwarranted  loss,  if 
any  ordinary  expenditure  would  avoid  it.  As  the  line  now 
stands,  an  avoidance  of  all  curves  on  the  line  would  have  a  con- 
siderable money  value,  but  to  simply  double  the  radius  would  be 
worth  little  or  nothing — as  is  sufficiently  evidenced  by  Figs.  189- 
190.  The  management  is  not  unintelligent  nor  unduly  parsi- 
monious, but   it   is  not  thought  of,  simply  because  it  would  not 

pay- 

869.  So  on  the  various  railway  lines  connecting  Boston,  New 
York,  Philadelphia,  Baltimore,  and  Washington.  The  value  of 
avoiding  any  considerable  amount  of  curvature,  and  especially 
curvature  sharper  than  3"  or  4°,  is  to  be  measured  only  by  a  vast 
sum,  under  the  growing  business  advantage  of  very  fast  trains. 
Its  existence  in  large  amounts  would  make  quick  time  impossi- 
ble ;  but  the  same  is  not  at  all  true  of  a  small  amount  of  curva- 
ture at  some  one  point,  even  of  very  short  radius,  for  reducing 


CHAP.   XIX^-LIMITING  EFFECT  OF  CURVATURE. 


649 


speed  for  one  tnile  only  from  60  to  30  miles  per  hour  means  only 
the  loss  of  li  to  2  minutes  time  (Table  183).  The  justifiable  ex- 
penditure to  avoid  it  would  certainly  be  far  less  than  one  tenth 
of  what  would  be  justifiable  on  the  same  line  to  avoid  ten  times 
^s  much  curvature  and  delay,  both  because  (i)  more  than  ten 
limes  as  much  time  would  be  lost  thereby,  and  because  (2),  even 
if  not,  the  loss  would  be  more  than  ten  times  as  injurious.  '  Two 
minutes  more  time  between  New  York  and  Philadelphia  might 
not  place  a  competing  line  under  measurable  disadvantage. 
Twenty  minutes  would  not  simply  decrease,  but  destroy  its 
chance  for  competition  on  equal  terms. 

870.  When  we  come  to  long  trips,  of  500  to  1000  miles,  we 
have  already  (par.  240)  seen  that  any  probable  loss  of  time  which 
is  remediable  by  any  expenditure  within  bounds  for  easing  curv- 
ature is  not  likely  to  have  any  effect  whatever,  measurable  in  dol- 
lars  and  cents,  upon  competitive  equality.  The  most  trifling 
differences  in  neatness  of  stations  and  equipment,  courtesy  of  em- 
ployees, character  of  "lunch  counters,"  etc.,  would  be  far  more 
important  for  that  purpose,  as  well  as  far  more  cheaply  obtained. 

871.  The  true  principle  in  regard  to  this  matter  w^uld  there- 
fore seem  to  be:  To  estimate  the  total  loss  of  time  which  is 
likely  to  result,  on  a  given  line,  from  the  location  naturally  re- 
sulting from  one  radius  of  curvature  instead  of  another,  and  the 
probable  money  value  of  so  much  competitive  business  as  is 
likely  to  be  lost  on  account  of  this  loss  of  time.  While  this  is  an 
exceedingly  delicate  and  difficult  matter  to  estimate  even  approx- 
imately, and  an  impossible  one  to  determine  with  exactness,  vet 
(par.  21)  "what  we  can  do  is  to  fix  a  maximum  and  minimum 
limit,  somewhere  within  which  lies  the  truth  and  anywhere  out- 
side of  which  lies  a  certainty  of  error.  Due  judgment  and  cau- 
tion require  that  we  should  do  so." 

872.  As  a  general  rule,  the  limiting  line  between  the  traffic  to 
which  every  minute  is  and  is  not  important  lies  at  the  point  where 
It  ceases  to  be  possible  to  make  a  round  trip  in  a  day,  with  some 
time  to  spare  at  destination.  For  distances  under  100  or  150 
miles  this  is  possible,  as  for  instance  between   New  York  and 


i: 


650      CHAP.   XIX.— LIMITING  EFFECT  OF  CURVATURE. 

Philadelphia,  and  time  is  valued  greatly.  For  longer  distances,, 
as  from  New  York  to  Boston,  this  is  not  possible,  and  fast  trains^ 
are  not  run,  nor  are  they  likely  to  be  until  over  50  miles  per  hour 
can  be  made,  when  there  will  be  demand  for  several  daily.  Be- 
tween New  York  and  Chicago,  until  it  finally  appeared  possible 
to  shorten  up  the  time  to  24  hours,  quicker  time  than  36  hours- 
was  not  important,  and  was  not  made.  To  St.  Louis,  which  is 
only  200  to  250  miles  further  from  New  York  than  Chicago,  or 
some  20  per  cent,  the  time  is  still  eight  or  ten  hours  longer,  for 
the  same  reason. 

The  effect  of  sharp  curvature  on  safety  and  the  comfort  of  travellers  is  con- 
sidered in  Chap.  VIII.,  pars.  247  and  279. 

873.  We  will  now  analyze  the  extent  to  which  the  third  and  chief 
cause  for  limiting  effect  from  curvature  operates — that  it  may  compel 
the  hauling  of  shorter  trains  by  its  addition  to  the  train  resistance : 

We  have  on  the  tangent  maximum  grade,  whatever  it  may  be,  two» 
resistances  to  overcome : 

1.  The  ordinary  rolling-friction. 

2.  The  resistance  of  gravity — a  known  and  constant  quantity. 

In  the  case  of  curvature  on  a  level  we  have  also  two  resistances : 

1.  The  ordinary  rolling-friction,  as  before. 

2.  All  additional  resistance  which  may  or  can  arise  from  the  curve. 

In  either  case,  it  is  evident  that  the  resistance  from  the  rolling-fric- 
tion proper,  being  the  same  in  any  case,  whatever  its  amount  may  be, 
may  be  entirely  neglected.  In  any  case,  also,  it  is  obvious  that  the  grade 
on  any  curve  may  be  reduced  to  a  level,  if  desired,  so  as  to  eliminate  all 
grade  resistance. 

874.  The  normal  rolling-friction  being  eliminated,  what  we  require, 
in  order  to  determine  the  proper  limit  of  maximum  curvature  so  far  as 
length  of  train  is  concerned,  i.e.,  the  point  at  which  a  LIMITING  EFFECT 
begins,  or  should  begin  on  a  properly  laid  out  line,  is  simply  the  curve  on 
which,  in  all  cases  and  under  the  most  utifavorable  circumstances,  the  same 
engine  can  haul  the  same  train  on  a  level  as  it  can  haul  on  a  tangent  up 
the  maximum  grade. 

It  is  not  sufficient  to  determine  merely  the  curve  on  which  there  will 
probably  be  no  greater  resistance  on  a  level  than  on  the  tangent  maxi- 
mum grade,  nor  the  curve  on  which,  under  average  or  favorable  condi- 
tions, there  will  be  no  limiting  effect.  When  there  is  even  a  possibility 
that  under  any  circumstances  whatever,  exceptional  or  unexceptional. 


CHAP.    XIX.— LIMITING  EFFECT  OF  CURVATURE.       65 1 


the  resistances  on  a  level  maximum  curve  may  exceed  the  known  and 
invariable  effect  of  gravity  on  the  actual  tangent  maximum  grade,  that 
curve  is  in  a  sense  a  limiting  curve,  because  there  is  a  certain  disadvan- 
tage in  even  the  possibility  that  curvature  may  at  times  limit  the  trains 
in  advance  of  gradients,  and  hence  a  certain  money  value  in  avoiding  it. 

875.  Viewed  from  this  standpoint,  with  our  existing  experimental 
knowledge  of  curve  resistance,  all  that  can  safely  be  assumed  is  that  an 
allowance  of  2  lbs.  per  ton  per  degree  of  curvature  is  none  too  great  to 
cover  the  highest  possible  curve  resistance  at  very  low  speeds,  with  well- 
worn  rails  and  long  trains  of  empty  cars,  especially  on  easy  curves.  So 
high  a  curve  resistance  is.  we  may  be  very  certain,  rarely  reached  in 
practice,  but  that  it  is  sometimes  reached  is  at  least  possible. 

On  the  other  hand,  the  very  lowest  limit  for  the  resistance  on  ordi- 
nary railway  curvature,  under  the  most  favorable  circumstances,  at  high 
speeds  and  with  new  rails,  is  probably  about  (somewhat  less  than)  \  lb. 
per  degree  of  curvature,  falling  on  the  very  sharpest  curves,  such  as  on 
the  elevated  railways  of  New  York,  to  something  less  than  \  lb.  per  ton 
per  degree ;  but  the  latter  curves  are  out  of  the  range  of  ordinary  expe- 
rience. 

876.  The  assumed  2  lbs.  per  ton  of  train  resistance  is  equivalent  to 
o.i  per  cent  of  grade,  and  o.  5  lb.  to  0.025  per  cent  of  grade.  Multiplying 
the  former,  therefore,  by  the  degree  of  any  curve,  gives  a  rate  of  maxi- 
mum grade  which  will  certainly  oppose  more  resistance  to  all  trains 
under  all  circumstances  than  the  given  curve  will  on  a  level,  while  mul- 
tiplying the  latter  by  the  degree  of  curve,  in  the  same  way.  will  give  a 
rate  of  maximum  grade  which  will  certainly  not  oppose  more  resistance 
to  any  train  under  any  circumstances  than  will  the  curve,  and  hence  the 
latter  will  be,  in  the  fullest  sense,  a  "  limiting"  curve. 

In  between  these  limits  sometimes  the  curve  and  sometimes  the 
grade  may  offer  the  maximum  resistance. 

877.  From  the  above  simple  data  we  may  construct  the  following 
Table  188,  showing  the  proper  limits  of  practice  in  respect  to  maximum 
curvature  : 

Table  188  assumes  that  the  most  which  can  possibly  be  done  to  elim- 
inate curve  resistance  is  to  reduce  the  grade  to  a  level,  which  is  the  case 
with  an  evenly  balanced  traffic  and  with  long  stretches  of  level  or  undu- 
latmg  gradients  having  a  great  deal  of  curvature.  It  is  evident,  how- 
ever, that  under  the  three  following  conditions,  at  least,  this  is  not  the 
case,  and  hence  that  the  table  will  not  then  apply: 


Mk. 


.652       CHAP.   XIX.— LIMITING  EFFECT  OF  CURVATURE, 


CHAP.    XIX.— LIMITING  EFFECT  OF  CURVATURE.      653; 


Table  188. 


Maximum  and  Minimum  Limits  for  the  Degrees  of  Limiting  Curvature 

ON  Various  Grades. 
[Being  the  degrees  of  the  curves  which  certainly  will  and  certainly  will  not  cause  a 
greater  resistance  on  a  level  than  a  given  tangent  rate  of  maximum  grade.     Subject  to  the 
limitations  of  pars.  878  et  seq.\ 


Tangent  M 

AxiMUM  Grade. 

Degree  of  Maximum  Curve  on  a  Level 

which  will 

which  certainly 

will  have  a  limiting 

effect  on  all 

Per  Cent. 

Feet 
Per  Mile. 

certainly  have  no 
limiting  effect 

on  any  train  under 

trains  under  all 

any  circumstances. 

circumstances. 

O.X 

5.28 

1° 

4" 

0.2 

10.56 

2" 

8** 

0.3 

15.84 

tT 

12* 

0.4 

21.12 

4' 

i6' 

0.5 

26.40 

5" 

ao* 

0.6 

31.68 

6' 

24' 

0.7 

36.96 

7' 

•  «  • 

0.8 

42.24 

8" 

•  •  • 

0.9 

47.52 

9' 

•  •  • 

I.O 

52.80 

lO" 

•  •  • 

etc. 

etc. 

etc. 

_ 

Fig.  19a. 


878.  I.  On  a  long  maximum  grade,  of  any  considerable  rate,  we  can, 
if  necessary,  not  only  reduce  it  to  a  level,  but  break  the  grade  to  a  de- 
scent, as  at  BB\  Fig.  192,  and  in  this 
way  completely  eliminate  the  limiting 
effect  of  the  curve  resistance  of  any 
curve,  however  sharp ;  for  we  have  to 
consider  trains  in  one  direction  only. 
To  descending  trains  the  break  of  grade  can  (ordinarily)  do  no  harm. 
On  such  a  grade,  therefore,  there  is  no  reason  why  any  curve  whatever 
should  not  be  used,  so  far  as  the  limiting  effect  of  its  resistance  is  con- 
cerned, and  the  other  two  causes  alone  (par.  865)  justify  fixing  a  limit  of 
radius. 

2.  When  the  grade  is  level  or  slightly  undulating  for  a  considerable 
distance,  and  the  percentage  of  curvature  is  not  too  great,  some  little 
assistance  at  least  from  momentum  may  be  relied  on,  to  eliminate  a  por- 
tion of  the  resistance  of  very  sharp  curves. 

3.  When  the  burden  of  traffic  is  heavily  in  one  direction,  as  in  min- 

•eral  traffic,  even  with   nearly  level  grades  and  with   no  assistance  from 

momentum,  quite  sharp  curves  can  be  used  wherever  the  necessary  com- 


pensation to  equalize  the  curve  resistance  for  trains  moving  in  one  direc^ 
Hon  can  be  made,  because  the  loaded  trains  return  light  with  a  surplus 
of  motive-power.  * 

879.  Summarizing  our  conclusions  as  to  limit  of  maximum 
curvature,  we  have  found:  * 

1.  That  there  is  rarely  (although  there  is  sometimes)  real 
difficulty  in  using  engines  of  any  desired  power,  of  types  approxi- 
mate for  efficient  service,  on  any  probable  alignment,  and  (par. 
285)  that  on  curves  below  10°  or  12°  there  is  no  difficulty  what- 
ever. 

2.  That  those  railways  are  the  exception  (although  they  do 
exist)  on  which  any  probable  loss  of  time  from  the  necessity  of 
slowing  up  at  sharp  curves  will  be  a  matter  of  much  financial 
importance,  and  that  the  gain  in  this  respect  by  any  modifica- 
tion of  curvature  ordinarily  possible  is  much  less  than  is  sup- 
posed. 

3.  That  all  danger  of  limiting  effect  upon  the  weight  of  trains 
from  sharp  curvature,  within  the  limits  specified  in  Table  188,. 
can  ordinarily  be  avoided,  and  that  these  limits  afford  sufficient 
range  for  using  those  curves  which  best  fit  the  ground  under  all 
ordinary  topographical  conditions. 

4.  That  the  difference  in  danger  of  accident  which  is  liable- 
to  result  from  any  modifications  of  curvature  ordinarily  possible 
is  too  small  for  estimation,  as  an  element  justifying  additional, 
expenditure. 

5.  That  the  effect  of  any  difference  of  radius  on  the  expenses^ 
due  to  wear  and  tear  and  consumption  of  fuel  per  train-mile,  the 
degrees  of  central  angle  remaining  the  same,  is  probably  either 
nil  Qv  in  favor  of  sharp  radii;  but  that  whether  this  be  so  or  not 
(par.  252)  is  a  question  which  should  be  allowed  no  weight  what- 
ever in  fixing  on  a  limit  of  radius. 

6.  That   the   effect   of  shorter  radii,   if   they  have   any,    to 
lengthen   the  line  or  increase  the  degrees  of  central  angle,  or    ^ 
both,  through  the  different  location  which  naturally  results,  is 
likewise  a  matter  which  does  not  directly  affect  the  question,, 
although  it  often  may  indirectly. 

880.  We  may  likewise  close,  as  we  began,  with  another  very- 
important  conclusion: 


'  1" 


654      CHAP.    XIX.— LIMITING  EFFECT  OF  CURVATURE. 


CHAP.    XIX.— LIMITING  EFFECT  OF  CURVATURE.      655 


7.  That  the  natural  tendency  of  inexperienced  engineers  is  to  go  to 
extremes  in  the  matter  of  curvature,  either  spending  too  much  money  to 
obtain  easy  curvature^  or^  when  convinced  that  that  is  impolitic,  going  to 
the  other  extreme,  introducing  recklessly  more  and  sharper  curvature 
than  there  is  any  real  necessity  for ;  in  both  cases  alike  failing  to  perceive 
and  utilize  to  the  utmost  the  topographical  possibilities, 

881.  It  may  at  first  sight  appear  to  follow  from  the  aggregate 
of  this  summary  that  there  is  little  reason  to  fix  any  minimum 
limit  whatever  to  the  radius  of  curvature  except  the  physical 
limit  of  the  capacity  of  the  locomotive,  and  this  is  so  far  correct 
that  it  is  entirely  indefensible  to  start  out  upon  surveys  with 
.a  limit  determined  in  advance,  or  to  adhere  to  a  limit  at  every 
point  because  at  all  but  one  or  two  points  there  is  little  difficulty 
in  so  doing.  If  at  such  exceptional  points  a  large  expenditure 
is  necessary  to  adhere  to  it,  the  expenditure  should  not  be  made 
without  a  correspondingly  good  reason.  In  such  a  case  we  are 
justified  in  making  a  moderate  additional  expenditure  for  the 
mere  sake  of  a  uniformity  which  may  prove  advantageous  for 
operating  certain  engines  or  for  certain  high  speeds;  but  it 
should  in  general  be  a  very  moderate  one. 

882.  In  view  of  the  ever-present  danger  of  overloading  the 
capital  account  of  new  enterprises,  the  better  course  in  such 
cases  is  to  build  a  light  bold  line  for  a  sliort  distance,  laid  out 
with  the  idea  that  it  may  be  subsequently  improved  if  desired, 
and  if  means  exist  for  doing  it,  in  the  manner  elsewhere  dis- 
cussed (par.  283  et  al.). 

Nevertheless,  it  is  not  true  that  the  conclusions  summarized 
above  do  not  warrant,  under  all  ordinary  circumstances,  the 
maintenance  of  a  reasonable  and  moderate  limit  of  curvature  ; 
considerably  more  favorable,  if  their  spirit  be  closely  adhered 
to,  than  has  been  adopted  without  adequate  necessity  on  many 
lines.  For,  although  each  of  the  conclusions  specified,  taken 
separately,  does  not  warrant  the  fixing  of  arbitrary  limits  to  be 
adhered  to  at  large  expense,  yet  they  do  in  the  aggregate  indi- 
cate, as  common-sense  also  indicates,  that  reasonably  easy  curva- 
ture is  a  matter  of  much  absolute  although  possibly  of  small  rela- 
tive importance. 


883.  The  true  conclusions  to  be  drawn  may  perhaps  be  better 
put  in  this  way  : 

8.  That  A  standard  harmonizing  with  the  natural  topo- 

ORAPHICAL  characteristics    AND    READILY    ADAPTABLE    TO    THEM 

is  the  only  right  and  proper  one,  until  the  topography  becomes 
so  rugged  that  the  physical  limit  of  the  capacity  of  the  locomo- 
tive, of  the  class  and  at  the  speeds  practically  required,  begins  to 
be  approached.  This  is  true  both  in  letter  and  in  spirit,  and 
should  be  rigidly  adhered  to.  When  so  adhered  to  it  will  rarely 
cause  embarrassment,  for  there  is  usually  a  certain  natural  limit 
of  radius  which  can  be  obtained  without  much  difficulty  or 
expense,  and  except  in  extremely  rugged  mountainous  regions 
this  limit  will  rarely  be  a  high  one.  This  implies  that  the 
limit  should  be  varied  from  point  to  point  along  the  line,  as 
the  general  character  of  the  topography  varies,  and  the  sharp 
curvature,  so  far  as  possible,  bunched. 

884.  In  proportion  as  the  natural  limit  of  radius  is  favorable 
the  justifiable  expenditure  to  obtain  a  still  more  favorable  limit 
decreases  rapidly,  and  it  can  never  be  amiss  to  bear  in  mind  that 
there  is  no  case  on  record  where  a  railway  has  been  brought  to 
bankruptcy  by  the  expenses  resulting  from  sharp  curvature,  nor 
is  there  any  likelihood  that  there  ever  will  be  such  a  case,  while 
the  instances  are  many  where  companies  have  been  bankrupted 
by  their  expenditures  to  obtain  easy  curvature.  Hence,  since 
the  money  of  even  the  richest  corporations  is  limited,  and  in  the 
case  of  new  roads  almost  always  more  limited  in  proportion  to 
its»needs  than  its  over-sanguine  projectors  have  any  idea  of,  true 
wisdom  requires  that  the  available  capital  should  first  be  devoted 
to  the  really  important  ends — getting  close  to  and  well  into  the 
large  towns,  getting  suitable  terminal  facilities,  getting  low 
grades,  building  what  is  built  well,  protecting  the  public  and  the 
railway  company  at  once  from  danger  and  loss  by  proper  inter- 
locking apparatus  at  grade  crossings,  or  by  under-  and  over-cross- 
ings, rather  than  by  expenditures  for  some  fanciful  standard  ot 
curvature,  which  probably  makes  the  largest  addition  to  the  cost 
of  construction  of  any  detail  and    (for  any  change  within  the 


I 


\.\\ 


^  ( 


656      CHAP.    XIX.— LIMITING  EFFECT   OF   CURVATURE. 

power  of  the  engineer  at  any  cost  whatever)  the  smallest  additioa 
to  either  the  safety  or  economy  of  operation. 

885.  The  argument  in  favor  of  adapting  curvature  to  the  nat- 
ural topography  of  the  country  is  greatly  strengthened  by  the 
fact  that  sharp  curves  frequently,  if  not  universally,  render  pos- 
sible LOWER  RULING    GRADIENTS  IN  DIFFICULT  COUNTRY  and  often 

permit  the  use  of  otlierwise  favorable  routes  wliich,  witiiout  this 
concession  to  natural  conditions,  would  be  wholly  impracticable. 
The  writer  could  readily  mention  a  number  of  important  in- 
stances of  the  kind  from  his  own  experience. 

886.  But  because  other  ends  are  more  important,  this  is  not 
therefore  unimportant.  Becauseit  is  unjustifiable  to  expend  any- 
large  proportion  of  the  available  capital  for  this  end,  it  does  not, 
follow  that  a  very  large  proportion  of  the  time  given  to  surveys 
should  not  be  devoted  to  it.  Almost  invariably  it  should  be,  and 
the  engineer  who  finds  himself  in  rough  country  devoting  little 
thought  and  time  to  saving  every  degree  of  curvature  possible 
may  be  tolerably  sure  that  he  has  fallen  into  that  most  danger- 
ous fault — blindness  to  its  undoubted  and  great  disadvantages. 

887.  It  is  so  important  that  the  proper  course  in  respect  to  fixing  ar- 
bitrary limits  of  curvature  should  be  so  plain  as  to  be  fully  understood, 
that  we  may  profitably  add  a  word  as  to  the  specific  manner  in  which 
these  conclusions  are  frequently  violated,  and  the  error  in  doing  so. 

Many  thousands  of  miles  on  this  and  other  continents  have  been  built 
on  standards  of  grades  and  curvature  closely  approximating  to  this : 

1.  No  grade  shall  under  any  circumstances  exceed  60  ft.  per  mile. 

2.  No  curve  shall  under  any  circumstances  exceed  6".     But, 

3.  These  limits  may  be  freely  used  in  combination  with  each  other; 
i.e.,  6°  curves  may  be  inserted  in  unreduced  6o-ft.  grades. 

This  precise  standard  has  been  perhaps  more  used  in  this  country  than 
any  other  one  combination.  It  was  used  on  the  Erie,  the  Cincinnati 
Southern,  the  Chesapeake  &  Ohio,  the  Blue  Ridge  of  South  Carolina,  and 
a  long  list  of  other  roads  of  less  engineering  pretensions ;  having  been 
copied  from  one  to  another,  apparently,  without  much  regard  to  topo- 
graphical requirements — perhaps  because  the  round  fij^ures  and  the  al- 
literation of  the  6's  had  a  certain  charm.  Far  less  defensible  combina- 
tions have  been  the  rule  throughout  the  vast  expanse  of  the  Mississippi 
Valley  from  the  causes  alluded  to  on  page  6 — such  as  2°  or  3"  or  4"  limits. 


CHAP.    XIX.— LIMITING  EFFECT  OF  CURVATURE.      657 


of  curvature  with  40  to  80  ft.  grades  (0.8  to  1.5  per  cent);  but  it  should  be 
added  that  in  general  the  topography  favors  long  radii,  and  the  chief  error 
has  been,  not  the  radius  of  curvature,  but  the  reckless  sacrifices  of  gradi- 
ents to  save  degrees  of  central  angle. 

888.  We  have  already  determined  (par.  825)  that  the  use  of  unreduced 
curvature  on  a  maximum  grade  is  never  defensible.  Except  that  it  has 
been  done  in  such  repeated  instances  and  on  so  large  a  scale,  it  would  seem 
incredible  that  any  one  could  spend  large  sums  of  money  to  keep  curva- 
ture down  to  6°,  and  grades  down  to  60  ft.  per  mile,  and  yet  pile  one  upon 
the  other  freely,  giving  in  effect  a  75-ft.  grade.  We  may  more  clearly  see 
the  folly  of  it  by  an  example  from  humble  life.  Suppose  some  plain  coun- 
try farmer  should  find  that  his  team  could  just  draw  him  up  a  steep  hill 
through  mud  a  foot  deep,  and  should  forthwith  draw  two  conclusions— 
that  it  could  not  draw  him  up  any  steeper  hill  without  any  mud,  nor 
through  any  deeper  mud  without  any  hill :  should  we  not  think  the  man 
less  intelligent  than  the  beasts  he  drove  }  Yet  this  is  precisely  what  has 
been  done,  and  to  some  extent  is  still  done,  on  thousands  of  miles  the 
world  over,  by  engineers  of  standing. 

889.  Passing  this  error  as  no  longer  likely  to  be  committed,  let  us 
consider  the  propriety  and  effect  of  the  joint  standard  of  60  ft.  per  mile 
and  REDUCED  6°  curves  maxima: 

A  60  ft.  per  mile  grade  is  1.14  per  cent.  If  we  may  use  6°  curves  on 
such  grades  by  reducing  them  to  0.96  or  0.84  per  cent  (0.03  to  0.05  per 
cent  per  degree  compenstion),  which  is  the  largest  compensation  used  by 
those  who  adopt  such  standards,  why  should  we  not  feel  free  to  use  some 
sharper  curves  with  more  compensation,  or  on  a  dead  level,  if  we  can 
thereby  save  some  money  to  put  where  it  will  do  more  good  } 
890.  The  answer  can  only  be  one  of  four  reasons  : 

1.  A  7°  or  8°  or  10°  curve  of  equal  angular  length  will  be  so  much 
more  costly  in  wear  and  tear,  that  on  no  single  curve  can  the  saving  m 
cost  for  construction  pay  for  the  loss  therefrom.    Or, 

2.  A  few  such  curves,  even  if  fully  compensated,  will  in  some  unex- 
plained way  so  limit  trains  that  the  same  engine  cannot  do  the  same 
work.     Or, 

3.  They  will  cause  such  loss  of  time  from  slowing  up  (and  certainlv 
require  slowing  up)  that  a  loss  of  speed  involving  greater  loss  of  traffic 
than  the  value  of  any  possible  saving  will  result.     Or, 

4-  They  are  so  exceedingly  unsafe  to  operate,  compared  with  a  6°, 
that  in  no  case  can  the  additional  danger  therefrom  be  repaid  by  an  ade- 
quate economy  m  construction. 
42 


I 


I 


658      CHAP.    XIX.-^LIMITING  EFFECT  OF  CURVATURE. 


891.  There  is  no  escape  from  accepting  one  or  more  horns  of  this 
double  dilemma  if  such  a  standard  is  to  be  justified  at  all ;  and  probably 
no  man  would  have  the  hardihood  to  attempt  to  maintain  any  one  of  them 
for  explicit  reasons  given.  It  is  not  thus  that  such  utter  and  evident 
blunders  as  this — which  simply  to  state  their  nature  clearly  is  to  con- 
demn— have  come  about ;  but  rather  by  the  vague  process  of  jumping  at 
conclusions  outlined  in  par.  245 — that  "the Railway  is  to  be  first- 
class  ;"  that  "  nothing  over  6°  curvature  is  generally  considered  first- 
class  ;"  ergo,  etc.  etc.  The  fact  that  most  of  the  great  trunk  lines  have 
8*  to  10°  curves  (Table  116),  and  that  the  lines  which  have  set  up  such 
purely  arbitrary  standards  have  been  to  a  very  large  extent  lines  of 
a  secondary  class,  increases  the  obviousness  of  the  error  committed. 


CHAP.  XX.— CHOICE   OF  GRADIENTS. 


659 


CHAPTER  XX. 

THE    CHOICE    OF    GRADIENTS,    AND    DEVICES    FOR    REDUCING    THEM. 

892.  We  have  seen  clearly  enough  in  preceding  chapters  that 
the  gradients  are  the  one  thing  among  the  purely  engineering 
details  on  which   the  engineer  should  concentrate  his  attention, 
subordinating  them  only  to  the  end  of  reaching  the  sources  o 
traflic,  if  even  to  that. 

We  have  seen  also,  in  Chap.  XVII.,  that  the  use  of  assistant 
engmes  for  short  distances  with  low  ruling  grades  elsewhere,  is 
generally  preferable  to  a  uniform    through  grade,  both    topo- 
graphically and  financially;  for  the  reason  that,  do  the  best  we 
can,  a  uniform  grade  must  usually  approximate  pretty  closely  to 
the  rate  of  the  pusher  grade  if  it  passes  over  the  same  summit 
and  by  adopting  it  we  throw  away  the  advantage  of  the  low  grades 
on  all  the  rest  of  the  line,  which  may  be  had,  as  it  were,  for  nothing. 
893.  Having  recognized  these  abstract  truths,  however,  the 
next  thing  IS  to  apply  them,  and  here  we  pass  beyond  the  point 
where  specific  instructions  can  be  easily  given,  since  the  circum- 
stances  will  vary  on  every  line.     A  great  part  of  the  danger  of 
error  has  been  overcome  when   the  comparative  importance  of 
he  various  details  has  been   realized,  but  even  with  that  advan- 
tage  the  inexperienced  engineer  is  almost  certain  to  conclude 
that  a  certain  grade  is  the  lowest  attainable,  when  with  longer 
practice  or  more  skill,  or  harder  work,  or  less  self-confidence 
he  would  readily  obtain  grades  a  third  or  a  half  lower  at  the 
same  cost,  and  not  unfrequently  at  less  cost. 

.nl.ff'  ^^^'u    ''; '''^"'^^«''  ""«'  g-^neral  rule,  which  directly  re- 

annfirK,''       ..'"■'"'''''  ""'^  ^^'''^''  ~"'«^  ^°  "««^  to  being 
an   nfallible  guide  for  the  correct  projection  of  lines  in  the  fielf 

om  >  ^  7  ;  ^"^'""''  '''°"''^   ^°"°^  "  ^'"^"y.  deviating 

"om  It  only  for  very  good  reason,  viz.:  ^ 


:    I 


\  I 


66o 


CHAP.  XX.— HOW   TO  PROJECT  LOW  GRADES. 


Follow  that  route  which  affords  the  easiest  possible  grades  for 
THE  LONGEST  POSSIBLE  DISTANCES,  using  to  that  end  such  amounts  of 
distance,  curvature,  and  rise  and  fall  as  may  be  necessary,  and  then  pass 
OVER  THE  intervening  DISTANCES  ON  SUCH  GRADES  AS  ARE  THEN 
FOUND  NECESSARY. 

This  law  is  to  be  applied  with  intelligence  and  not  pushed 
too  far,  but  so  far  as  there  can  be  said  to  be  any  universal  and 
fundamental  law  for  location,  this  is  such  a  law. 

895.  When  the  higher  grades  are  in  danger  of  exceeding  2  per 
cent  or  2\  per  cent,  it  is  to  be  accepted  only  with  great  cau- 
tion, and  anything  beyond  3  per  cent  will  be  probably  bad  prac- 
tice, except  in  very  mountainous  country.  As  a  line  falls  below 
100  miles  in  length  the  economy  of  using  pushers  decreases,  and 
the  practical  advantage  of  a  uniform  gradient  increases. 

Accepting  this  general  rule  as  an  axiom,  our  problem  then 
divides  itself  into  two  parts: 

1.  How  to  obtain  the  lowest  possible  low  grades. 

2.  What  to  do  as  to  the  rates  of  the  high  grades. 


HOW    TO    PROJECT    LOW    GRADES. 

896.  Considering  only  a  naturally  low-grade  country  with  no  long- 
continued  ascents  to  encounter,  but  only  a  more  or  less  rolling  topog- 
raphy, three  fourths  of  almost  every  line,  or  of  the  part  thereof  lying  in 
such  low  country,  will  naturally  admit  of  an  extremely  low  gradient,  if 
some  considerable  lateral  deviations  to  throw  the  line  into  a  generally 
favorable  country  are  considered  admissible,  as  they  ought  to  be,  so  that 
such  alternates  between  any  two  points  as  those  sketched  to  a  rude  scale 

in  Fig.  193  are  considered 
as  prima  facie  equally  eli- 
gible. To  obtain  the  same 
grades  on  the  remaining 
fourth  will  often  involve 
some  disagreeable  sacrifices,  especially  when,  as  so  often  in  the  Western 
States,  we  can  take  an  air-line  by  accepting  i  per  cent  or  \\  per  cent 
grades,  if  we  are  foolish  enough  to  do  so. 

These  disagreeable  sacrifices,  however,  ought  ordinarily  to  be  met, 
even  to  the  extent  of  doubling  the  distance  on  one  quarter  of  the  line  if 
we  can  thereby  reduce  the  grades  to  half  as  high  a  rate.    We  shall  then 


CHAP.  XX.-HOW   TO  PROJECT  LOW  GRADES.  661 


simply  have  a  line  11 2i  miles  long  with  0.5  per  cent  grades,  as  against  a 
line  100  m.les  long  with  i.o  per  cent  grades.  The  former  is  immensely 
preferable  from  every  point  of  view.  But  usually  a  smaller  sacrifice  will 
make  a  greater  gain. 

897.  Let  us  consider,  for  example,  the  case  of  a  long,  low  ridge  or 
swell  m  a  generally  flat  country,  wliich  cannot  be  run  around  at  all,  by 
,^      any  device,  since  it  continues  indefinitely.    Assume 
Bv^        this  swell  to  be  three  miles  across  and  50  feet  high 
\        by  the  grade-line,  after  making  as  large  cuts  and 
%^^        fills  as  seem  expedient  at  A,  B,  C,  and  D,  Fig. 
194.     A  tangent  over  this  ridge  will  give  the 
profile  shown  in  Fig  195,  with  two  miles  of  i 
per  cent  grade  and  a  mile  of  level  interven- 
ing.   The  exaggerated  vertical  scale  makes 


■P,  «  ^'°-  '95. 

i-LAN  AND  Profile  of  a  Break  in  a  Long  Tangent  to  pass  over  a  Long,  Low  R.dgb  in 

Flat  Country. 

the  rise  seem  considerable,  but  on  the  ground  it  will  be  hardly  percep- 
tible to  the  eye  as  an  objectionable  feature  to  the  railway  line. 
^     This  is  especially  likely  to  be  the  case  because  the  ground  approach- 
ing such  a  rise  will  not  ordinarily  be  on  a  dead  level,  but  is  more  likely 


662 


CHAP.  XX.— HOW   TO  PROJECT  LOW  GRADES. 


to  have  about  half  as  steep  a  rise,  perhaps  for  a  long  distance  back,  giv- 
ing a  long  0.5  grade  approaching  the  ridge.  This  we  will  assume  to  be 
the  case,  as  also  that  except  for  this  swell,  and  a  few  others  like  it,  the 
0.5  grade  might  be  the  maximum  of  the  whole  line.  Such  conditions 
have  existed  on  thousands  of  miles. 

898.  Now  to  the  eye  of  a  country  farmer,  and  to  the  eye  of  many  an 
engineer,  perhaps,  who  may  inspect  the  line  during  construction,  as  it 
runs  over  the  surface  of  an  apparently  flat  cornfield,  this  whole  region 
will  seem  practically  a  dead  level.     In  the  first  place,  the  long  o.s^'ap-^ 
proach  will  invariably  be  taken  by  the  eye  to  be  a  level,  or  perhaps  even 
(by  well-known   optical   illusion)  a  slight  descent.     This  at  least  takes 
off  a  full  half  of  the  apparent  vertical  angle,  and  hence  of  the  apparent 
height  of  the  ridge;  and,  more  probably,  there  will  seem  to  be  a  slight 
dip  of  the  ground  toward  the  ridge  and  merely  a  corresponding  rise  be- 
yond it.     In  the  second  place,  even  if  the  approach  were  a  dead  level,  a 
rise  of  only  i  per  cent  in  a  natural  surface  seems  to  the  eye  a  very  small 
thing,  especially  before  the  track  is  laid,  so  that  it  would  seem  ridiculous 
to  turn  four  right  angles  "  for  nothing"  and  lose  two  or  three  miles  of 
distance,  at  the  cost  of  four  such  ugly  curves  through  the  cornfields  as 
are  shown  in  Fig.  194. 

899.  Nevertheless,  under  all  the  given  circumstances,  THAT  is  pre- 
cisely THE  THING  TO  DO.  The  Very  fact  of  the  long  0.5  approach, 
which  diminishes  the  visible  necessity,  makes  it  the  more  essential  to  do 
so,  because  it  forbids  us  to  resort  to  the  assistance  of  momentum  to  sur- 
mount the  ridge,  which  otherwise,  by  approaching  the  foot  of  it  at  30 
miles  per  hour  and  reaching  the  top  at  10,  would  take  off  (Table  118) 
31-95  -  3-55=  28.40  vertical  feet,  and  give  us,  out  of  our  i  per  cent 
grade,  a  virtual  profile  of  0.5  per  cent,  with  something  to  spare. 

900.  On  arriving  at  the  pointy^,  therefore,  even  if  it  be  with  a  30- 
mile  tangent  which  might  be  continued  for  30  miles  more  by  running 
straight  over  the  ridge,  a  sharp  turn  to  the  right  of  something  over  60* 
should  be  made  in  the  fiat  cornfield,  on  about  a  3'  curve,  for  the  sole 
purpose  of  lengthening  out  the  one-mile  ascent  into  two  miles,  so  as  to 
give  half  the  grade.  To  start  the  curve  A  farther  back,  as  shown  by  the 
dotted  line  A',  so  as  to  diminish  the  central  angle,  would  do  no  good, 
but  rather  destroy  the  very  purpose  of  the  curve,  which  is  xo gain  dis- 
tance between  A  and  B  and  not  to  reach  B'. 

When  the  line  reaches  B\  another  curve  of  60°  +  ,  in  another  corn- 
field, brings  it  back  again  parallel  with  itself,  but  nearly  two  miles  off. 
In  a  mile  more,  a  third  curve  of  60°+  enables  it  to  descend  the  ridge  on 
the  0.5  maximum  by  losing  another  mile  of  distance,  and  at  D  another 


<^^-^^»  XX.-HOW   TO  PROJECT  LOW  GRADES.  663 

curve  of  60°  +  brings  it  back  to  its  proper  position ;  giving  in  all  2  miles 
mterpolatea  distance  in  a  distance  of  3  miles.  250°  of  curvature  wher^ 
before  there  was  none,  and-what  would  sometimes  be  the  hardest  blow 
of  all-utterly  runnng  the  60-mile  tangent  which  had  been  run  in  ex^ 
actly  straight  by  foresights  only ;  and  all  for  the  sake  of  obtaining  a  line 
so  ugly  that  numerous  fingers  of  scorn  may  well  be  pointed  at  it 

901.  And,  no  doubt,  the  same  end  might  ordinarily  be  accomplished 
in  such  a  case   m  some  more  pleasing  and  economical  fashion  ,  as  bv 

dot^liie^^^^^^^^  ""^'^^  ^"  ^"^»^  --"-  ^^atthe 

dotted  Ime  C B"  Fig.  194.  m.ght  be  used  for  the  descent,  so  as  to  utilize 

most  of  the  otherwise  waste  distance.  Or.  by  going  further  back  and 
swmgmg  the  Ime  at  this  point  loor  2omiles  to  the  north  or  south,  beuer 
ground  may  be  obtained  with  less  aggregate  loss  of  distance  (Fig.  10,) 
than  on  this  three  miles  alone.  The  instance  has  purposely  been  made 
somewhat  extreme  in  this  respect  to  enforce  the  principle.  But  in  an! 
other  sense  it  is  not  extreme.  If  none  of  these  things  can  be  done  to  ad- 
vantage. IF  there  is  nothing  to  be  gained  by  deviating  from  an  air-line  be- 

tweentwopo.nts  ioomilesapart,andiFthis  air-line  will  admit  of  o.5grades 
each  way  except  for  one  or  two  or  three  or  five  or  six  such  ridges  as  that 
described,  then,  as  between  the  air-line  AD,  which  will  give  a  surface-line 
hundred-mile  tangent  on  i  per  cent  grades  and  six  breaks  like  AB'CD 
F'g.  194,  which  will   introduce  1500°  of  curvature  and  lose   12  miles  of 
distance,  and  break  the  hundred-mile  tangent  into  five-and-twentv  pieces 
but  give  05  percent  grades-the  ugly  and  crooked  line  is  beyond  a^l 
possibility  of  question  in  every  instance  the  line  to  take,  as  of  ve'ry  much- 
greater  operating  value,  unless  the  line  be  an  exception  to  most  Ameri- 
can roads,  by  having  a  preponderance  of  passenger  traffic,  which  is  both 
large  and  competitive.     Almost  every  general  principle  connected  with 
laying  out  railways  admits  of  more  or  less  doubt,  and  requires  exceptions 
lliis  particular  example  admits  of  no  doubt  and  requires  no  exceptions.' 

902.  For,  computing  the  values  of  the  losses  and  gains,  we  have- 
Yearly  saving  by  avoiding  an  increase  of  0.5  per 

cent  in  a  0.5  grade,  by  Table  178,  per  daily 

tram,  $4,300  x  5  = f     .     .     .  ft2i  coo  00 

Per  contra  :  ....     ?>2 1,500  00 

Cost  of  1500°  of  curvature  by  Table  115,  per  daily 

train.  $0,433  X  1500= $640  co 

^ostof  12  miles  of  distance,  by  Table  89.  per  dailv 

tram,  $290x12= \     ZA^o  oc^     4,12950 

Difference,  being  excess  of  value  of  the  low  grade-  " 

line,  with  six  such  breaks  of  tangent  as  is' 

shown  in  Figs.  194,  K)^,  per  daily  train,    ....  $17370  50 


HI 


664 


ff 


CH^P-  XX.— I/O IV  TO  PROJECT  LOW  GRADES. 


This  IS  equivalent  to  the  addition  of  a  capital  sum  of  nearly  $350,000  (at 
S  per  cent)  to  the  value  of  the  property,  or  $3500  per  mile,  per  da.fy  tra.„. 
For  en  daily  trams  each  way  the  line  will  pay  interest  on  $,5,000  per 
mile  larger  valuation.  '^ 

Tliis  assumes  that  all  trains  are  affected  by  thedifference  in  gradients 
as  by  the  difference  in  other  details.  No  passenger  train,  however,  would 
under  atiy  circumstances  be  much  benefited  by  the  reduction  of  ffrade 
so  that  ,f  one  quarter  or  one  half  the  trains  are  passenger  trains  the 
estimate  should  be  corrected  correspondingly.  On  the  other  hand,  no 
credrt  side  whatever  has  been  assumed  for  the  loss  of  distance,  whereas 
there  must  always  be  some  (par.  227  et  seg.)  and  often  enough  to  wipe  out 
the  debit  side  altogether.  How  the  account  will  then  stand  is  worthy  of 
careful  study.  ' 

903.  This  example  makes  it  clear  that  the  assumption  may  be  still 


Figs.  i,«,  ,„._Plai.  and  Profile  op  a  Break  in  a  Long  Tangent  to  obtain  0.4  rer  cent 

INSTEAD  OF   l.o   PER  CENT  GRADES. 

more  extreme,  as  by  assuming  that  the  attainable  through  grade,  except 
at  a  few  such  points  as  this,  is  0.4  per  cent.  We  then  have  the'  condi- 
tions of  Figs.  196-7.  if  we  are  to  obtain  0.4  per  cent  in  the  same  way; 


CHAP.  XX.-HOW   TO  PROJECT  LOW  GRADES.  665 


the  lateral  deviation  from  the  air  line  being  2.39  miles  and  the  loss  of 
distance  at  each  such  point  3  miles,  in  an  air-line  of  3  miles  Even  L 
that  case  three  or  four  or  even  five  such  points  might  be  s  ood  before  t 
was  concluded  to  give  up  the  low  grade,  but  at  six  the  loss  of  dis'ancl^ 
.8  miles-would  be  too  great,  threatening  to  discourage  traffic  and  the 
indication  would  be  very  strong  that  a  different  gener!.  route  should  L 

low'°r!dJr'  *^'""^'  P''"''P'^  ^^'""^  '''°"'<^  «°^«"'  the  laying  out  of 
ow  grade-lmes  or  sections  of  lines  cannot  be  made  much  clearer  than  by 

confineT,'"''  ;•       ''  '"^'""'"^  °'  °''^'"'"8  ^  '"^  g^^^e  are  ordinarHy 
confined  to  a  few  points  on  the  section.    Adopt,  then,  the  rate  which  can 

be  obtained  without  much  difficulty  on  three  fourths  or  four  fifths  of  ^e 
iTh^he'dT  °^.  ='=«''^"- r <>  concentrate  attention  on  the  remainder 

MERr   All  T'"  '"''   ™'    "-"^   ^'^^"^    "^"ST    BE    PRESERVED 

THERE  ALSO,  if  ,n  any  way  possible.     A  way  will  generally  appear  after 
careful^  study,  and  a  very  much  neater  one  than  tL  sket^che^ni  f£ 

909.  Much  of  the  lamentably  prevalent  bad  practice  in  such  details  as  we 

or  bit  bTh-r     h"'"^  '°"'"  '"™  '"^  '"='  ""'  '"^  "-  «  ''""-d  i"  det^l  onr; 
or  bit  by  bit,  and  not  as  a  whole,  as  ^' 

it  should  be.     If  we  allow  ourselves 
to  think  only  of  the  three-mile  stretch 
AD,  Figs.   194,  196,  198,  and  think 
of  the  consequence  of  throwing  the 
line  out  to  C B'  to  pass  from  A  to 
A  the  mind  revolts  from  it  at  once. 
The  rectangle  CCB'B,   Fig.  198,  ob- 
trudes   itself    upon    the  mind   while      "" 
the  project  is  inchoate,  and  thus  the 

rJseel'.T'"  T'"'^  ""^  •'  '^""  "^""  '^"  ^"™P^^^^  ^'"^  ''  »-'d  down,  as  may 
be  seen  at  once  by  comparmg  Figs.  198  and  194.  which  are  really  "  similar"  to 
^ach  other,  although  they  do  not  look  it.     If  the  mind  were  able  to   "ke   n    n 
due  proportion  the  vastly  greater  distances  on  each  side  which  are  not  injuri 
osy  affected  at  all,  while  they  are  made  passable  for  twice  as  heavy  trains  ther" 

^  nd  "n'rr^  T'  ''"■"""  "°"^'  ''  °"^^  '^^'"  ^°  '^'^  -^>'     B-  this  the 

less  of  ^   u       '''^''  '^''""^  P'"^^'"^  ^^°"^^  b«  kept  up  during  the  prog^ 

less  of  surveys  with  even  greater  care  than  those  on  working  scales 


/ 


'■\ 


666 


CHAP.  XX.— PROJECTING  PUSHER   GRADES. 


I 


■•1 


HOW    TO   PROJECT    PUSHER   GRADES. 

906.  Suppose  that  instead  of  there  being  five  or  six  such  low- 
ridges  as  that  shown  in  Figs.  194  or  196,  scattered  irregularly 

over   the   division,   there   is 
only  one,  but   six  times  as 
high,  as  sketched  in  Fig.  199. 
Fig.  199.  Fig.  196  may  still  serve  as  a 

map  of  such  a  point.  As  between  the  air-line  and  the  bowed 
line,  IF  EACH  IS  to  be  operated  in  THE  SAME  WAY,  the  case  is  not 
affected  in  the  slightest  by  the  greater  height  of  the  ridge  and 
length  of  the  lines  AB'  and  CD.  The  bowed  line  is  much  the 
best.  The  bunching  of  the  obstacles  at  one  point  does  make 
this  difference,  however,  that  there  is  now  a  rational  choice  in 
favor  of  assistant  engines.  For  any  considerable  traffic  the  short 
line  with  pusher  grades  will  be  very  probably  the  better.  The 
volume  of  traffic  makes  a  difference  in  two  ways:  First,  the  as- 
sistant power  can  be  more  exactly  adapted  to  requirements  ; 
second,  a  heavy  traffic  is  almost  sure  to  be  largely  competi- 
tive, thereby  diminishing  the  credit  side  to  the  value  of  dis- 
tance, . 

Pusher  grades  may  be  divided  into  two  classes,  each  of  which 
requires  different  treatment  and  will  be  considered  separately  : 
T.  Those  surmounting  low  elevations  by  the  easier  gradients. 
2.  Those  making  long  ascents  (say  over  700  or  800  feet)  on 
rates  which  must  be  conspicuously  more  severe  than  the  through 
grades  on  either  side,  as  where  li  per  cent  grades  or  over  are 
required. 

PUSHER  GRADES   ON   EASY  GRADIENTS. 

907.  When  it  is  seen  that  the  use  of  pushers  is  unavoidable  if  a  low 
through  grade  is  to  be  obtained,  the  first  question  which  arises  is  :  Which 
is  to  be  the  limitinjr  gradient.-the  low  through  grade  operated  by  one 
engine,  or  the  pusher  grade  operated  by  two  engines?  Ordinarily  Jt 
will  be  the  pusher  grade,  for  two  reasons : 

I.  The  lower  pusher  grades  must  be  reduced  in  rate  nearly  twice  as 


CHAP.  XX.-PROJECTING  LOW  PUSHER   GRADES.       667- 

fast  as  the  through  grades  to  keep  the  balance  equal,  as  is  evident  from 
tiie  following  figures,  taken  from  Table  182  : 

Through  Grade....       Level  o.i  0.2  0.3  0.4  0.5  0.6 

l^f^^^^^^- 0.38  0.57        0.76        0.95         1.12        1.29         1.47 

^'^"^'^""^ °-^9         0.19        0.19        0.17        0.17        018 

I-or  a  uniform  difference  in  through  grade  of  o.io. 

It  will  usually  be  very  much  easier  to  reduce  the  through  grades 
compl.cated  by  no  high  elevations,  from  0.6  to  0.4.  than  to  reduce  the 
corresponding  pusher  grade  from  1.47  to  1.12.  especiallv  as  the  through 
grade,  from  the  nature  of  the  case,  will  be  mostly  in  short  undulations  • 
and  hence,  *■ 

2^  The  influence  of  momentum  (par.  397  et  seg.,  and  see  also  close 
of  this  chapter)  will  frequently  assist  greatly  in  reducing  the  virtual 
through  gradients  below  the  nominal  maximum,  or  can  be  made  to  • 
whereas  long  pusher  grades  must  be  taken  at  their  actual  rate. 

908.  Assuming,  therefore,  the  pusher  grade  to  be  the  one  that  fixes- 
the  virtual  gradient  of  the  whole  line  or  division,  all  that  has  been  said 
above  about  reducing  through  grades  applies  to  it  in  an  intensified  de- 
gree.    The  saving  of  distance  or  curvature  should  be  wholly  subordi 
nate  to  the  end  of  reducing  the  rate  of  grade  to  the  lowest  limits,  taking 
care,  however,  not  to  introduce  development  which  adds  so  much  to  cur- 
vature that  the  compensation  destroys  nearly  all  the  gain.    A  resource  in 
extreme  instances  may  be  to  introduce  a  temporary  sag  in  a  grade-line. 

sL  M  K  Tu^^'-  ^^'-     ^^"^P  ""'^^'"^^'  ^^  absolutely  unavoidable 

should  be  used  here,  if  nowhere  else. 

In  this  way  reductions  of  grade  which  are  far  beyond  the   apparent 

seltd  ''r  "J  r''?  'u'  '''"'"''•     ''  ''^  ^"^'"^^^  '^^'^^  has  at  last 
secured  what  he  thinks  the  best  the  country  admits  of.  will  then  throw 

aside  all  his  preconceived  impressions,  and  start  in  afresh  with  the  idea 
tha   he  IS  all  wrong,  and  might  reduce  his  grade  o.i  per  cent  or  more  as 

ITZ  "^''k    .'  ''^'''^'''''''  '''  ^•^»^^'  ^he  chances  are  many  to  one  that 

ne  will  not  be  disappointed,  and  reductions  rising  to  even  0.3  to  o  c  per 

cent  may  sometimes  be  obtained  without  a  dollar  of  extra  cost,  by  ab- 

u.dly  simple  means,  as  in  the  instance  described  below,  and  illustrated 

omf  ''^•',  "^^'"^  "^^^  '^^  ''"y-"^'^  ^^^  ^  reduction  of  a  2  per  cent  grade 
some  ,5  miles  long  to  a  1.5  per  cent  grade,  with  a  cheaper  line. 

run^r*  ^"  '^^  '^'*'  illustrated  in   Fig.  200  a  located   line  aaa  had  first  been 

^.alT  A  '  ^'',""'  ^'^"^"^  '^'""^^  ^  "^^^^  attractive  saddle  A  over  which  the 
highway  already  ran,  requiring  a  short  tunnel  of  about  looo  ft.     The  sura 


1 


668        CHAP.  XX.— PROJECTING  HIGH  PUSHER   GRADES. 


CHAP.  XX.— PROJECTING  HIGH  PUSHER   GRADES       669 


mit  of  the  grade  was  but  a  short  distance  back,  and  A  was  approached  by  a  much 
lighter  grade;  but  accepting  /i  as  a  finality,  it  was  utterly  impossible  to  find  sup- 
porting ground  for  the  grade  at  a  saddle  about  4  miles  below  A  with  a  less 
grade  than  2  per  cent.  The  grade  was  in  all  some  20  miles  long,  in  two  suc- 
cessive sections  of  9  and  6  miles,  respectively,  with  some  little  broken  grade  in- 
termixed. 


Fig.  aoa 


Examination  indicated  (i)  that  except  over  this  stretch  at  the  head  of  the 
grade  there  would  be  ho  serious  difficulty  in  reducing  the  whole  grade  to  1.5  per 
cent,  and  (2)  that  the  only  chance  for  reducing  it  above  was  by  gaining  develop- 
ments around  the  hill  DG.  The  very  capable  and  experienced  engineer  who 
had  made  the  first  location  was  therefore  instructed  that  the  hill  must  be  turned 
if  possible.  He  ran  the  line  bbb,  accordingly,  to  the  point  Z,  turned  a  maximum 
curve  K,  and  reported  it  absolutely  impossible  to  turn  the  hill,  without  two  very 
high  viaducts  over  the  deep  gorge  H  and  a  tunnel  at  K, 

This  looked  plausible  on  the  ground,  if  it  does  not  on  the  map.  Standing 
at  L  there  was  an  abysmal  gorge  below,  a  precipitous  knife-edge,  G,  of  soft 
Tock  above,  and  the  smoother  side  of  the  hill,  M,  wholly  invisible  and  almost 


inaccessible,  but  known  to  be  very  steep.  Really,  however,  there  was  no  diffi- 
culty. Running  an  approximate  line  EM  from  below,  and  connecting  across 
the  top  of  the  hill,  it  was  found  that  the  entire  line  could  be  fitted  closely  to  a 
steep  side-hill  except  for  one  deep  rock  cut  at  G  so  very  narrow  in  proportion 
to  its  height  that  a  single  heavy  blast  would  remove  it  all  at  once.  This  threw 
the  line  nearly  100  ft.  lower  at  E,  saved  the  tunnel  A,  and  gave  much  better 
ground  below  as  well,  while  enabling  the  1.5  grade  to  be  easily  obtained. 

It  is  especially  important  to  exhaust  all  such  possibilities  on  low  and  short 
pusher  grades  (down  to  the  limit  which  balances  the  lowest  attainable  through 
grade),  because  the  use  of  two  pushers,  or  still  less  the  breaking  up  of  trains,  i& 
rarely  expedient,  as  it  often  is  on  the  longer  and  higher  pusher  grades,  which 
we  will  next  consider. 

LONG    PUSHER    GRADES    ON    HEAVY    GRADIENTS. 

910.  This  second  class  of  pusher  grades  should  ordinarily  be 
studied  by  tliemselves,  quite  apart  from  the  remainder  of  the 
line.  Their  cost,  both  for  construction  and  for  operation,  will 
be  a  leading  factor  in  the  finances  of  the  line,  and  hence  should 
be  a  controlling  factor.  They  are  sufficiently  prominent  features 
in  the  operation  of  the  line  to  enable  the  motive-power  to  be  well 
adapted  to  the  requirements  of  the  gradients,  whatever  they  may 
be. 

911.  These  causes  favor  the  adoption  of  low  rates  of  grade  for 
such  a  line: 

I.  As  the  gradients  rise  above  2  per  cent  the  loss  of  net  haul« 
ing  capacity  becomes  more  serious,  owing  to  the  weight  of  the 
engine  and  tender,  and  (for  freight  trains)  caboose,  becoming  a 
larger  and  larger  factor,  as  shown  in  Table  189,  p.  dZZ.  From 
Table  170  we  see  that  on  grades  differing  by  i  per  cent  the  net 
hauling  capacity  is — 


Grade 
per  cent. 

I.O 

2.0 

30 


Net  tons  load 
for  St'nd. 
American  engine. 

192 
118 


Per  cent 

(2  per  cent 

grade  =  100). 

193.2 

ico.o 
61.46 


Net  tons  load  Per  cent 

Grade                for  St'nd.  (2  per  cent 

per  cent.       American  engine,  grade  =  100). 

4'0                    7^  40.62 

50                  SZ  27.60 

6.0                        36  18.75 


2.  The  lower  grade  (if  obtained  by  development)  not  only  re- 
duces the  cost  of  operation,  but  increases  the  revenue  somewhat, 
by  giving  a  larger  mileage.     On  some  costly  lines  of  thin  non- 


•670      CHAP.  XX.— PROJECTING  HIGH  PUSHER   GRADES. 


CHAP.  XX.-PROJECTING  HIGH  PUSHER   GRADES       671 


competitive  traffic  this  may  justly  be  regarded  as  an  additional 
advantage  from  a  low  grade.  On  other  lines  it  might  be  an  al- 
most unmixed  disadvantage. 

3.  As  grades  rise  above  2  per  cent  or  2^  per  cent,  such  great 
caution  has  to  be  used  to  keep  trains  under  full  control,  both  in 
going  UD  and  down,  as  to  add  considerably  to  the  theoretical 
disadvantage,  both  in  loss  of  time  and  danger  of  accident. 

4.  A  lower  grade  will  often  be  found  to  lie  on  such  ground  as 
to  decrease  rather  than  increase  the  total  cost  per  mile  to  sub- 
grade  (as  we  have  just  seen  in  par.  909),  so  that  the  difference  in 
cost  of  a  low-grade  or  high-grade  line  will  be  at  the  most  not 
great. 

5.  A  large  portion  of  a  continuous  descent  will  often  not  ad- 
mit of  using  a  higher  grade  than  a  certain  rate.  It  then  becomes 
a  regrettable  sacrifice  to  use  a  higher  grade  elsewhere  on  the 
same  descent,  although  if  the  grade  be  long,  traffic  small,  and 
difference  of  cost  great,  it  should  be  done. 

912.  The  Jalapa  line  between  Vera  Cruz  and  Mexico,  described  in 
Appendix  C  and  its  accompanying  plates,  is  a  good  example  of  the  effect 
of  every  one  of  these  causes  favoring  low  grades.  On  the  first  30  kilo- 
metres (20  miles)  of  the  descent  from  the  summit,  although  a  slightly 
steeper  than  2  per  cent  grade  might  have  assisted  somewhat,  a  4  per  cent 
grade  would  have  thrown  the  line  so  low  as  to  bring  it  on  much  worse 
ground. 

913.  The  descent  from  Tepic  (see  par.  917).  on  which  the  spiral  oc- 
curs, shown  in  Figs.  207,  208,  is  a  good  illustration  of  the  fifth  cause 
above.  From  the  summit  down  to  the  foot  of  the  spiral  more  than  the 
adopted  rate  of  2.6  per  cent  could  not  possibly  be  used,  except  by  throw- 
ing away  elevation  with  level  stretches,  since  that  grade  brought  the  line 
down  to  the  very  bed  of  the  stream  under  the  viaduct.  The  same  grade, 
in  the  main,  fitted  the  bed  of  the  stream  very  well,  although  for  5  or  6 
miles  it  was  necessary  to  hold  up  above  the  bed  somewhat  at  some  expense. 
As,  therefore,  there  were  only  some  5  or  6  miles  out  of  the  30  miles 
of  2.6  grade  (broken  by  some  short  unavoidable  levels  below)  in  which 
the  descent  of  3000  feet  to  sea-level  was  made,  it  would  have  been  an  un- 
warrantable sacrifice  to  break  the  grade  on  the  short  stretch,  where 
(only  by  raising  it  to  about  4  per  cent)  some  appreciable  economy  might 
be  realized,  even  for  the  thin  traffic  expected. 


914.  The  following  causes  favor  the  selection  of  high  rates 
of  grades  for  such  sections  of  line: 

1.  It  usually  very  much  reduces  the  cost  of  construction 
which  IS  probably  high  at  best— a  consideration  of  great  impor- 
tance (par.  29).  ^ 

2.  If  the  rate  of  a  higher  grade  can  be  maintained  unbroken. 
so  that  Its  length  is  decreased  in  proportion  as  its  rate  is  increased  the 
total  motive-power  is  not  increased  (Table  181  and  par  747) 
^ven  if  the  total  length  of  the  line  between  termini  is  not  de- 
<:reased  by  the  higher  grade,  i.e.,  if  the  respective  profiles  be- 
tween  the  two  termini  are  as  in  Fig.  201.  If  the  lower  grade 
IS  only  to  be  obtained  by  interpolated  distance,  so  that  the  foot 
of  both  the  low  grade  and  high  grade  falls  at  nearly  the  same 
point,  the  advantage  in  motive-power  needed  is  still  more  in 
favor  of  the  high-grade  line. 

3.  The   loss   by   multiplication    of   trains    and    train-wa^es 
which  IS  otherwise  so  very  serious  ' 

on  high  grades,  is  obviated  in  part 
by  using  two  or  three  engines  per 
train,  which  it  is  not  practicable 
to    do  with  heavy  through    trains 

over  a  whole  division.  This  advantage  is  to  be  assumed  with 
caution,  however,  as  within  the  extreme  limits  of  choice  which 
the  engineer  has  ordinarily  before  him  (say  not  over  i  per  cent 
in  most  cases)  the  same  number  of  engines  per  train  can  be  used 
on  either  the  highest  or  the  lowest  rate. 

915.  4.    The  case  is  much  stronger  in  favor  of  high  grades 
when   the  low  grade  is  only  to  be  obtained  by  hanging  on  a 
rough  side-hill  as  against  lying  in  the  bed  of  a  stream,  or  with 
other  great   contrasts    in   facilities    of   construction,  as  in    the 
bt.  Gothard  Railway,  where  a  low  grade  was  obtained  onlv  by 
the  desperate  expedient  shown  in   Figs.  202   to   2o6:-~turning 
spiral  tunnels  into  the  solid  rock  and  thus  introducing  so  much 
pure  development  between  the  same  termini,  so  that  a  hio-her 
?:rade  would  have  shortened  the  pusher  runs  almost  exactly/r^ 
>ata,  and  left  the  same  amount  of  motive-power  required  for  the 
passage  between  termini  in  either  case.     On  the  Italian  side  of 
t'le  mountain,  indeed,  these  spirals  appear  to  have  been  an  en- 


Fig, 


30I. 


6/2       CHAP.  XX.— PROJECTING  HIGH  PUSHER   GRADES. 


CHAP.   XX.— PUSHER  GRADES 


tirely  superfluous    luxury  (see    note   to   Figs.   202-206  on   page 
following  them),  not  even  serving  to  reduce  the  grades. 

Apart  from  the  cost  of  these  spirals,  had  the  grade  been  higher 
it  would  have  lain  for  a  considerably  larger  portion  of  its  length 
nearer  to  the  bottom  of  the  valley,  and  hence  on  better  ground. 

The  St.  Gothard  line,  therefore,  furnishes  a  good  example, 
although   certainly    not   an   extreme   example,  of   unjustifiable 
adoption  of  low  grades.     It  is  mag- 
nificent, but  in  this  detail  of  its  loca-  «^  I  r 
lion  it  is  not  engineering,  because  it              ^  '^     ^* 
does  not  accomplish  the  desired  end 
in  the  most  economical  way. 

assL 


7""^ 


Figs.  202-3.— Profile  of  St.  Gothard  Railway,  Swiss  Side 


43 


6/4  CH.  XX.^REDUCmC  RATE  AND  COST  OF  HIGH  GRADES. 


Figs.  202  and  204  are  profiles  of  the  bed  of  the  valleys  approaching  the  St. 
Gothard  tunnel,  with  the  scale  shown  in  miles.      On   the  Italian  side  of  the 
mountain  the  bed  of  the  stream  was  broken  by  cataracts,  and  it  will  be  seen  by 
the  dotted  grade-lines  plunging  below  the  river-bed  that  by  simply  developing 
the  spiral  tunnels  into  straight  ones,  adding  nothing  to  their  length,  the  same 
grade  up  the  mountain  would  have  been  obtained  with  a  material  saving  of  dis- 
tance and  curvature,  and  hence,  of  course,  of  cost.     Such  a  straight  tunnel 
would  start  in  at  the  lower  portal  of  the  fifth  rising  curve,  near  K,  Fig.  205.  and 
take  a  straight  course  through  the  words  "  Fig.  205"  to  a  point  beyond  the  limits 
of  Fig.  205,  where  it  would  again  emerge  into  the  valley,  requiring  a  tunnel  of 
a  trifle  over  3  miles  long,  or  about  what  there  is  nos^  of  tunnel  oxv  the  same 
stretch,  saving  all  the  other  work  and  distance.     The  same  is  true  in  substance 
of  the  two  lower  raising  curves,  or  of  the  upper  one  at  least. 

The  fact  that  this  throws  the  grade-line  below  the  bed  of  the  stream  looks 
bad  on  the  profile,  but  should  not  be  allowed  to  deceive.  The  tunnels  plunge 
into  the  bowels  of  vast  overhanging  mountains  of  solid  rock,  and  can  be  kept 
as  far  away  from  the  stream  as  desired,  if  there  were  need  to  consider  it  at  all. 
The  only  visible  gain  from  the  spirals,  therefore,  was  to  have  the  same  engi- 
neering curiosities  on  one  side  of  the  mountain  as  on  the  other. 

On  the  Swiss  side  of  the  mountain,  Fig.  202,  the  spiral  developments  shown 
in  Fig.  203  were  essential  for  the  purpose  sought,  to  reduce  the  grade  to  137  ft. 
per  mile.  To  have  followed  the  natural  grade  of  the  valley  would  have  required 
from  197  5  to  237.5  ft.  per  mile  grades,  according  to  how  closely  the  bed  of  the 
valley  was  followed.  By  the  aid  of  the  long  Table  170  we  may  see  how  much 
real  economy  in  motive-power  was  effected  by  these  developments  in  taking  the 
traflSc  from  Silenen  to  the  St.  Gothard  tunnel.  Neglecting  the  actual  distance, 
which  it  would  be  unfair  to  consider,  we  may  say  that  the  length  of  the  moun- 
tain grade  in  miles  should  be  about  inversely  as  the  rate  of  grade.  Then  we 
have,  for  a  standard  Consolidation: 


Grade. 
Ft.  Per  Mile. 

137 

219 

237i 


Comparative 
Length. 

lOO.O 

693 
62.5 

57.7 


Comp.  Net 
Tons. 

319 
210 
184 
165 


Load  of  Eng. 
Per  Cent. 

lOO.O 

65.9 
57.7 
51.7 


Comp.  Enor.  Miles 
Per  Through  Ton. 

100 

105 
108 


In  other  words,  comparing  the  constructed  grade  with  the  197.5-ft.  grade 
only,  in  a  valley  distance  of  10  miles.  44  miles  {~\  of  tunnel  development  vi?,s 

introduced  with  the  effect  of  saving  only  5  per  cent  of  the  engine-miles  necessary 
to  move  a  car  through,  and  perhaps  2^  per  cent  of  the  cost  of  movement.  Such 
errors  result  from  lack  of  study  of  the  economic  side  of  railway  location.  There 
could  be  no  better  illustration  of  the  broad  distinction  between  reducing  the 
rates  of  through  grades  and  of  pusher  grades  stated  in  par.  747. 


CH.  XX.-REDUCWG  RA  TE  A.VD  COST  OF  HICII  GRADES.  6/5 
EXPED,E.XS   POK  KEOUCNG  THE  RATE  AND  COST  OP  HIGH  GRADES 

TION   AND    WORK    EACH    WAY    FROVf    it     ;nc^o    A       c  THIS  SEC- 

i'KUM  IT,  instead  of  eoino-  alwav«  tr^  tK^ 

What  are  or  ought  VZTlZ^Llll^.^l''::^-  '"'''''  '"'  °"' 
be  the  summit,  and  work  from  them       7n  f     ""^^  °'  ""^^  "°' 

nar,  .  U  or.narU,  .est  toTa^tl  tt  r:Xhut  LTsfX'it 
.t  ,s  rather  the  rule  thau  the  exception  that  it  should  not  be  dTne 

VU.  F,g.  ao7  shows  a  remarkable  example  of  the  advantao-^,  of  ,w. 
from  the  location  of  the  lower  end  of  the  pLific  Branl  o  ^  m-  ^-Tetai 
Radway.  onr  the  descent  from  the  citv  of  Tenir  tr.  ru  ^^^^      a"  Central 

efforts  were  made  by  various  engin:!;  i  ob't  „  .  pj,-::;  ^T  JT""' 
d>sting>.ished  as  first,  second,  and  third  lines  in  Fig  "TL  witl,  "' 
very  satisfactory  result,  until,  aided  by  the  knowledge  gained  L  th.  ""'' 

surveys,  the  idea  of  the  spiral  line  w/s  conceived  an!  pushed  -  a  s^erul 

.a,r  z:^  r  sr:  — —  - — hy- -  -e  - 

to  be  rade       '    7  '"'  ^'"^^  '"^  ^^^'  =°  ""''  ""=  -"-  "- wou^d  have  h'd 

Destn-fn  To^  tpTc  ';:T^'t;i:';''''TiT "'  --  --  --« 

Tepic  River  until  it  dleL  .h^re;rt  ^  il'l^ L^ Tn^^  ^ 7g  1^ 
.on  and  becomes  impracticably  rough)  and  strikes  across  into  the  vallev  of  7hJ 

subhmuy  and  beauty  over  the  rugged  and  abrupt  descent  to  the  coast  flats 
•igiy  snarp.       in  an  air-line  distance  of  two  miles    frnm  m-  ^      .     m- 

:r  ^f  r:  irLr;- ^ '--'  r  "-^  --'  ^  ^-  -"  "^-"  - 

practi<^breTor  Hn^  '°'"'  "■'  '""'^  °'  '"=  '"K^"i°.  «""'=  "tirely 

cfcable  for  a  hue  .n  or  very  near  to  the  bed  of  the  stream,  had,  for  many 


(>^^  CH.  XX.— REDUCING  RATE  AND  COST  OF  HIGH  GRADES. 


miles  below  the  spiral  (to  near  B,  Fig.  207),  abrupt  and  rugged  banks  several 
hundred  feet  high,  of  the  same  impracticable  character  as  those  shown  imme- 
diately below  the  spiral  bridge,  Fig.  208,  although  below  B  the  valley  became 
more  tractable. 

918.  Under  these  circumstances,  since  it  was  impossible  to  descend  into 
the  bottom  of  the  valley  on  any  practicable  grade,  and  since,  unless  this  were 
done,  the  line  must  be,  for  a  long  distance  below  the  spiral  afterward  adopted, 
entirely  above  the  immediate  slopes  of  the  valley  ;  to  avoid  the  most  excessive 
work,  a  comparatively  light  trial  grade,  2  per  cent,  was  not  unwisely  adopted 


0<r«^wy^ 


KILOMETERS 

234 

I  I   t   I  I  I 


CH  XX.— REDUCING  RATE  AND  COST  OF  HIGH  GRADES.  ^77 

ding,  involving,  in  spite  of  the  use  of  17°  curves,  a  number  of  tunnels  and 
many  retaining-walls  and  small  viaducts. 

These  facts  made  it  clear,  if  it  had  not  been  before,  that  the  attempt  to  find 
a  line  by  starting  from  the  summit  as  a  controlling  point,  and  letting  it  fall 
thence  where  it  would,  must  be  abandoned,  and  a  line  chosen  lying  in  the  botr 
tom  of  the  valley  as  a  fixture  and  worked  from  at  each  end  ;  that  being  the 
only  place  where  a  really  economical  line  could  lie  for  the  entire  distance  down 
to  C,  Fig,  207. 

A  random  line  in  the  bed  of  the  stream  showed  that  a  2.6  per  cent  grade 


.0^^' 


*««••• 


Fig.  207.— Routrs  of  Various  Surveys  for  the  Grade  dEscENDiNC.  to  the  Coast 

[Black  figures  give  elevation  in 


Furs  FROM  Tepic,  Mexico,  on  Pacific  Branch  of  the  Mexican  Central  Railway. 
metres.    The  spiral  shown  in  Fig.  208  is  fe  shown  above.] 


1  ,■» 


for  running  the  three  first  lines  shown  by  dotted  lines  on  the  map.  These 
lines,  otherwise  differing  from  each  other  greatly,  agreed  in  swinging  around 
the  area  covered  by  the  spiral  and  close  to  the  latter,  although  off  the  area  cov- 
ered by  the  map  of  the  spiral  in  Fig.  208.  To  trace  them  on  Fig.  208,  start 
from  near  the  scale  and  title  and  pass  thence  to  the  right,  then  down,  and  then, 
at  the  bottom  of  the  map,  to  the  left,  to  a  point  between  A  and  B  on  the  small 
scale  map,  Fig.  207.  At  this  point  they  were  already  far  above  the  grade  o»* 
the  spiral  bridge,  so  that  they  soon  left  the  excessive  slopes  of  the  valley  and 
struck  comparatively  easy  work  on  the  narrow  ridg:e  lying  between  the  valleys 
of  the  two  parallel  streams  shown. 

Nevertheless,  the  work  on  all  three  of  the  lines  was  excessive,  while  the 
low  grade  required  a  great  amount  of  otherwise  unnecessary  development  and 
curvature.  Two  of  these  lines  were  located  on  paper  and  profiles  made,  but 
no  accurate  estimates  were  ever  made  of  them,  as  the  work  was  very  forbid - 


(137  feet  per  mile)  was  the  lowest  adapted  to  it,  and  in  assuming  the  line  to  be 
in  this  position,  and  extended  from  each  end  (i.e.,  conceiving  the  line  fixed 
under  the  bridge  in  Fig.  208),  the  ascent  thence  up  the  upper  small  stream  was 
(for  the  country)  mere  surface  work,  and  the  extraordinarily  favorable  point 
for  the  high  crossing  (the  narrowest  for  miles)  naturally  suggested  sweeping 
the  line  around,  through  a  deep  but  narrow  cut,  into  the  lower  small  valley,  so 
as  to  cross  over  itself  by  a  high  viaduct,  and  thence  ascend  to  the  summit. 
Above  the  viaduct  it  follows  up  the  right  slope  of  the  small  stream  shown  just 
under  the  title  to  Fig.  208,  being  on  the  opposite  side  from  the  three  previous 
lines,  which  chanced  also  to  be  somewhat  the  best  side. 

It  was  found  on  extending  the  line  up  to  the  summit  that  it  left  some  spare 
•elevation,  and  this  was  properly  concentrated  within  the  spiral,  in  order  to 
make  the  bridge  as  low  as  possible. 

919t  There  was  a  possibility  of  a  direct  line  from  Tepic  to  the  head  of  the 


mm 


m 


&«w.— The  fine  water-power  of  the  R.v.  rf'.  t     • 
one  side,  with  the  mills  already  on  i    and  ,he  n,K    ""  7°'"'^  "^^^  "«"  ''"  « 
be  ^.ed  .h.e-water,ower  ^inXnc^ ll!  Meli^  ""^  "^^  "^''^  '° 

beyond  u-;:yhrw\r;hTc;tT:^;^L",'""^ "°'"  ^  ^--•"•--^  p-"- 

.He::::t:rtr:^'  r::---  f — -i--  -- subsu^ted  .r  o„e  o, 

Paci6c  Branch  (and  for  the  main  iTne  of  the  M  %'°'  '"'  ''="=^  °'  ">« 

tourist  traffic,  and  much  of  the  renainde    ^f^he'r"    k"'"'  "  ""="'  "='"« 
beauty,  this  alone  was  deemed  a  dccis.ve  consLra.ior     ""^  °'  «'"'  "^"'^ 

WhV  'T'"'  ''""^'°"  °'  "'  ^'""'  ^""^  "^''""  "-  -  '°"°-: 
1-ength  of  spiral,  2,637  metres. . .  _  „  , 

(405  -f  60  =  66g  +  30.  with  io-m;tVeV  ^i^^   ~    '^"  ^"'  =      ^•^•*  °^""^ 
Descent  in  spiral,  actual. . . .  ^' 

Descent  in  spiral,  on  2.6  grade..  !*.*..  ;*'.*.*.*.* ^'^  "'^J''^^  =  '73-9    feet. 

Loss  of  elevation  in  do  "I      7 

* 15.56  metres. 

Utilized  as  follows: 

^°'  degrir™^'"''''""'  ^""^  '^'^''''  ^^'  °*^  P*^' 

Spare  elevation.' u'tiliVed  VoVa  station 'g;ound'a'r; d    ^'^^  """''"'* 

water  station  at  south  end  of  spiral ^o  00      - 

Viaduct:  Length.  200  metres 

Height,     53      "       —656       feet. 

=173.9 

The  height  is  above  the  grade-line      Ahr.tr.  i 
more.  **  "*"'     ^^°^^  low-water  it  was  some  7  feet 

Other  resources  for  reducing  the  rates  of  Ion,  ascents  are  : 

point'L^h^Hn^'^ornT^a^f!:,^^^  ^^   «"^^"^    ^    favorable 

mensely  facilitate  a  favorable  result  e„Hr        J""  "^^^  '''''^'  ^^^^"  ^"^- 
vorable  section  of  a  lon/de  cen  "o  We  "t   "  P^-^iiities  of  any  fa- 

the  line  to  .eep  away  fr^^t^  ^re^t ^ dTf.^^^^^^  ^^^'^"^ 

ment  on  the  Jalapa  line,  Appendix  C  i,  a  „^  J  ?  develop- 

The  privilege  of  using  a  shafrctve  occLrali; u"''''  °'  '""  '^^'^^• 
this  end,  and  often  ^si„.fua„a„       """'^'""'"'J' ''  »  g™at  assistance  ta 


100 

■  I  ■  I  ■  I  ■  I  '  I 


METERS. 
200  300 


Fig.  208. 


I  7%e  topography  of  this  map  is 
minutely  accurate.  The  curves 
are  Aotm  off  sett  ed  for  transit 
(ton  curves.) 


ibo        2(iO         300       46o        5^0 

Mexican  Central   Railway - 

Branch  to  the 
SPIRALoFTHE  BARRANCA  BLANCA 

BETWEEN  SAN  BLAS  AND 
JAN.  1883. 


(First  three  lines  passed 
around  and  near  the  limits 
of  the  map  in  this  direction.) 


•  Reiueed  one-fifth  scale  from  the  original  field 
^kteU  on  a  scaU  of  j^  or  83i  ft.  per  in. 

Co:rroiTBS.  2  Meteks  (6  56^1.)  apabt. 


iLinefrom  here  nsrerds 
the  tmail  ttream  abort.) 


I  V'ltHfii  c»iiiinue.s  of 
this  nenernl  character  to 
p..  Fiff.  20T  ) 


(First  three  lines  ran 
near  here.) 


CH.  XX.^REDUCING  RATE  AND  COST  OF  HIGH  GRADES.  679 


SAN    JUAN 


Fig.  209  is  another  example  to  scale  of  such  zigzag  or  horseshoe  develop- 
ment, on  the  Lima  &  Oroya  Railway,  in  Peru.  The  distance  from  A  to  B  hori- 
zontally is  570  feet, 
and  vertically  is  365 
feet.  The  horizontal 
distance  from  C  to  D 
is  495  feet,  vertical  dis- 
tance 360  feet;  length 
of  line  from  A  to  D  is 
4  miles.  The  usual 
rule  on  this  road  was 
to  use  switchbacks  for 
such  developments,  as 


SACRAPE 


Fig.  209. 


shown  in  Figs.  218-21.     In  all  these  cuts  the  dotted  lines  represent  tunnels. 
The  curve  at  Sacrape  is  14°  30'. 

922.  3.  Spirals  might  be  used  to  great  advantage  much  oftener  than 


1 


i 


,y-y\- 


'' I  hill  II- 


Fig.  3IO.— Bridge  Shral. 


Fig.  211. — Tunnel  Spiral. 


they  are.     A  spiral,  also  sometimes  called  a  "loop,"  is  a  doubling  back 

of  the  line  upon  itself  so  that  it  returns  under  itself  at  a  lower  elevation. 

They  are  of  two  classes  :  bridge  spirals.    Fig.  210,   in  which  the 

upper  end  of  the  spiral  is  carried  over  the  lower  on  a  high  viaduct,  and 


fS 


68o  CH.  XX.— REDUCING  RA  TE  AND  COST  OF  HIGH  GRADES. 


m 


CH.  XX.— REDUCING  RATE  AND  COST  OF  HIGH  GRADES.  68l 


TUNNEL  SPIRALS,  Fig.  211,  in  which  the  lower  end  of  the  spiral  passes 
under  the  upper  end  with  a  tunnel.  Figs.  215-217  show  one  of  the  most 
•extensive  applications  of  the  principle  of  spiralling  (made  possible  only 
by  very  peculiar  topographical  conditions)  which  was  ever  attempted, 
but  a  better  line  was  afterwards  found.  In  the  typical  bridge  spiral  the 
line  swings  around  the  slopes  of  a  valley  or  basin,  and  in  the  typical 
tunnel  spiral  the  line  swings  around  the  slopes  of  a  central  hill.  The 
tunnel  spirals  of  the  St.  Gothard  line  (Figs.  202-206)  are  also  tunnel 
spirals,  in  a  sense,  but  of  a  third  class,  which  does  not  swing  around  any- 
thing. 

923.  The  bridge  spiral  on  the  descent  to  Tepic,  Figs.  207,  208,  illus- 
trates the  advantage  gained  by  them,  which  is  to  make  a  sudden  and 
great  drop  at  one  spot.  They  are,  when  well  laid  out,  not  costly  feat- 
ures, and  bridge  spirals  especially  facilitate  that  most  important  end  of 


sUi 


Half  MM 


Fig.  213. — Map  of  Spiral  on  Union  Pacific  Railway,  shown  in  Fig.  212. 

getting  down  into  the  bed  of  a  stream  as  soon  as  it  has  descended  so  far 
from  its  source  that  it  may  be  said  to  have  a  bed.  It  is  to  be  remem- 
bered in  laying  out  bridge  spirals  that  the  height  of  iron  viaducts  is  a 
nimor  factor  in  their  cost  (par.  102).  They  are  a  rare  feature  in  location, 
and  must  always  remain  so,  but  might  sometimes  be  used  to  advantage 
where  they  are  not.  Figs.  212-214  show  the  only  bridge  spiral  in  the 
United  States. 


ft 


i? 


'  Ml 


682  CH.  XX.— REDUCING  RATE  AND  COST  OF  HIGH  GRADES. 


ts) 

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i    i    I 


924.  4.  In  making  » 
descent  into  a  river  val- 
ley it  is  an  almost  invari- 
able   rule    to    DESCEND 
against  the   slope  of 
THE  VALLEY,  even  at  the 
cost  of  turning  a   half- 
circle  as  soon  as  the  bot- 
tom   is    reached.     The 
length   of  the    side-hill 
descent     is    much     de- 
creased.    It  is  still  bet- 
ter,  if  possible,  for  the 
same  reasons,  to  descend 
against  the  slope  of  some- 
tributary  valley,  turn  a 
half-circle,  and  then  de- 
scend in  its  bed  to  the 
main  valley.     Figs.  215- 
217   give   an   actual    in- 
stance on  a  large  scale. 

In    Fig.   215  a  descent 
was  to  be  made  from  E,  at 
an  elevation  above  sea  of 
about  3000  ft.  (910  m.),  to 
A,  into   the  valley  of  the 
Ameca  River,  at  an  eleva- 
tion of  1120  feet  (340  m.) 
above  sea,  a  drop  of  some 
1880  feet,  to  be  made  within 
an  air-line  distance  from  E 
to  A  of  only  5  miles.     The 
Ameca  River  lies  along  tht 
bottom  of  Fig.  215,  flowing 
to  the    left  with  a  sharp 
descent    of   over   one   per 
cent,  so  that   beneath   the 
spirals  EG,  shown  in  detail 
in  Figs.  216,  217.  the  bed 
of  the  river  was  only  1020 
feet  (310  m.)  above    sea. 
The   tributary  AB  had  a 


CH  XX.^REDUCING  RATE  AND  COST  OF  HIGH  GRADES.  683; 

still  sharper  descent  of  over  2  per  cent,  and  the  circumstances  of  the  locatioa 
made  it  clear  that  the  ruling  grade  on  the  descent  must  beat  least  2f  per  cent. 
The  location  shown  in  Fig.  216  is  3  per  cent  compensated,  about  2.6  per  cent 
actual. 

At  the  left  of  Fig.  215  was  another  tributary,  EG,  falling  far  too  fast  for  any 
line  to  follow  it  directly,  but  making  a  very  high  and  steep  backbone  or  knife- 
edge  at  EG  of  solid  basaltic  rock,  overlaid  for  the  most  part  with  a  thick  surface 
deposit  of  volcanic  tufa,  or  tepetate.      This  knife-edge   had  excessively  steep 
slopes  on  both  sides,  as  will  be  seen  from  Fig.  216,  extending  down  to  the  river- 
bed 1000  feet  below,  and  had  the  further  remarkable  peculiarity  that  the  sides- 
swelled    in    and   out,  making  it  very  thin    at   points    and  thicker   at   others. 
These   unusual    topographical    features    made    conveniently  possible  such  an 
unparalleled    series  of  spiral    developments  as   are    shown  in  Figs.  216,  217, 
which  took  very  kindly  to  the  natural  surface,  so  that  they  could  be  executed 
at  very  moderate  cost,  as  the  minutely  accurate  topography  of  Fig.  216  will 
show. 

925.  Under   these  circumstances  there  were  two  possibilities  for  the    de- 
scent from  E\o  A:  First,  the  line  EDCBA,  which  subsequently  proved  to  be 
by  far  the  best;  and,   secondly,   the   line  EEGHA.      Influenced  by  the  ease 
with  which   great    development    could   be    obtained  in  a  small   space   and  at 
small  cost  at  EG,   Fig.  215,    as  shown  in  detail  in  Figs.  216,   217,  the  latter 
line  was  examined  first;  the  only  useful  result  of  this  work  having  been  that 
it  is  possible  to  present  to  students  the  instructkre  study  in  location   shown 
in    Figs.  216,  217,  where  six   successive    spirals   are    shown  (the  lowest  one 
finally  abandoned),  accomplishing  a  descent  of  613  feet  (187  m.)  within  a  hori- 
zontal distance  of  about  1800  feet,  measuring  from  the  highest  to  the  lowest 
points  shown  on  the  map.     The  developed  distance  between  these  same  points 
was  4  45  miles  (7.18  kilos.).     Measuring  from  the  nearest  points  of  the  first 
and  fifth  spiral,  a  descent  of  426  feet  and  a  development  of  nearly  3^  miles 
was  obtained  between  points  only  5 58  feet  apart  horizontally.      The    lowest 
(abandoned)  spiral  gave  a  further  development  of  .855  mile  and  a  descent  of 
125  feet  within  a  horizontal  distance  of  263  feet.      A  striking  feature  of  the 
development  was  the  two-story  iron  viaduct  outlined  on  Fig.  216;  a  precipice 
over  200  feet  high  for  a  short  distance  at  one  point  enabling  the  line  to  pass 
twice  over  the  same  viaduct  at  elevations  100  feet  apart. 

The  value  of  such  a  feature  as  an  advertisement  and  attraction  to  trave. 
for  a  line  which  must  in  any  case  be  largely  dependent  on  tourist  travel,  was 
an  element  not  to  be  despised;  but  it  was  all  but  certain  that  the  true  loca- 
tion must  have  been  by  the  northerly  route,  as  was  found  to  be  the  case: 
for  (i)  the  stretch  ED  lay  along  the  natural  surface;  (2)  the  stretch  AB,  accom- 
plishing nearly  one  fourth  of  the  rise,  lay  in  the  bed  of  a  tributary  stream 
nsing  nearly  as  fast  as  the  desired  grade.  All  that  was  necessary  by  this 
route,  therefore,  was  to  find  ground  on  which  the  descent  from  D  to  B,  and  the 


II 


li 


I 
i  * 


684  CH.  XX.— REDUCING  RATE  AND  COST  OF  HIGH  GRADES. 


turn  at  B,  could  be  made.  In  other  words,  granting  that  a  turn  at  B  could 
be  made,  more  than  half  the  descent  could  be  made  on  very  easy  ground.  Ex- 
amination showed  favorable  points  at  B  and  C  for^the  turn,  and  a  very  favor- 
able location  was  obtained  for  the  entire  descent.  This  line  also  had  engi- 
neering and  scenic  features  of  great  interest;  chief  among  the  latter  being  a 
gigantic  natural  obelisk  of  stone,  produced  by  erosion,  572  feet  high,  and 
pierced  through  the  centre  of  its  base  by  a  tunnel  279  feet  long. 

926.  Besides  these  four,  which  may  be  called  normal  expedients,  there 
.are  the  following,  as  difficulties  multiply  : 

5.  Switchbacks:  the  proper  laying  out  of  which,  and  the  arguments 
in  favor  of  using  them  when  so  laid  out,  are  described  in  Appendix  C. 


Fig.  3x5. 

When  descents  of  over  1000  feet  are  to  be  grappled  with,  and  often  with 
less,  the  writer  believes  they  should  be  used  much  more  freely  than  they 
are.  if  laid  out  in  the  way  described,  so  that  the  stop  and  reversal  of  the 
direction  of  motion  involves  no  loss  of  time  or  power,  either  theoretically 
or  practically.  If  laid  out  in  the  ordinary  way  they  are  far  more  objec- 
tionable. Their  effect  to  reduce  the  cost  of  construction  is  very  great,  and 
there  is  no  necessary  loss  of  time  or  power  from  the  stop.  Figs.  212-214 
show  a  locality  where  well  laid  out  switchbacks  would  have  been  vastly 
more  economical,  and  have  given  better  results  in  other  ways. 


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Fig.  ai6.— Topographical  "Map  of  the  Spirals  at  thk  "Cuchillo"  (Knifb-edgk)  ok  Huavacan,  J-G,  Fig.  215, 
[Reduced  to  ,„'„,  (^^^4  ft.  per  Inch)  from  the  original  field-maps,  to  a  scale  of  io\re.] 


Fig.  ai7.— Section  of  the  Crest  or  the  "Cu- 
chillo" OK  Hlavacan,  pkujected  onto  a 
yEknCAL  Pla.ve,  showing  iHE  Spirals  in 
PosnioN. 

Kyurticai  Scale  exaggerated  only  three  times, 
so  ihai  ihe  pruulc  dot*  not  in  ilie  leasi  exagj^cr- 
aie  the  cffcci  upon  the  eye  of  the  slopes  mcm- 
selvcs.  1  he  siOc-slopcs  will  be  seen  10  be  much 
Sleeper  than  ihc  siopes  on  the  ciest  or  ridge.) 


60i 


Note  to  Figs.  216.  217.— The  base-lines  for  the  topography  (which  is  minutely  ac- 
curate) are  shown  by  dotted  lines  covering  the  hill.  The  whole  body  of  the  ridge  was 
basaltic  lava,  which  is  solid  underneath,  but  cracks  on  the  surface  in  cooling  into  loose 
blocks.  The  elevations  of  the  contour-lines  are  not  put  on  in  the  best  manner  They 
should  be  written  across  the  lines,  or  across  gaps  in  them.  The  degrees  of  the  curves 
are  for  metric  curves  of  20-metre  (65.6-ft.)  chords.  Thev  should  be  increased  about  one 
half  (53  per  cent)  to  be  correct  for  loo-ft.  chords.  The  facilities  which  a  judicious  sys- 
tem of  transition  curves  offers  for  conducting  location  is  apparent  from  Fig.  216.  The 
curves  are  all  projected  at  an  offset  for  introducing  transition  curves,  making  no  effort 
to  obtain  any  particular  offset,  and  any  curve  or  tangent  on  the  map  can  be  shifted,  re- 
gardless of  the  rest  of  the  line. 

The  grade-contour  is  shown  throughout  the  map,  from  which  it  can  be  seen  at  once 
that  minor  improvements  are  possible  at  a  number  of  points.  Including  the  lower 
spiral,  shown  by  dotted  lines.  4.45  miles  of  development  and  613  ft.  of  elevation  were 
here  gained,  practically  at  a  single  point,  without  anv  loss  of  distance  whatever  The 
localities  are  few  on  the  face  of  the  globe  where  such  a  result  would  be  so  conveniently 
possible.  In  this  case  it  was  probably  cheaper  than  a  system  of  switchbacks  such  as 
suggested  in  Appendix  C 

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CH.  XX.-REDUCING  RA  TE  AND  COST  OF  HIGH  GRADES.  685 

T  •  ^^l'  ^^^  ^°"°^'"g  F-igs.  218  to  221  are  examples  of  switchbacks  from  the 
Lima  &  Oroya  Railway  in  Peru.  They  give  an  idea  of  the  advantage  which 
they  give  for  location,  uvauiagc  wnxcn 

but    they    were     not  ^/\C 

properly    laid    out    to  00    ^  ^ 

reduce  the   disadvan- 
tage  of  a  stop   10   a 
minimum.      Fig.    218 
shows  a  rather  unusu- 
al    and     unfavorable 
method  of  laying  them 
out,    the    switchbacks 
being  usually  in  pairs, 
as   in    Figs.    219-221, 
and  as  near  together 
as   possible,  so  as  to 
reduce  the  distance  on  which  the  train  runs  backward  to  a  minimum.     From  A 
to  B  IS  3i  miles  by  the  line.     In  an  air-line  they  are  855  feet  apart  horizontally, 
and  545  feet  apart  vertically. 

From  I  to  2,  Fig.  219,  is  5  miles  by  the  line  and  i^- 
miles  in  an  air-line.  The  horizontal  distance  between- 
A  and  £  is  985  feet,  vertical  distance  625  feet.  The 
horizontal  distance  between  E  and  F  is  465  feet,  vertical 
distance  535  feet,  showing  an  average  slope  steeper  than 

I  to  I.  Many  such  places 
were  entirely  inaccessible  to 
bipeds,  and  the  line  was  only 
located  by  making  as  careful  • 
topographical  maps  as  possi- 
^pA^  ble,  projecting  a  location,  and 

ff'^  triangulating  in  points  on  it 

for  beginning  construction. 
At  the  "Infiernillos,"or  "Little  Hells,"  Fig. 
220,  the  river  passes  for  some  distance,  with  a 
succession  of  falls,  between  two  walls  of  rock  that 
rise  perpendicularly  to  a  height  of  2000  to  250c 
feet.  In  passing  under  these  high  points  the  line 
leaves  one  tunnel,  crosses  the  river  on  a  bridge 
of  160  feet  span  at  a  height  of  165  feet  above  the 
water,  and  enters  another  tunnel. 

From    I  to  2,   Fig.  220,  by  line  of  road  is  4f 

miles,  comprising  eight  tunnels.    An  air-line  from 

The  horizontal   distance  from  A  to  B  is  445  feet,  vertical 


Fig.  2x9. 


'  to  2  is  If  miles, 
distance  310  feet. 


6S6  CH.  XX.— REDUCING  KA  TE  AND  COST  OF  HIGH  GRADES. 


Fig    221   shows    another   very    peculiar    development— a    combination    of 
switchbacks  and   horseshoes.     From  ^  to  ^  by  line  of  road  is  4-9  miles,  by 

air-line  1.6  miles.  This  portion  of  the 
line  has  1776°  of  curvature— an  aver- 
age of  362°  to  the  mile.  From  C  \.o  D 
the  horizontal  distance  is  730  feet,  ver- 
tical distance  570  feet.  The  profile  in 
this  vicinity  was  not  inappropriately 
known  as  "  Gothic." 

These  maps  taken  together  will  in- 
dicate, what  is  the  fact,  that  even  in 
the  roughest  country  there  are  certain 
locations  where  zigzag  developments 
are  more  economical  than  switchbacks, 
and  others  where  switchbacks  alone 
are  practicable,  without  the  heroic  ex- 
pedient of  spiral  tunnels. 

928.  6.  Inclined  Planes  and 
Cable  Traction.— This  device,  in 
a  crude  form,  antedates  the  loco- 
motive itself,  and  was  at  first  the 
almost  universal  resort  for  dealing 
with  what  were  then  considered 
high  grades.  It  is  still  used  to  some 
extent,  but  early  passed  out  of  gen- 
eral use  as  an  accredited  auxiliary 
to  railway  transportation.  We  may 
admit  that  this  at  the  time  was  wise 
and  right,  and  still  regard  the  device  as  one  deserving  of  a  recognized 
standing  at  the  present  day.    In  all  probability,  within  a  few  years,  it  will 

be  much  more  used 
than  it  is  now  for 
moving  large  traffic 
over     high     eleva- 

_  . ,. .  tions. 

A'  *^^^^  "^   ^^  "^"^  "**^        929.   The   argu- 

ments against  the 
use  of  planes  are 
these : 

I.  It  introduces  a  break  in  the  continuity  of  the  movement  of  traffic— 
an  argument  of  minor  importance  which  must  always  exist  in  some  degree. 


aao. 


CH.  XX.— REDUCING  RA  TE  AND  COST  OF  HIGH  GRADES.  68/ 

2.  The  power  and  working  force  necessary  to  operate  the  planes  must 
always  be  on  hand  and  available,  at  nearly  the  same  cost  whether  work- 
ing or  idle,  and  possibly  a  good  part  of  the  time  idle. 

This  was  a  very  serious  matter  in  early  days  when  traffic  was  light, 
but  it  grows  less  so  as  the  movement  of  traffic  becomes  so  great  as  to 
approximate  to  a  steady  stream  of  cars — a  condition  which  exists  on 
many  lines  now  operating  steep  grades  with  locomotive  power.  It  was  a, 
leading  factor  in  causing  the  abandonment  of  planes  in  the  early  days  of^ 
railways  ;  hardly  subordinate  to  the  following,  which  was  perhaps  alone 
decisive : 

3.  Formerly,  planes  operated  by  stationary  power  were  necessarily 
short,  straight,  and  on  a  uniform  gradient.  This  made  it  essential  topo- 
graphically, even  if  it  had  not  been  mechanically,  that  the  planes  should 
not  be  long,  but  that  a  number  of  them,  separated  by  intervening  stretches 
of  "  level,"  should  be  used,  greatly  increasing  the  awkwardness,  delay, 
and  expense  of  the  process. 

4.  A  certain  element  of  danger  from  runaways  and  breakages  existed 
and  still  exists,  which  was,  however,  not  a  serious  nor  governing  consid- 
eration, even  when  the  only  cable  was  a  hemp  rope,  as  in  the  early  planes 
at  the  Alleghany  Portage  on  the  Pennsylvania  State  canal  and  railway 
svstem,  and  it  is  still  less  so  now. 

930.  On  the  other  hand,  besides  the  advantage  of  the  vast  increase  of 
traffic  which  would  enable  stationary  power  to  be  constantly  employed  at 
many  points,  the  perfection  to  which  the  cable  system  has  been  brought 
in  recent  years  has  greatly  changed  the  conditions  of  the  problem,  and 
favored  the  use  of  well-designed  inclined  planes  in  connection  with 
railways.  Passing  the  question  of  how  they  should  be  designed  for  the 
moment,  the  arguments  favoring  the  use  of  inclined  planes  of  whatever 
type  are  these : 

1.  The  great  expense  is  saved  of  lifting  the  ponderous  motor  itself 
up  and  down  hill.  Assuming  every  engine  to  be  fully  loaded,  and  assum- 
ing a  light  Consolidation  engine  with  tender  and  caboose  to  weigh  80 
tons,  we  may  deduce  from  Table  170  the  following  Table  189,  showing 
the  proportion  of  the  total  power  exerted  which  is  thrown  away  in  non- 
productive work  on  the  motor. 

2.  The  power  is  not  only  wasted  in  the  proportion  shown  in  Table 
J 89,  but  is  more  costly  per  horse-power  for  several  reasons : 

{a)  The  fuel  burned  per  horse-power  is  much  greater  than  in  a  good 
and  powerful  stationary  engine  (Table  168,  page  531). 

(^)  As  one  stationary  engine  does  the  work  of  from  five  to  thirty 


MM 


I 


688  en.  XX.— REDUCING  RATE  AXD  COST  OF  HIGH  GRADES. 


locomotives,  there  is  a  corresponding  saving  in  maintenance  of  machinery 
and  in  wages  of  engine-  and  train-men. 

Table  189. 

Proportion  of  the  Dead  or  Waste  Weight  (of  Engine,  Tender,  and 
Caboose)  to  the  Total  Paying  Weight  (of  Cars  and  Freight)  on 
Various  Grades. 

[An  addition  of  $  tons  has  been  made  to  the  weight  of  an  average  Consolidation  in 
Table  170,  cis  better  corresponding  to  the  more  recent  practice  (Table  129),  and  a  corre- 
sponding subtraction  of  5  tons  from  the  load  given.  In  addition,  a  deduction  of  20  per 
cent  has  been  made  from  the  load  given,  as  an  allowance  for  the  lighter  winter  loads,  the 
scant  loading  of  many  trains,  and  light  trains  in  one  direction.  As  an  average,  this  allow- 
ance should  be  larger.] 


Weight  in  Tons. 

Per  Cent 
Weight  Engine 

Grade 

Per  Cent. 

Engine, 

Train 

Do.  Average 

to  Average 

Tender,  and 

by 

of 

Paying  Weight. 

Caboose. 

Table  170. 

All  Trains. 

I.O 

80 

706 

565 

14. 1 

1-5 

499 

399 

20.0 

2.0 

378 

302 

26.5 

2.5 

299 

239 

33-4 

30 

244 

195 

41.0 

3-5 

202 

162 

49.4 

4.0 

170 

136 

58.8 

50 

124 

99 

80.8 

6.0 

92 

74 

1350 

{c)  The  wear  and  tear  of  track  due  to  the  locomotive  is  saved,  which 
is  about  half  of  the  whole  cost  of  running  them  (par.  780).  Against 
this  is  to  be  balanced  the  loss  of  power  by  the  friction  of  the  rope  or 
cable,  but  this  is  comparatively  a  small  percentage  on  a  grade  plane, 
although  a  very  large  percentage  on  level  cable  railways.  The  cable 
friction  being  constant  per  mile  decreases  in  relative  importance  as  the 
grade  is  higher. 

{d)  The  modem  cable  system  possesses  several  advantages,  as  notably 
that  of  being  used  on  curves,  which  none  of  the  older  and  simpler  forms 
of  inclined  planes  possessed. 

3.  Apart  from  the  cost  of  the  mechanism  for  operating  the  planes 
(which  may  be  balanced  roughly  against  the  cost  of  locomotives),  the  use 
of  inclined  planes  will  ordinarily  cheapen  the  cost  of  construction  ma- 
terially, although  this  may  not  be  invariably  the  case. 


CH.  XX.— REDUCING  RA  TE  AND  COST  OF  HIGH  GRADES  689 

931i  If  we  conceive  the  normal  type  of  a  passage  over  a  summit  to  be  that 
shown  in  Fig.  222,  the  manner  of  adapting  the  %ame  summit  to  the  use  of  in- 
clined planes  may  be  that  of  either  Fig.  223  or  Fig.  224.  In  Fig.  223  the  cars 
are  hauled  directly  up  an  inclined  plane  (or,  q 

if  necessary,  up  two  or  more)  at  A  and  B  to 
some  point  a  and  h  which  is  high  enough  for 
the  cars  to  descend    thence  over  the  entire       .        ^  ^  p 

distance  aCB  or  bCA,  presumably  in   short      "     '  

trains  in  charge  of  one  or  more  brakesmen.  Fig.  222. 

The  power  stored  in  the  cars  is  thus  not  lost,  by  having  to  be  shortly  after 

destroyed  by  the  brakes,  but  in  great  degree  utilized  for  propulsion. 

932i  This  economy  of  power  may,  under  favorable  circumstances,  be  carried 
still  further  by  the  construction  of  the  auxiliary  lines  r^/and  ce.  Fig.  224,  so  as 
to  extend  the  plan  in  Fig.  223  to  that  shown  in  Fig.  224.  By  these  auxiliary 
lines,  after   the   cars   have  as-  — >.  .^       .^— - 

cended  the  planes  A  and  B  \o  a  [  ~^^yn^^  \ 

or  b,  they  run  by  gravity  to  the  fj  y^    '     \^,^     1* 

points  e  or  d,  where   they  de-  /        y^  ^^^Aj^ 

scend  the  plane,  thus  assisting 5J —  ^ 

by  their  gravity  to  pull  other  Fig.  223. 
cars  up  it,  and  making  the  only  motive-power  required  (in  excess  of  cable-friction) 
— that  necessary  to  lift  the  cars  through  the  distance  da  or  eb,  which  Is  necessary 
to  enable  them  to  run  by  gravity  to  the  opposite  plane.  If  the  distance  ab  were 
great  enough  to  make  it  desirable,  a  nearly  level  track  might  be  laid,  and  loco- 
motive-power used,  but  this  involves  the  disadvantage  that  the  location  is  more 
difficult  and  costly,  because  the  gradients  have  to  be  considered  in  both  direc- 
tions, whereas  the  duplicate  gravity  tracks  may  be  laid  out  on  different  routes, 
each  of  which  need  be  favora- 
ble to  motion  in  one  direction                   ^ q^  h 

933.  Theoretically,  the  sys- 
tem sketched  in  Fig.  224  com-  |     ^  ^^^B 

pletely  eliminates   the   disad- -  „ 

,    ,        ,  Fig.  224. 

vantage  of  the  elevation  sur- 
mounted, however  high,  leaving  the  only  loss  of  power  that  which  would  result 
if  the  track  were  vertically  projected  onto  the  plane  AB.  Practically,  it  will 
of  course  fall  far  short  of  this,  but  may  be  made  to  give  some  approach  to  it,  and 
with  the  privilege  of  introducing  a  few  easy  breaks  of  line  and  grade  on  the 
plane,  which  is  practicable  by  the  cable  system,  no  great  difficulty  is  likely  to 
arise  in  laying  out  long  planes  advantageously. 

934.  The  modern  cable  system  has  not  yet  been  used  to  any  consid- 
erable extent  as  an  auxiliary  to  ordinary  railway  traffic,  although  it  is 
tending  in  that  direction.     It  originated  at  the  city  of  San  Francisco, 
44 


690  CH.  XX.— REDUCING  RATE  AND  COST  OF  HIGH  GRADES. 


from  the  necessity  of  supplying  street-railway  transportation  on  high 
grades.  In  its  essence  it  consists  in  using  a  continuously  moving  and 
endless  wire  cable  to  which  the  cars  are  attached  by  friction-grips,  instead 
of  winding  up  on  a  large  drum  a  rope,  chain,  or  flat  band  of  metal  of  the 
length  of  the  incline,  requiring  that  the  engines  should  start  and  stop 
again  after  taking  up  each  load.  The  modern  system  has  been  brought 
to  great  perfection  for  street  use,  and  has  spread  very  rapidly  in  spite  of 
the  difficulty  and  expense  involved  in  covering  up  the  cable  below  the 
street  level.  It  has  been  described  with  remarkable  fulness,  in  all  its 
details  of  construction  and  working,  in  various  papers  before  engineering 
societies  and  in  the  leading  technical  journals. 

935,  Circumstances  favoring  the  use  of  this  particular  form  for  rail- 
way traffic  are  :  (i)  The  cable  would  not  need  to  be  covered  up  and 
gripped  at  some  disadvantage  through  a  narrow  slit;  (2)  being  primarily  re- 
quired for  vertical  and  not  for  horizontal  transportation,  the  incline  could 
be  made  steep  at  the  expense  of  length  and  speed,  reducing  the  chief 
source  of  loss  in  street  service,  friction  and  wear  of  cables ;  (3)  the  grips 
having  to  be  applied  only  at  the  bottom  of  the  plane,  and  released  only 
at  the  top,  could  be  made  very  powerful  by  duplicating  them,  or  other- 
wise ;  the  grades  at  the  bottom  of  the  plane  could  be  made  favorable  for 
getting  the  cars  quickly  under  way,  and  with  speeds  of  not  exceeding 
three  or  four  miles  per  hour,  which  would  be  quite  fast  enough  for 
economy,  the  grips  could  be  applied  and  released  by  men  jumping  onto 
the  grip-car  for  that  purpose,  so  that  there  would  be  no  necessity  for  any 
one  riding  up  or  down  the  plane  with  the  cars. 

The  system  is  certainly  one  of  much  promise  for  such  localities  and 
qonditions.  and  the.  necessity  of  the  utmost  economy  in  transportation 
warrants  its  careful  study,  and  will  probably  bring  about  its  gradual 
adoption,  with  details  adapted  to  the  peculiar  requirements. 

936.  A  final  expedient  for  reducing  the  disadvantages  of  gradients  is 
the  RACK  RAILWAY,  the  most  perfect  form  of  which,  and  the  only  one 
promising  general  usefulness,  is  the  Abt  system. 

The  Mt.  Washington  Railway,  in  New  Hampshire,  designed  by  Silves- 
ter Marsh,  was  the  first  example  of  a  rack  railway.*  The  device  con- 
sists, as  its  name  implies,  in  a  pinion  operated  by  a  separate  cylinder  on 
the  locomotive,  which  engages  in  a  fixed  rack  laid  between  the  rails.     It 

*  The  Rhigi  Railway,  M,  Richenbach,  engineer,  was  an  almost  exact  copy  of 
every  essential  detail  of  the  Mt.  Washington  line,  but  in  a  not  particularly  cred- 
itable way  was  labelled  the  "  Syst^me  Richenbach,"  and  is  so  known  through- 
out Europe. 


CH.  XX.— DUPLICATE  TRACKS  FOR  PUSHER  GRADES.     69I 


thus  eliminates  what  we  have  seen  to  be  the  most  serious  theoretical 
defect  of  the  locomotive— that  its  tractive  power  cannot  be  increased  in- 
definitely at  the  expense  of  speed,  but  only  within  narrow  limits.  In  its 
original  form  it  had  many  defects  which  the  Abt  system  eliminates,  but 
its  practical  utility  as  an  adjunct  to  the  normal  operation  of  railways  has 
not  yet  been  fully  demonstrated,  and  must  for  the  present  (1886)  be  re- 
garded as  somewhat  doubtful. 

937.  The  salient  features  of  the  Abt  system  are  these :  The  ingenious  en- 
gaging rack  by  which  a  locomotive  may  approach  the  foot  of  a  rack  grade  at 
some  considerable  speed,  with  certainty  that  the  pinion  will  engage  quickly 
and  without  shock  with  the  rack  ;  the  improved  manner  of  constructing  the  rack 
of  parallel  bars  with  the  teeth  staggered  ;  the  pinion  or  driving-wheel,  which  is 
constructed  in  sections,  each  capable  of  a  slight  spring,  so  as  to  ensure  perfect 
and  smooth  contact  with  the  rack  ;the  use  of  the  ordinary  adhesion  cylinders 
continuously  to  lend  what  aid  they  can. 

On  the  other  hand,  there  is  the  complication  of  the  machine,  and  the  diffi- 
culty of  keeping  the  rack  in  working  order,  especially  in  the  winter  in  cold  cli- 
mates.* 

938.  A  device  for  accomplishing  the  same  end  as  the  rack  railway  in  a  dif- 
ferent way,  which  has  not  proved  equally  meritorious  in  practice,  is  the  fric- 
TION-GRIP  RAILWAY.  In  this  device  two  friction  driving-wheels  engage  with  a 
central  rail,  being  pressed  against  it  with  any  desired  force,  regardless  of  the 
weight  on  the  engine  itself.  While  the  device  has  been  used  successfully  in 
several  special  locations,  it  possesses  no  features  to  make  it  of  general  utility. 
It  is  generally  known  as  the  Fell  System,  and  was  used  at  the  Mt.  Cenis  Rail- 
way. 

DUPLICATE  TRACKS  FOR  PUSHER  GRADES. 

939.  In  the  main,  all  climbing  done  by  train^  on  pusher  or  high 
grades  is  so  much  clear  loss.  The  power  thus  stored  in  the  train  by 
lifting  it  up  not  only  does  no  good,  but  costs  more  money  to  destroy  by 
means  of  brakes.     It 

is  a  peculiar  advan- 
tage of  the  use  of 
pushers  that  this  need 
not  be  invariably  nor  A^ 
necessarily  the  case, 
for  under  certain  fa- 
voring circumstances 
It  is  possible  to  utilize  a  portion  of  the  work  thus  wasted  by  securing 


Fig.  225.— Typical  Profile  of  a  Gravity  Railway. 


*  The  Abt  system  is  more  fully  described  in  a  paper  by  W.  W.  Evans,  Trans. 
Am.  Soc.  C.  E.,  March,  1886. 


I 


%fe,. 


1 


692  CHAP.  XX.— DUPLICATE   TRACKS  FOR  PUSHER  GRADES, 


from  it  something  of  the  advantages  of  a  gravity  railway,  a  typical 
profile  of  which  is  shown  in  Fig.  225. 

The  gravity  railway  does  of  set  purpose  and  to  secure  an  advantage 
what  the  ordinary  railway  only  does  of  necessity  as  an  unmitigated  dis- 
advantage;  viz.,  it  seeks  out  certain  high  elevations,  and  ascends  to  them 
as  quickly  and  by  as  steep  a  grade  as  possible. 

This  it  does  for  precisely  the  same  reason  that  coal  is  put  on  the 
tender,  viz.,  to  store  power  in  the  train  ;  only,  in  this  case,  the 
power  is  ready  for  instant  application  without  change  of  form.  It  is 
utilized  for  propulsion  instead  of  being  thrown  away  in  wearing  out 
wheets  and  brake-shoes,  by  laying  out  from  the  high  elevation,  to  which 
the  train  is  lifted  by  a  plane,  a  continuous  descending  gradient,  on  a  0.7 
to  i.o  per  cent  grade,  until  the  lowest  possible  point  is  reached.  The 
train  is  then  hauled  up  to  another  high  elevation,  and  the  same  process 
continued,  giving  a  profile  like  Fig.  225.  The  ascent  is  made  by  sta- 
tionary power;  but  that  does  not  affect  the  principle,  which  is,  ^hat,  as  high 
elevations  must  at  points  be  surmounted,  it  is  better  to  do  so  by  a  sys- 
tem which  utilizes  the  work  thus  done  for  propulsion  instead  of  wasting 
it  destructively. 

940.  There  is  one  serious  drawback  to  this  system,  that  cars  can  pass 
over  the  line  in  only  one  direction,  so  that  it  necessitates  an  entirely  in- 
dependent return  track,  however  light  the  traffic.  Nevertheless,  it  has 
been  and  is  still  used  to  some  extent.  It  originated  (in  this  country)  at 
Mauch  Chunk,  before  the  locomotive  had  fairly  been  invented,  and  was 
afterward  embodied  in  two  prominent  lines  in  Pennsylvania,  and  in  a 
number  of  smaller  ones.  One  of  these  lines  has  recently  been  abandoned  ; 
but  for  reasons  largely  independent  of  the  engineering  merit  of  the  sys- 
tem ;  the  other  is  still  in  operation. 

These  two  lines  are: 

Pennsylvania  Coal  Co.—\l  miles  double  track;  4  ft.  3  in.  gauge;  36-lb.  rails; 
23  stationary-engine  houses  and  as  many  planes,  or  about  one  for  every  four 
miles.  Average  speed  of  passenger  trains,  15  miles  per  hour;  freight  trains,  10 
miles  per  hour. 

Delaware  b*  Hudson  Canal  Co.— 2,2  miles  of  double  track;  4  ft.  3  in.  gauge; 
45  to  56  lb.  rails;  30  stationary  engines  and  as  many  planes,  or  about  one  every 
two  miles. 

The  advantage  of  the  plan  is  that  it  puts  the  undulations  of  the  sur- 
face which  cannot  be  avoided  into  the  harness,  as  it  were,  by  making  them 
a  necessary  part  of  the  system  of  operation.  Moreover,  motion  in  only 
one  direction  has  to  be  considered,  so  that,  so  long  as  the  train  keeps  de- 


CHAP.  XX.-DUPLICATE  TRACKS  FOR  PUSHER  GRADES.  693 

scending,  we  are  in  a  measure  independent  of  the  rate  of  grade,  and  econ- 
omy of  construction  is  promoted. 

To  balance  the  disadvantage  of  having  to  construct  two  independent 
tracks  there  is  a  certain  economic  advantage  in  a  double  track  even 
when  traffic  is  light. 

941.  The  extra  cost  of  having  to  construct  two  independent  lines  has 
undoubtedly  been  in   years  past   a   leading  factor  in  impeding  a  more 
general  use  of  this  plan,  until  now  engineering  practice  seems  to  condemn 
It,  but  that  under  certain  exceptional  circumstances  it  might  still  be  ad- 
vantageously used,  hardly  admits  of  doubt.     The  merits  or  demerits  of 
the  gravity  system  in  its  entirety  depend  chiefly,  it  is  plain,  on  whether 
or  not  inclined  planes   operated  by  stationary  power  are  economical  as 
compared  with  the  locomotive.     But  whether  or  not  the  plan  as  a  whole 
be  advantageous,  it  is  plain  that,  if  we  have  lifted  a  train  by  any  kind  of 
power  to  a  high  elevation,  that  feature  of  the  gravity  plan  is  economical 
which  utilizes  the  work  thus  done  instead  of  throwing  it  away,  and  this 
may  often  be  done  with  pusher  grades,  provided  the  traffic  be  sufficient 
to  make  certam  short  sections  of  double  track  in  the  immediate  vicinity 
of  the  pusher  grades  a  desirable  feature;  which  is  veiy  apt  to  be  the  case 
since  the  mere  existence  of  those  grades  practically  doubles  the  demand 
upon  the  track.  • 

942.  Thus,  supposing  a  summit  is  to  be  passed  over  from  one  valley 
to  another  or  a  plateau  of  some  width  to  be  ascended  to  and  descended 
irom.     Ordinarily   the    pro- 
file over  such  a  section  would  •-•-"^ 

be  something  lilce  the  solid  '       '^ 

line  in  Fig.  226,  there  being 
certain  natural  difficulties  in 

getting  favorable   grades    in /^  \  £ 

more  than  one  direction  be- 
tween B  and  D  so  that  the  whole  stretch  AE  is  practically  a  single 
pusher  run.  If  in  such  case,  the  grade  ^5  can  be  prolonged  to  some 
Mgher  po.nt  and  from  thence  carried  on  a  favorable  grade  for  trains  go- 
mgto  £•  to  a  junction  at  some  point  A  the  expense  of  running  pusher 
engmes  both  ways  over  the  distance  BD  will  be  saved,  at  the  expense  of 
constructmg  the  short  section  of  duplicate  track  BFCD. 

943.  Again,  let  ussuppose  a  common  case,  that  we  are  carryingaline 
1  rough  a  valley,  a  part  or  all  of  which  has  an  irregular  descend  so  that 

vallevrh  '  T"       k"^  "'^  '^  """"  '"'  '^^'"^  ™""'"8  down  the 
valley  such  as  Fig.  227.  but  favorable  grades  for  ascending  it  can  only  be 


'1 


1. 


i 


694  C//AF.  XX.— DUPLICATE   TRACKS  FOR  PUSHER  GRADES. 

had  with  some  difficulty  and  expense.  In  some  cases — not  by  any  means 
in  all  cases — it  would  be  possible  for  a  return  track  to  make  at  once  for 
some  high  point  C  on  a  ridge  or  crest,  and  thence  to  make  for  the  point 
A  with  level  or  descending  or  but  slightly  ascending  grades,  by  a  ridge 
line  or  a  different  valley  line  which  would  be  for  the  most  part  lights 


CHAP.  XX.^DUPLICATE  TRACKS  FOR  PUSHER  GRADES  695 


Not  only  is  lighter  construction  per  mile  of  track  almost  certainly  attain- 
able, when  this  is  possible  at  all,  but  economy  of  operation  is  much  pro- 
moted, because,  instead  of  having  to  run  short  trains  both  ways  between 
A  and  B,  because  of  the  opposing  grades  aa,  our  motive-power  is  only 
taxed  appreciably  on  the  pusher  grade  BC,  throughout  the  round 
trip. 

Nevertheless,  if  there  be  not  traffic  enough  to  require  or  justify  twa 
tracks  any  attempt  of  this  kind  would  probably  be  uneconomical. 

944i  But  after  all,  a  plain  continuous  descent  from  a  summit  to  the 
plain  below  will  ever  remain  the  normal  type  for  location,  such  devices  as 
spirals,  switchbacks,  and  others  being  the  exception.  In  all  but  the 
most  rugged  country,  say  wherever  most  of  the  surface  to  be  built  over  is 
not  bare  rock,  good  and  cheap  lines  can  usually  be  obtained  by  following 
these  two  rules  : 

First.  Do  not  attempt  to  secure  too  low  a  grade-line  by  more  than 
a  moderate  amount  of  development,  remembering  that  on  pusher  planes 
the  RATE  of  grade  is  comparatively  unimportant  (par.  747  and  Table  181). 

Secondly.  Do  not  adopt  a  limit  of  curvature  too  easy  for  the  topog- 
raphy, unless  the  importance  of  the  line  and  its  probable  revenue  will 
certainly  warrant  it.     (See,  however,  par.  883). 

945.  The  railway  system  of  Colorado  is  a  splendid  example  of  what 
may  be  accomplished  by  the  application  of  these  two  rules.  The  fact 
that  it  was  laid'to  narrow  gauge  probably  gave  courage  for  adopting  such 
alignment,  but  it  was  not  at  all  necessary  for  its  success,  as  we  have  else- 
where s^n  sufficient  grounds  to  believe  (in  Chaps.  VIII.  and  XXIII). 
In  fact,  it  is  only  a  question  of  time  when  these  lines  will  be  relaid  to- 
standard  gauge  without  any  essential  change  in  their  alignment. 


4 


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i 


696  CJ/AP.  XX.— DUPLICATE  TRACKS  FOR  PUSHER  GRADES. 

There  is  probably  no  system  of  roads  in  the  world  which  are  so  well 
Worthy  of  the  study  of  engineers,  because  of  the  marvellous  cheapness 
with  which  it  has  been  carried  through  the  most  forbidding  regions,  and 
certainly  as  good  an  illustration  as  any  of  what  has  been  done  in  this 
way  is  the  "  High  Line  to  Leadville,"  on  the  Denver,  South  Park  &  Pacific 


-dRnwIioH  oioM  &• 


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Fig.  230. — Profilk  of  the  Last  62  Miles  of  the  '"  High  Line  to  Leadville." 

[Grades  indicated  in  feet  per  mile.     The  heavy  black  line  indicates  the  section  shown  in   Fig. 
229,  a  view  from  the  lower  end  of  which  is  shown  in  Fig.  228.] 


Railway,  now  a  part  of  the  Union  Pacific  system.  The  total  cost  of  this 
line  was,  as  nearly  as  may  be,  §20,000  cash  per  mile,  and  this  was  like- 
wise very  close  to  the  cost  of  the  short  section  shown  in  the  large  map 
in  Fig^229,  one  of  the  most  interesting  views  on  which  is  shown  in 
Fig.  228. 

For  this  sum  the  line  was  carried  over  three  summits  over  11,000  ft. 


.ML^'i&ij^. 


w 


Fig.  229. Location  Map  of  the  Descent  from  Bokhas  Summit  to  DnECKENP.iDCF,  Col. 

(The  View  in  Fig.  227  is  taken  irom  the  right  angle  in  the  line  nearly  south  of  "  Illinoir.  Park.'") 


Inset  to  face  fig.  230,  p.  696 


t 


CHAP.  XX.— DUPLICATE  TRACKS  FOR  PUSHER  GRADES  697 

high,  two  of  which  are  shown  in  Fig.  230,  and  for  a  large  part  of  the  re- 
mainder of  the   distance  was  carried  through  the  narrow  and  tortuous 
channel  of  the  Platte  Gall- 
on, where  long  stretches 
of  the  work  are  in  solid 
rock,  and  where  fills  were 
impossible,  it  being  neces- 
sary to   support  the   line 
on    retaining- walls    when 
not  in   the  solid.     These 
retaining-walls  are  among 
the  most    interesting  en- 
gineering  features  of  Col- 
orado.     They     are     dry 
and  very  cheap,  but  very 
solid,  and  give  no  trouble. 
They  were  generally   the    ^ 
first    work     started,    and 
were  carried  along  as  far 
as    possible     before     the 
rock  excavation  was  be- 
gun. 

946.  The  probabilities 
are  that  in  the  hands  of 
engineers  not  driven  to 
economy  by  necessity,  and 
constructing  by  what  have 
been  regarded  as  ortho- 
dox standards,  these  works 
would  have  cost  four  or 
five  times  what  they  actu- 
ally have,  while  many  of 
them  would  have  been 
wholly  impossible  at  any 
<:ost.  In  Fig.  229  we  have 
clearly  before  us  the  chief 
cause  of  their  economy — 

the  comparatively  free  use   [The  section  of  line  shown  by  profile  in  Fig;.  23ois  indicated 
of  very  sharp  curves.      On  ^"^  ^^^  heaviest  line  above!] 

the  1 1.2  miles  shown  in  Fig.  229  there  are  in  all  127  curves,  or  11.3  curves 
per  mile,  divided  as  to  degrees  as  follows : 


Fig.  231.— Map  of  the  "  High   Line  "  from  Denver  to 

Lbadville. 


\      •1 


m 


I 


l|: 


fH 


698  CHAP,  XX,— DUPLICATE   TRACKS  FOR  PUSHER  GRADES. 


o 
6 

3 
6 


5  . 
6°. 

8°. 


,  I 

13 


Total 40 


10" 
11° 

12° 

13' 

14°. 

15°. 

16°. 


I 

,14 
,  2 

4 
I 

3 
4 
4 


Total 33 


17° 

18° 

19° 
20° 

21° 

22° 

23» 

24° 
25i' 


.  I 
.  a 
.  I 

.25 
.  I 

.  I 

.  o 

.24 

.  I 


Total 54 


Strike  out  all  curves  sharper  than  10°  (573  ft.  radius)  from  this  list^ 
and  we  multiply  the  cost  by  at  least  four  or  five  at  once ;  besides  which^ 
this  particular  line  becomes  wholly  impossible,  since  the  turn  could  not 
have  been  made  around  "  Nigger  Hill  "  nor  in  "  Illinois  Park"  in  the 
centre  of  the  view.  A  far  steeper  grade  or  an  entirely  different  route 
would  therefore  have  had  to  be  chosen.  It  should  also  be  noted  that  one 
rides  over  these  curves  without  the  slightest  sense  of  insecurity  or 
danger,  nor  have  they  proved  to  be  especially  dangerous  in  operation. 
The  motion  around  them  is  as  smooth  as  around  any  of  the  easier 
curves. 

The  writer  has  no  definite  knowledge  as  to  whether  the  general  route 
which  gave  so  very  bad  a  profile  as  this  line  has  was  really  the  best  one^ 
and  must  be  understood  to  speak  only  of  the  details  of  the  location. 

947.  Fig.  232  shows  comparatively,  on  the  same  sheet,  a  number  of 
the  great  inclines  of  the  world,*  and  Table  190,  with  its  long  foot-note, 
adds  details  of  many  others,  the  whole  not  making  a  complete  list  by  any 
means. 


*  Only  the  lines  shown  in  comparatively  heavy  lines  on  this  plate,  viz.: 
The  Jalapa  line  from  Vera  Cruz,  the  Denver  &  Rio  Grande,  the  Pennsylvania, 
and  the  Baltimore  &  Ohio  are  of  the  writer's  compiling.  The  remainder  has 
been  reproduced  from  a  plate  prepared  by  Mr.  W.  W.  Evans,  M.  Am.  Soc.  C. 
E.,  to  show  the  Peruvian  lines,  and  he  in  turn  was  indebted  to  European  au- 
thorities for  the  admirable  presentation  of  European  railways.  Comparative 
distances  are  of  course  to  be  estimated  by  the  horizontal  distance,  since  the  ex- 
aggerated vertical  scale  exaggerates  the  slant  length  greatly. 

A  small  profile  of  the  Mexican  Railway  is  shown  on  the  map  in  Appendix  C. 
It  could  not  conveniently  be  added  to  this  plate  for  comparison  with  the  Jalapa 
line.  Its  general  nature  will  be  indicated  by  projecting  a  4  per  cent  grade  (par- 
allel with  the  Peruvian  line)  from  Las  Vigas  summit  to  the  level  of  Jalapa,  and 
then  continuingtiown  to  sea-level  with  mixed  i^  to 4  percent  grades,  with  some 
lost  elevation. 


Fig.  2 j2.— Comparative  Profiles  of  some  of  the  Great  Inclines  of  the  World.    (See  par.  947). 

[The  jalapa  line  is  that  described  in  Appendix  C  J 


CHAP.  XX.— DUPLICATE   TRACKS  FOR  PUSHER  GRADES,  699 

Table  190. 

Various  Great  Inclines  of  the  World. 

[The  body  of  this  table  is  (with  correction  of  a  number  of  errors)  a  list  g^ven  in  The 
Engineer  of  July  17,  1885,  as  a  complete  one.  The  notes  beneath  give  various  other  and 
much  gjeater  inclines  omitted  from  the  list.] 


Name  op  Inclinb. 


Giovi 

Semmering 

Bhore  Ghaut 

Allegheny 

Tabor  (Chili) 

Kadugannawa  (Ceylon) 
Ambagamuvjra         *' 


Length 

of 

Incline. 

Miles. 


6 

15 
12 

III 
19 


Toul 
Rise. 
Feet. 


884 

1,325 
1,831 
1,690 
1.360 
1,388 
2,227 


Grade. 

Av. 

Max. 

p.  c. 

p.  c. 

2.78 

3  45 

2.13 

2.50 

2.08 

2.70 

2.13 

•  •   •   • 

2.15 

2.25 

2.22 

2.22 

2.22 

2.27 

M 

axi- 

mum 

Curve. 

4° 

20' 

8° 

40' 

5" 

45' 

q'' 

30' 

9 

30 

8" 

40' 

0 

A9 

0' 

Leng-th  of 

Tunnels, 

Miles. 


2.25 
2.66 
2.26 


.88 
•30 


[In  addition  to  this  list  there  is  to  be  an  extension  of  the  same  Ceylon  railway  which 
"will  also  involve  a  further  incline  of  12  miles  rising  1359  ft.,  on  which  an  average  gra- 
dient of  2.15  per  cent,  with  a  maximum  of  2.227  P^^  cent,  will  be  compulsory,  as  will  also 
the  adoption  of  curves  as  sharp  as  19°."] 

To  the  above  very  inadequate  list  may  be  added  the  following,  the  whole  not  making  a 
complete  list  by  any  means  : 

Mexican  Railway. — Rises  6412  ft.  in  53.9  miles,  4  per  cent  maximum  grade  (214,  aver- 
age), with  325  ft.  curves  radius  (17=40')  and  16  tunnels.  In  this  distance  it  also  rises 
2372  ft.  in  12.58  miles,  3.57  per  cent  average  grade  and  4  or  5  tunnels. 

The  air-line  distance  between  the  extreme  points  of  this  latter  section  is  less  than  four 
miles,  but  it  includes  the  bota,  or  boot,  so  called  from  its  shape,  nearly  eight  miles  long, 
and  rising  to  a  point  on  the  slope  of  the  mountain  which  to  the  eye  seems  almost  vertically- 
over  the  point  at  which  the  "  boot"  began  16,50  ft.  below,  and  which  is  certainly  not  over 
one  mile  distant  from  it  horizontally,  giving  an  outlook  which  is  even  more  startling  to  the 
engineer  than  to  the  average  traveller. 

Oroya  Railroad,  Peru. — Rises  2352  ft.  in  26  miles  on  2i^  per  cent  (i  in  40)  maximum 
grade,  to  reach  the  foot  of  the  main  grade ;  then, — 

Rises  12,845  ft.  in  71  miles,  on  4  per  cent  grade,  with  141^°  curves  (396  ft.  radius),  to  an 
elevation  of  15,645  ft.,  with  42  tunnels. 

On  this  line  there  are  several  switchbacks  (Figs.  217  to  221),  but  the  first  thirteen  miles 
rises  2105  ft.  without  any  switchback. 

There  are  one  or  two  other  lines  in  Peru  of  the  same  general  character,  but  rising  to 
less  elevations. 

Among  the  European  inclines  not  included  above  are  : 

St.  Gothard. — Rising  2750  ft.  in  20V2  miles ;  142.5  ft.  per  mile  maximum  grade  (2.7per 
cent) ;  130  ft.  average  grades.  Also  rising  2090  ft.  in  15^  miles,  with  28  per  cent  of  the 
distance  tunnels,  including  (on  both  these  inclines)  seven  spiral  tunnels  turned  into  the 
mountain  to  gain  distance  (Figs.  202  to  206).  ^ 

Brenner. — Rising  2584  ft.  in  22>^  miles,  132  ft.  per  mile  (2.5  per  cent)  maximum  grade ; 
1 14. 6  ft.  average. 


«  *< 


■r 


700  CHAP,  XX.— DUPLICATE  TRACKS  FOR  PUSHER  GRADES, 


In  the  United  States  there  are  : 

Southern  Pacific— ^is^^  2674  ft.  in  25.4  miles;  116  ft.  per  mile  (2.20  per  cent)  maxi- 
mum  g:rade;  io»  maximum  curve;    11  tunnels,  including  a  "loop,"  or  more  properly 
spiral  or  helix,  j8oo  ft.  long  and  rising  78  ft. 

Denver  &>  Rio  Grande,  Marshall  Pass .—^xsfts,  ^75  ft.  in  25  miles,  4  per  cent  (211  ft. 
per  mile)  maximum  grade  ;  24°  maximum  curve.  Height  of  summit,  10,852  ft.  above  the 
sea.    Also, 

La  Vela  Pass.—mses  2368  ft.  in  15  miles  ;  same  grades  and  curves  as  above.  Height 
of  summit,  9339  ft. 

The  lines  over  Fremont  Pass,  11,540  ft.  above  the  sea,— the  highest  point  reached  by 
the  locomotive  anywhere  in  the  world  except  in  Peru,— and  the  Tennessee  Pass,  10,418  ft. 
high,  are  of  the  same  general  character. 

Another  very  notable  heavy  grade  on  this  same  road  is  : 

Calumet  Mine  Branch,  Denver  &>  Rio  Grande.— Rises  some  2700//.  in  seven  miles 
on  an  eight  per  cent  grade  (nearly  406  ft.  per  mile)  with  25°  maximum  curves. 

This  unparalleled  line  is  used  to  bring  ore  to  the  Bessemer-steel  works  at  Pueblo,  and 
is  operated  by  one  train  per  day  each  way.  It  is  undoubtedly  the  heaviest  grade  on  any 
regularly  operated  railroad  in  the  world,  although  10  per  cent  temporary  grades  (528  ft. 
per  mile)  were  successfully  operated  for  over  two  months  over  the  Kingwood  Tunnel  of 
the  Baltimore  &  Ohio  Railroad  by  the  late  Benj.  H.  Latrobe  as  early  as  1852.* 

These  latter  lines  are  narrow-gauge,  but  need  not  remain  so  unless  they  choose. 

Mexican  National.— Kxs^  2628  ft.  in  17  miles;  on  3.8  per  cent  (201  ft.  per  mile)  max- 
imum grade;  15°  maximum  curves;  with  a  descent  of  1325  ft.  in  nine  miles  on  a  3.5  per 
•cent  grade  on   the  other  side  of  the  summit.     Laid  to  narrow-gauge,  but  expressly  built 
throughout  to  be  adapted  to  standard  gauge.     On  same  road  : 

Mexican  National,  Northern  Division.— UoTiicrey  to  Saltillo.  Rises  3465  ft.  in  54 
miles,  at  an  average  rate  of  d»  ft.  per  mile,  most  of  the  rise,  however,  concentrated  on  a 
short  portion  of  the  distance  on  grades  of  2M  per  cent. 

Less  important  inclines  which  are  for  one  reason  or  another  notable  are ; 

Tyrone  &*  Clearfield.— A  little  branch  of  the  Pennsylvania  Railroad.  Rises  1064  ft. 
in  10  miles.     Tangent  maximum.  138  ft.  per  mile. 

Central  Pacific— Rises  992  ft.  in  13  miles;  2  per  cent  (105.6  ft.  per  mile)  maximum 
grade;  io»  curves;  eight  tunnels. 

Northern  Pacific— Rises  1668  ft.  at  116  ft.  per  mile  (2.2  per  cent)  in  an  air-line  dis- 
tance of  13  miles. 

Mexican  Central.— Rises  1750  ft.  in  19  miles  at  San  Juan  del  Rio  with  easy  grades  and 
curves  and  1650  ft.  at  Zacatecas. 

Among  lines  located,  but  not  yet  built,  may  be  mentioned  : 

Luckmanier  Pass  (near  the  St.  Gothard).-Rises  on  a  development  of  29^  miles 
between  two  points  six  miles  apart,  on  a  maximum  grade  of  132  ft.  per  mile  (2.5  per 
cent)  implying  a  descent  of  something  less  than  3900  ft.,  with  maximum  curves  of  084  ft. 
radius  (5"  49').  "^ 

Mexican  Central.— Two  lines  ascending  from  the  coast  to  the  central  plateau  of  Mex- 
ico, one  from  the  Gulf  of  Mexico  at  Tampico  and  the  other  from  the  Pacific  at  San  Bias, 
fcoth  of  which  rise  some  4500  ft.  on  2  to  3  per  cent  grades. 


♦  Fora  full  and  most  interesting  account  of  these  and  other  works  by  Mr.  Latrobe,  see 
Railroad  Gazette,  December  5,  1874. 


CHAP.  XX.— DUPLICATE  TRACKS  FOR  PUSHER  GRADES.  70I 

Vera  Cruz  to  City  0/  Mexico,  via  Jalapa.— The  line  more  fully  described  in  Appen- 
dix  C.     Rismg  7323  ft.  (2232  metres)  in  one  unbroken  2  per  cent  (average)  gradient  for 
72.64  miles  (1 16.9  kUometres)  or  from  an  elevation  of  600  ft.  to  an  elevation  of  702^  ft 
above  the  sea.  /^  o   ». 

948.  The  great  effect  of  fluctuations  of  velocity  to  modify  the  nom- 
inal rates  of  short  gradients  may  be  illustrated  by  the  following  tests 
made  by  Mr.  C.  H.  Hudson,  a  prominent  and  able  railway  manager.  The 
tests  are  thus  described  :* 

••Recently,  for  the  purpose  of  testing  a  new  engine  of  the  Consolidation 
pattern  just  received  by  the  East  Tennessee,  Virginia  &  Georgia  Railroad  we 
weighed  a  train  of  30  loads,  caboose  and  private  coach,  and  took  it  with'  the 
engine  to  a  heavy  grade  about  a  mile  long,  averaging  67.1  ft.  per  mile  The- 
grade  was  not  even,  but  undulating  ;  some  being  more  and  some  less  than  the 
average.  In  one  place,  100  ft.  were  at  the  rate  of  98  ft. ;  another,  spots  of 
300  ft.  at  the  rate  of  91.  and,  of  course,  to  match  it  other  spots  were  less  than 
the  average.  ^  Before  reaching  the  grade,  there  were  about  1600  ft  of  level- 
mostly  on  a  3  curve  to  right,  which  curve  continued  800  ft.  up  the  grade  Then 
k)llovved  [curves  and  tangents  for  4800  ft.  in  all]  when  the  summit  was  reached 
I  he  day  was  warm  and  dry,  and  circumstances  favorable.  The  weight  of  train 
was  as  follows  :  ^ 

X  AT^^SfiK^'  '??'?^^  ^^^-^  tt"'^^''..  55.000  lbs.;  32  cars.  1.453.160  lbs.;  total, 
1,617,160  lbs.  Cylinders,  20  by  24  in.;  diameter  of  drivers,  59  in.;  weight  on 
drivers,  97,000  lbs.  ^ 

''  First  Test.— The  engine  stood  at  start  at  water  tank  about  1500  ft   from 
foot  of  grade,  and  when  grade  was  reached  was  making  about  18  miles  per  hour 
At  a  point  3700  ft.  from  the  grade  the  engine  came  to  a  stand,  unable  to  taki 
tram  through.     It  was  then  backed  down  and  two  cars  set  off,  weighing  123  500- 
lbs.,  leaving  weights  as  follows :  '        6      ti,    -«.j.ow 

I     '    66o*lbs'    ^^'°°^  ^^^■'   '^"'^^'''    55.000  lbs.;   train,  1,329,660   lbs.,-    total. 

Second  Test— This  time  the  engine  started  from  the  same  place  as  before 
struck  the  grade  making  22.3  miles  per  hour,  and  in  seven  minutes  turned  the 
summit,  making  4.5  miles  per  hour.  The  engine  averaged  145  lbs.  steam  was 
worked  most  of  the  way  in  the  second  notch  from  bottom,  or  at  aboilt  an 
i«-inch  cut-oflf.  the  last  1200  feet  being  in  lowest  notch,  or  what  was  called 
full  stroke  (22-inch  cut-oflf).  Very  little  sand  was  used  ;  engine  did  not  slip^ 
any.  ^ 

••  While  this  grade  was  undulating,  it  seemed  fair  to  take  the  average  —which 
has  been  stated  67.1  per  mile,  or  1.27  per  cent,— giving  a  resistance  due  gravity 
per  ton  of  .0127  X  2000  =  25.4  lbs.  &         J' 

The  locomotive- power  indicated  by  these  records  is  then  computed  in 
the  following  manner— correct  numerically,  but  wholly  incorrect  in  its 
apparent  indications : 

"Train  resistance Lbs.  pej  ton. 

Curve  resistance  on  6°  curve ....*....*.* .V.V.  *  60 

Grade  resistance  (1.27  per  cent) ...i  ...!...!!.*.'!..'.*...* .       25  4 

Total  resistance  to  be  overcome 36.4  lbs 

*Jour.  Assoc  Eng.  Societies,  18S6. 


I 


[ 


I 


il 


l^Hi 


702  CHAP.  XX.— DUPLICATE  TRACKS  FOR  PUSHER  GRADES. 

**  Weight  of  engine  and  train  being  747  tons  ;  747  X  36.4 =  27,191  lbs. 

But  about  icxD  ft.  of  the  train  will  be  on  a  10°  curve,  where  the 
resistance  per  degree  is  .05,  or,  for  the  10°,  .50  percent ;  theesti 
mated  resistance  on  a  6°  curve  was  .30  per  cent  :  here  is  an  ex- 
cess of  .20  per  cent,  or  per  ton,  4  lbs.     Now,  three  cars  are  all  of 
the  train  on  this  curve,  and  we  have  69  tons,  which  gives  69  X  4  =        276  lbs. 

Making  a  total  resistance  to  overcome  of 27,467  lbs. 

**  You  will  note  that  here  we  develop  a  tractive  force  of  28.2  per  cent  of  the 
weight  on  drivers  ;  not  so  great  as  in  other  cases,  but  much  over  ordinary  prac- 
tice. 

•'The  theoretical  power  of  the  engine  would  be  as  follows: 

50 
X  cylinder  pressure  =  192  X  130  (assumed)  =  24,960  lbs. 

"  The  estimated  resistance  per  ton  is,  including  the  correction  for  the  lo" 
curve,  36.8  lbs. 

"  Divide  the  theoretical  power,  24,960,  by  this  resistance  36.8,  and  we  have  : 
24,960  -t-  36.8  =  678  tons  =  1,356,000  lbs. 
Being  the  theoretical  amount  the  engine  would  move  up  this  grade,  or  about 
137,000  lbs.  less  than  the  actual  amount  moved.      7'Ae  actual  work  exceeds  the 
theoretical  by  about  the  weight  of  the  engine  and  tender.'" 

949.  The  true  explanation  of  this  apparent  anomaly  is  that  the  en- 
gine in  reality  did  no  such  thing  as  to  develop  a  tractive  force  of  27,467 
lbs.,  nor  is  there  any  real  discrepancy  between  the  actual  and  theoreti- 
cal v^rork  done.     The  true  way  of  computing  the  tests  is  as  follows : 

Per  cent. 

Nominal  average  rate  of  grade  (that  of  the  profile) 1.27 

Correct  for  curvature  at  0.03  to  0.05  vertical  feel  for  each  degree  of  cen- 
tral angle,  which  is  in  effect  an  addition  to  the  grade  of 0.12 

And  we  have  as  the  equivalent  nominal  grade,  including  effect  of  uncom- 
pensated curvature 1.39 

Where  the  curvature  is  makes  no  great  difference,  unless  it  stalls  the 
train,  and  we  need  not  now  go  into  that  detail. 
Then  to  compute  the  first  test  we  have :  * 

Train  struck  foot  of  grade  at  velocity  of  18.0  miles  per  hour,  and  stalled 

in  3700  ft.  Vel.-head  for  18.0  miles  (Table   118),  11.50  ft.;  111?  =   0.311  vert. 

37.00 
ft.  per  station  as  the  work  done  by  momentum.     1.39  —  0.31 1  =  1.08  per  cent 
as  the  virtual  grade,  or  the  one  up  which  the  unassisted  traction  of  the  engine 
hauled  the  train. 

Miles  per  hour.      Vel.-head. 

Second  Test. — Speed  at  foot  of  grade  (4800  ft.  long). . . .       22.3  17.67  ft. 

**      •'  top  ♦•        4.5  .73ft. 

16.94 

*  For  strict  correctness  the  distance  travelled  up  the  grade  by  the  centre  of 
gravity  of  the  train,  and  not  the  engine,  should  be  used  in  this  test,  but  as 
the  initial  velocity  was  taken  from  the  engine  it  is  impossible  to  do  so. 


CHAP.  XX,— DUPLICATE  TRACKS  FOR  PUSHER  GRADES   703 

16.94  vert.  ft.  _ 

48.00  stations  ~  °'^^3  ^^'*'-  ^^'  P^*"  station  as  the  assistance  derived  from  mo- 
mentum, and  1.39 -0.353  =  1.04  per  cent  as  the  virtual  grade  in  the  second 

All  this  is  shown  graphically  in  Fig.  233.     At  the  foot  of  the  grade 
the  vertical  head  corresponding  to  the  given  velocities  is  erected,  and 


5tf 

Z 


j  1600' 


-also  at  the  head  of  the  grade,  although  it  is  so  small  as  to  be  hardly  visible. 
1  he  dotted  Imes  show  the  virtual  grades.  The  two  tests  coincide,  it  will 
be  seen,  almost  exactly  in  the  virtual  grade  which  they  indicate,  espe- 
cially ,f  we  remember  that  the  engine  used  a  little  more  steam  on  the 
upper  part  of  the  second  run. 

This  virtual  grade  includes  the  effect  of  curvature,  and  for  the  power 
developed  by  the  engine  we  have : 

Train  resistance ^**^-  P^*"  ^°"- 

Grade  worked  by  engine  powVrYsaV"  i!(i6peVcem)V.V.V^*. '.*.**.*  .*.';;*.*.;;     2?;2 

Total  per  ton ~7~~ 

26.2  lbs.  per  ton  X  747  tons 'L ^^ 

Against  Mr.  Hudson's  computation  oVactual  work  o'f .  .*  .*  *.  .* .'  .*  *. .' .'  .* '  ~  2?'467     - 
And  of  theoretical  work  with  130  lbs.  pressure  of .i  24:960    " 

,^  5'^J^  ^^^"^^  ^""^^  ^°"^  requires  an  average  effective  piston  pressure  of 
~~-  =  a  fraction  over  100  lbs.  per  square  inch,  which  is  coming  down 

within  the  bounds  of  reason  (and  barely  that)  for  a  Consolidation  engine 

""^'oiJo^Axf  ^^''  ""^  ^''''^'  P'"^^^"''^  ^"d  rnnnm^  over  15  miles  per  hour. 
950.  We  may  see  how  these  variations  of  velocity  may  tend  to  in- 
crease grades,  and  how  nearly  our  process  of  computing  them  will  check 
by  considering  what  took  place  between  the  starting-point  and  foot  of 


704  CHAP.  XX.^DUPLICATE  TRACKS  FOR  PUSHER  GRADES 


the  grade,  1 5cx>  ft.  off,  over  a  nominally  level  grade.    The  virtual  grade 
may  be  tlius  determined  : 


Speed  acquired  in  1 500  ft 

Corresponding  vel.-head,  ft 

Then  we  have,  as  the  virtual  grades  per  station.. 


In  first  test. 

In  second  test. 

18.00 

22.30 

11.50 

ii.ro 

=  0.77 

17.67 

15.00 


15.00 


In  other  words,  in  the  first  test  the  engine  started  off  lazily  and  did 
not  do  as  much  work  as  after  it  struck  the  grade.  In  the  second  test  the 
engine  succeeded  in  doing  somewhat  more  work  than  it  did  after  it  struck 
the  grade,  as  is  but  natural  from  the  fact  that  its  average  velocity  was 
less  and  (probably)  it  used  more  sand  and  had  a  somewhat  higher  boiler 
pressure.  But  the  correspondence  is  close  without  these  allowances ; 
quite  sufficient  to  indicate,  what  is  beyond  question,  that  the  method  is 
essentially  trustworthy. 

Now,  had  this  grade,  instead  of  being  only  4800  ft.  long,  been  48,000 
ft.  long,  it  will  be  evident  that  the  same  initial  velocity  would  have  done 
very  little  to  help  out  the  engine.  To  derive  equal  aid  from  momentum 
we  should  have  needed  to  have  a  vertical  head  ten  times  as  great  in  that 
case,  or  176  ft.,  which  would  have  carried  the  necessary  initial  speed  up 
to  the  impracticable  limit  of  nearly  71  miles  per  hour.  Consequently, 
while  short  grades  and  short  sags  may  be  operated  almost  as  levels  with 
speeds  of  30  to  50  miles  per  hour,  long  grades  or  bad  sags  can  be  but 
little  helped  out  by  momentum.  In  the  one  case  the  profile  tells  the 
truth,  and  in  the  other  it  does  not. 


PART  IV. 


LARGER  ECONOMIC  PROBLEMS. 


*•  The  rich  man's  wealth  is  his  strong  city :  the  destruction  of  the  poor 
is  their  poverty." — Proverbs  x.  15. 

•'  For  whosoever  hath,  to  him  shall  be  given,  and  he  shall  have  mor« 
abundance :  but  whosoever  hath  not,  from  him  shaU  be  taken  away  even 
that  he  hath."— Matthew  xiii.  12. 

•♦  For  which  of  you,  intending  to  build  a  tower,  sitteth  not  down  first, 
and  counteth  the  cost,  whether  he  have  sufficient  to  finish  it  ?  Lest  haply, 
after  he  hath  laid  the  foundation,  and  is  not  able  to  finish  it,  all  that  be- 
hold it  begin  to  mock  him,  saying,  This  man  began  to  build,  and  was 
not  able  to  finish." — Luke  xiv.  28-30. 

45 


^1 


PART  IV. 


LARGER  ECONOMIC  PROBLEMS. 


CHAPTER  XXI. 

TRUNK    LINES    AND   BRANCH    LINES. 

9«.  That  the  most  elementary  conditions  on  which  the  suc- 
cess or  failure  of  railway  enterprises  depend  are  often  radically 
misunderstood,  almost  necessarily  follows  from  the  fact  that  the 
world  IS  so  full  of  examples  of  misdirected  enterprise-of  lines 
built  with  great  hopes  of  profit   which  have  proved  miserable 
failures;  while,  on  the  other  hand,  there  are  so  many  examples  of 
roads  built  for  local   purposes,  or  otherwise  without  particular 
expectation  of  a  brilliant  future,  which  have  proved  magnificent 
properties.    Among  innumerable  examples  which  might  be  men- 
tioned we  may  take  the  West  Shore  Railroad  of  New  York  as 
an  example  of  the  first  class,  and  the  parallel  New  York  Central 
of  the  last:  the  present  New  York  Central  &  Hudson  River  Rail- 
road   having  been  made  up  by  the  consolidation  of  six  or  eight 
different  local  lines,  built  with  little  or  no  reference  to  the  forma- 
tion of  a  great  trunk  line.    These  two  lines  are,  in  their  different 
ways,  striking  examples  of  the  fact  that  the  conditions  which  con- 
trol the  future  prosperity  of  such  properties  are  often  wholly 
misunderstood.  ""ii>- 

r..  f";  It  seems  for  many  reasons  probable  that  by  far  the  larger 
part  of  this  very  general  misunderstanding_of  the  blundering 
into  unexpected  success  on  the  one  hand,  and  into  dismal  and 


^ 


li'^l"^  I  ilili     mith» 


708      CHAI\  XXI.^TRUNK  LINES  AND  BRANCH  LINES. 


M 


*!H    ':1| 


m 


utter  failure  on  the  other— arises  from  a  single  cause,  viz.,  an- 
imperfect  understanding  of  certain  elementary  facts,  wh.ch  we 
will  now  consider,  as  to  the  effect  upon  the  productiveness  of  the 
property  of  any  increase  in  the  sources  of  traffic.  The  unex- 
pectedly good  or  bad  fortune  of  hundreds  of  properties  can  be 
traced,  in  part  or  whole,  to  this  single  cause. 

953.  Let  us  suppose  a  railway  to  be  projected,  say  loo  miles 
lone,  to  connect  t*wo  traffic  points  of  some  importance.  A,  B,  !•  ig. 

^'  233.    We  will  assume  for 

^ ?-t    simplicity  that   there  is 

Fig.  ^33'.  little  or  no  intermediate 

local  traffic,  as  often  happens.  We  will  consider^  and  ^  to  be 
equal,  not  necessarily  in  population,  but  in  traffic-contnbut.ng 
capacity  to  this  particular  line.  The  traffic  which  the  railway 
has  to  support  it  may  be  then  represented  by  the  combination 
AB,  being  that  which  naturally  exists  between  two  traffic  points 
of  the  importance  of  A  and  B. 

954.  Let  us  now  suppose  that  another  alternate  route  may  be 
chosen,   which  by  a  slight  detour  will   stake  an    i"t«""^<l-;; 

(,  traffic  point  C,  Fig.  234, 

^ — ■ — -*" ____S       of  equal  potential  mag- 

#Atrrr:^^^ nitude   with   A   and   B: 

Fio.  »34-  how   have    we    affected 

the  revenue-earning  capacity  of  the  line  ? 

A  most  natural  answer-beyond  all  question  a  very  common 
answeT-is  that  we  have  increased  it  just  50  per  cent  Instead  of 
er"  g  perhaps  ,00,000  people  in  the  -o  towns  ^  and^  we 
nnw  serve  1^0  000  people  in  the  three  towns  A,  B,  C.  Fifty  per 
Z  more  people,  «ty  per  cent  more  traffic,  fifty  per  cent  more 
rammers— seem  natural  corollaries  of  each  other, 
'on'  he  contrary,  it  may  be  shown  at  once  that  we  have 
doubled  our  probable  traffic,  and  really  we  have  trjpled  our  traffic 

and    ler  m'ore  than  tripled  it.  ^'^1^^<'J f^^^^^^ 
A  /?  Fi^  2X^  we  have  Traffic  AB,  Traffic  AC,  Traffic  CB,  Fig.  234. 
Yhe  value^^^  the  latter  is  obviously  twice,  and  really  consid- 
erably  more  than  three  times,  that  of  the  former.. 


CHAP.  XXL— TRUNK  LINES  AND  BRANCH  LINES.      7O9 

To  have  the  traffic  tripled  we  must  assume  that  Traffic  AB, 
Traffic  AC,  and  Traffic  BC,  Fig.  234,  are  of  equal  financial  value 
— which  they  are,  as  nearly  as  may  be. 

955.  An  objection  to  this  statement  will  naturally  suggest  it- 
self— that  in  Fig.  234,  although  the  traffic  points  A,  B,  C  are 
equal  in  magnitude,  yet  the  haul  on  the  Traffic  AB  is  twice  that 
on  Traffic  ^Cor  CB,  Therefore,  if  the  volume  of  each  be  the 
same  and  the  rates  be  the  same,  we  apparently  have  Traffic  AB  = 
Traffic  AC  +  Traffic  CB,  so  that  we  have  only  doubled  instead  of 
tripling  our  traffic  from  a  revenue-producing  point  of  view. 

But  these  latter  assumptions  are  not  correct,  either  as  respects 
the  volume  of  or  rates  on  traffic. 

As  respects  the  effect  of  distance,  it  may  be  said  in  a  general 
way  that,  if  we  consider  only  great  and  decided  differences  of 
-distance,  the  volume  of  traffic,  both  passenger  and  freight,  will 
be  at  least  inversely  as  the  distance  :  that  is  to  say,  if  two  given 
traffic  points,  100  miles  apart,  could  be  moved  up  to  a  distance 
of  only  50  miles  from  each  other,  and  remain  otherwise  un- 
changed, the  volume  of  traffic  between  them  will  be  at  least 
doubled.  New  York  and  Philadelphia,  for  example,  are  90  miles 
apart,  and  New  York  and  Boston  231  miles.  Could  these  cities 
be  moved  up  to  within  45  and  1 15  miles  of  each  other  the  volume 
of  traffic  between  them  might  even  be  quadrupled,  and  certainly 
the  lines  connecting  them  would  be  very  much  better  properties, 
because  the  loss  of  haul  would  be  more  than  made  up  by  the 
increase  of  volume,  even  as  respects  gross  revenue,  leaving  the 
saving  in  expenses  by  the  shorter  haul  and  the  probable  higher 
rates  per  mile  almost  a  clear  gain. 

956.  As  to  rates,  it  is  an  entirely  safe  general  rule,  that  freight 
hauled  only  half  as  far  will  pay  a  materially  larger  rate  per  mile 
for  the  haulage  proper,  excluding  the  terminal  charge,  which  is 
in  effect  a  part  of  every  rate. 

The  passenger  rates  per  mile  might  well  be  the  same  or  even 
lower,  but  this  would  only  be  for  the  reason  that  it  was  profita- 
able  to  make  them  lower,  to  secure  the  far  greater  net  gain  from 
the  increase  of  volume.  The  traffic  would  in  all  such  cases  bear 
a  materially  higher  rate  per  mile  without  decreasing  its  volume 


( :  Ml 

i  ■ 


.M 


MmwUliin 


'Ill 


710       CHAP.  XXL—LAW  OF  INCREMENT  OF   TRAFFIC, 

below  what  would  exist  with  twice  the  haul.  Taking  both  these 
considerations  together,  it  is  quite  certain  that,  whether  we  con- 
sider  great  distances  or  small,  nearness  of  traffic  points  is  cer- 
tainly no  disadvantage  to  the  financial  productiveness  per  unit 
of  the  traffic  between  them.  For  example,  if  the  haul  on  wheat 
to  the  seaboard  were  only  half  as  great,  it  cannot  be  questioned 
that  it  would  be  a  more  profitable  traffic,  and  it  would  possibly 
pay  quite  as  large  gross  rates.  The  New  York-Newark  traffic,. 
9  miles,  is  far  more  profitable  and  far  larger  in  the  aggregate,, 
in  proportion  tO  the  size  of  the  two  places,  than  the  New  York- 
Philadelphia  traffic,  90  miles.  If  Philadelphia  were  as  near  to 
New  York  as  Newark,  both  the  volume  and  the  productive  value 
of  their  interchanged  traffic  would  be  enormously  greater  than  it 
is  now. 

957.  There  are,  of  course,  certain  possible  exceptions  to  this 
general  rule.  The  tonnage  between  the  anthracite-coal  mines 
and  New  York,  for  example,  might  not  be  much  larger  than  it  is 
if  the  haul  were  only  50  miles  instead  of  150,  for  about  so  much 
must  be  had  at  any  cost,  and  more  than  that  is  not  needed.  And 
yet  it  probably  would  be  larger,  both  because  the  more  favorable 
conditions  for  coal  supply  would  have  greatly  stimulated  manu- 
factures, and  so  the  growth  of  population  as  well,  and  because 
the  rates  per  mile  hauled  would  be  higher. 

958.  We  see,  therefore,  the  reasons  why,  assuming  the  points 

D  _#^  ^'  ^'  ^'  ^'^'  '^^^'  ^°  ^^  ^^ 

^rtrrnr^J--rrrrrrri^  inherently  equal  traffic- 
producing  capacity,  the 
short-haul  traffics,  AC 
and  CB,  should  each  one 
of  them  be  of  more  rath- 
er than  less  value  than 
the  long-haul  traffic,  AB\ 
from  which  it  follows 
that  the  aggregate  of  the 
three  traffics  AB^  AC,  CB,  Fig.  234,  will  be  worth  more  rather 
than  less  than  three  times  as  much  as  the  traffic  AB  alone. 


Fig.  234. 


B 


CHAP.  XXI.^LAW  OF  INCREMENT  OF  TRAFFIC.        71I 

This  being  determined,  let  us  now  extend  the  inquiry  by  de- 
termining, in    the  same 
manner    as    above,    the       A,^- — ^"""^""^---^.^   C 

probable       comparative       pic.  236. 

traffic  on    five  different 

lines     of   any     common 

length.    Figs.      233-237, 

having  two,  three,  four, 

five,  and  six  traffic  points  on  them,  each  point  being  assumed 

for   the   sake   of   simplicity,    to   be    of   equal    traffic-producing 

capacity. 

We  then  have, 


Fig.  237. 


Traffic  Umits. 

In  Fig.  233,    2  traffic  points,         A  B  only, 


(i 


i< 


4i 


« 


234,    3 

{< 

« 

AB, 

AC, 

CB, 

^ZSy      4 

« 

« 

SAB, 

\ad, 

AC, 

CB, 

BD, 

CD, 

(AB, 

AC, 

CB, 

236,    s 

M 

« 

\ad. 

BD, 

CD, 

[AB, 

BE, 

CE, 

'  AB, 

AC, 

CB, 

AD, 

BD, 

CD, 

237,    6 

i« 

"       . 

AE, 

BE, 

CE, 

DE, 

AF, 

BF, 

{CF, 

DF, 

EF, 

} 

J 


comparativb 
Traffic 

Z 

3 
6 


10 


IS 


Comparing  Fig.  233  with  Fig.  237,  by  multiplying  our  traffic 
points  by  three  we  have  multiplied  the  traffic  by  fifteen,  or 
have  increased  the  productiveness  of  each  separate  traffic  point 
five  times. 

959.  This  process,  with  certain  corollaries  which  follow  there- 
from, is  extended  somewhat  further  in  Table  191  and  illustrated 
graphically  in  Fig.  238. 

It  will  be  seen  from  Fig.  238  that  when  on  any  given  line  with 


I 


712        CHAP.  XXL— LAW  OF  LNCREMENT  OF   TRAFFLC, 


any  given  number  of  traffic   points  of  equal  weight  on  it,  we 
have — 

No.  of  traffic  points,        2|     3     |        4         |  ...«, 

We  have  for  the  com.)      ,  ^^^  ,  .^^^^  ,  ,+,+3 +..  .+(„_,). 
parative  traffic,        ) 

In  other  words,  the  comparative  aggregate  traffic  for  any  num- 
ber of  traffic  points  n  is  given  by  the  sum  of  the  natural  mem- 
bers to  «  —  I  inclusive.  The  sum  of  such  a  series  to  n  inclusive 
is  given  by  the  formula 


o 
*o 
Cu 

u 
iB 

e 


o 


1 

2 
8 
4 
6 
6 

7 
8 


d 

0 

.-i 

•0 

T3 

< 

« 

4-* 

Xi, 

c 

u 

(4 

0 

U 

0. 

0 

% 

u 

3 

1 

t 

E 

c 
8 

2 
H 

2 

c« 

C 

0 

iz: 

H 

^_  ;?(«  +  i)  __  «*  +  « 


(0 


A 
B 
C 
D 
E 
F 
G 


H 


0 

1 
2 

3 
4 


o 

1 
3 

6 

10 


15 
21 


So  that  for  the  aggregate  traffic  7",  due  to 
n  traffic  points,  we  have 

/  being  any  coefficient 

1 


AB 


28 


AC 


AD 


AE 


fKr 


AG 


AH 


BC 


BD 


BE 


BF 


BG 


BH 


CD 


CE 


OF 


CG 


CH 


DE 


DF 


DG 


DH 


EF 


EG 


EH 


F6 


FH 


GH 


Fig.  238.— Illustrating  thk  Law  of  Incrembnt  in  Traffic  result, 

ING   FROM    THR    INTERPOLATION   OF  THE   ADDITIONAL  TRAFFIC  POINTS 

C,  £>,  E,  F,  ETC.,  Figs.  233  to  237. 

For  any  larger  number  of  points  N  we  have  similarly 


(3) 


CHAP.  XXL— LA  IV  OF  LNCREMENT  OF   TRAFFLC.        713 


whence  the  ratio  of  increase  is 


V  _N{N-  i) 
T         n[n  —  i) 


(4) 


As  n  becomes  a  larger  number,  the  ratio  of  « to  «  —  i  becomes 
more  and  more  nearly  unity,  until  finally  the  ratio  of  r'  to  T 
becomes  sensibly 


n 


3 ) 


(5) 


which  is   THE   EQUATION   GIVING    THE   GENERAL   LAW   OF   INCREASE 
IN   EARNINGS   DUE  TOAN    INCREASE   OF    TRIBUTARY    TRAFFIC    POINTS 

ON  THE  SAME  LENGTH  OF  LINE  ;  i.e.,  the  productive  traffic  varies 
as  the  SQUARE  of  the  number  of  tributary  sources  of  traffic. 

Table  191. 

Showing  the   Effect   upon   Aggregate  Traffic   of   Interpolating 
Additional  Traffic  Points  in  the  Line. 

[See  Figs.  233-238.] 


Per  Cent 

Absolute 

No.  OF 

Traffic 

Increase  of 

Increase  of 

Traffic 

Relative 

Per  Unit  of 

Traffic 

Traffic 

Points. 

Traffic. 

Population. 

by  Addinif 

by  Adding 

One  Traffic 

One  Traffic 

Point. 

Point. 

2 

I 

0.5 

•    • 

3 

3 

I.O 

200.0 

2 

4 

6 

1.5 

100. 0 

3 

5 

ID 

2.0 

66.7 

4 

6 

15 

2.5 

50.0 

5 

7 

21 

30 

40.0 

6 

8 

28 

3-5 

33.3 

7 

9 

36 

4.0 

28.6 

8 

10 

45 

4.5 

25.0 

9 

II 

55 

5.0 

22.2 

ID 

12 

66 

5.5 

20.0 

II 

13 

78 

6.0 

18.2 

12 

14 

91 

6.5 

16.7 

13 

15 

105 

7.0 

15.4 

14 

etc. 

etc. 

cts. 

etc. 

etc. 

It  will  be  seen  from  the  last  column  of  this  table  that  the  absolute  gain  from  a  given 
addition  of  tributary  population  is  greater  in  proportion  to  the  amount  of  other  tributary 
population,  but  that  the  addition  per  cent  is  very  much  greater  on  light-traffic  roads. 


;il! 


714        CHAP.  XXI.— LAW  OF  INCREMENT  OF   TRAFFIC, 


CHAP.  XXI.— LAW  OF  INCREMENT  OF   TRAFFIC.        7 1 5- 


II 


Table  192. 
Growth  of  New  York  City  Internal  Passenger  Traffic 

[Compare  tables  noted  below.] 


In  the  years  1871-72-73,  the  report  of  a  committee  of  the  American  Society  of  Civil 
Engineers  shows  3,000,000  to  5,000,000  more  passengers  per  year  than  above,  probably 
by  inclusion  of  some  omitted  line  above,  but  it  has  not  been  attempted  to  correct  thfr- 
error. 

*  Actual  population,  1885,  1,439,037. 


Summary. 


City  Passbnger  Traffic 

1 

Ybak. 

Estimated 
and  Actual 
Population. 

(Thousands). 

Per  Inhabitant.                            ■ 

EIcTated 
Roads. 

Horse 
Cars. 

Toul. 

Blerated.     Horse. 

Total. 

1853 

581. 

None. 

6,836 

•  •  • 

II. 8 

II. 8 

54 

605. 

6.817 

II. 3 

11.3 

1855 

629,810 

18,488 

29.4 

29.4 

56 

663. 

23.153 

350 

35.0 

57 

698. 

22,190 

31.9 

31.9 

58 

734. 

27.900 

38.0 

38.0 

59 

773- 

32,889 

42.7 

42.7 

i86o 

813,669 

(Same  as 

36.455 

44.7 

44-7 

61 

826. 

26,272 

31.8 

31.8 

62 

838. 

next 

35.878 

42.8 

42.8 

63 

850. 

40,412 

47.6 

47.6 

64 

863. 

column.) 

60,900 

70.6 

70.6 

1865 

876. 

82,055 

93.8 

93.8 

66 

889. 

88.953 

100. 0 

100. 0 

67 

903. 

100,542 

III.O 

III.O 

68 

915. 

105.817 

115. 6 

115. 6 

69 

929. 

114.349 

123.5 

123.5 

1870 

942,292 

115.139 

122.0 

122. o* 

71 

962. 

•  •  •  • 

133.894 

139.4 

139.4 

72 

982. 

136 

143.561 

143,697 

0.1 

146.0 

146. 1 

73 

1,003. 

644 

144.715 

145.359 

0.6 

»       144.4 

145.0 

74 

1.024. 

796 

151. 131 

151.927 

0.8 

147.8 

148.6 

1875 

1,045,223 

921 

165.997 

166,918 

0.? 

1       158.8 

159.7 

76 

1,076. 

2.013 

166,401 

168.414 

I.^ 

►       154.5 

156.4 

77 

1.107. 

3.012 

160,924 

163,936 

2.7 

135.3 

148.0 

78 

1. 139. 

9,291 

160,899 

170,190 

8.1 

131.0 

149.1 

79 

1,172. 

46,045 

141.939 

187,984 

39.4 

\       121. 4 

160.8 

1880 

1,206,299 

60,832 

150,390 

211,222 

50.5 

124.7 

175.2 

81 

1.242. 

75.586 

155.801 

231.387 

60.8 

125.4 

186.2 

82 

1,278. 

86.361 

166. 511 

252,872 

67.6 

•       130.8 

198.4 

83 

1.315. 

92.125 

176.625 

268,750 

70.1 

134.2 

204.3 

84 

1.354. 

96,703 

187,413 

284,116 

71  5 

138.2 

209.7 

1885 

1.393* 

103.355 

193.762 

297.117 

74.2 

139.0 

213.2                1 

Year. 

Popula- 
tion. 

Trips  per  Inhabitant. 

No.  OF  Lines. 

No.  Trips 
per  Inbab't 

Horse. 

Elevated. 

Total. 

Horse. 

Elevated. 

per  100,000 
of  Popula- 
tion. 

1853 

1855 

i860 

1S65 

1870 

1875 

1880 

1885 

1890 

581. 
630. 
814. 
876. 
942. 

1.045. 
1,206. 

1.393. 

•    •    •    • 

II. 8 
29.4 

44-7 
93.8 
122.0 
158.8 
124.7 
139.0 

•  •   •   • 

0.9 

50.5 
74.2 

•   •  •   • 

II. 8 

29.4 

44.7 

93.8 

122.0 

159.7 

175.2 

213,1 

. .  •  • 

2 

4 
6 

12 

12 

19 
23 
25 

•   • 

I 
4 
4 

•  • 

2.03 
4.67 

5.5 
10.7 

13.0 

15.3 
14.5 
15.4 

•    •   •   • 

Since  1885  a  further  and  great  increase  has  begun,  so  that  there  is  every  prospect  that 
it  will  be  more  notable  in  prof)ortion  than  heretofore. 

While  the  growth  of  city  travel  is  in  some  respects  a  special  problem,  since  its  increase 
results  in  great  part  from  the  increasing  distances  which  larger  population  brings,  yet  it  is 
mainly  but  one  expression  of  a  general  law  brought  out  in  Chap.  XXI.,  that  traffic  tends 
to  increase  about  as  the  square  of  the  population  or  sources  of  traffic  united  by  con- 
venient means  of  communication.  Quite  as  forcible  an  illustration  of  this  law  is 
obtained  by  studying  the  growth  of  traffic  of  States  and  the  United  States  as  elsewhere- 
presented.     Compare  Tables  14,  15,  16;  also  Tables  2,  3,  7,  21  to  28,  34,  etc. 


960.  It  is  plain  that  we  cannot  always,  nor  ordinarily,  count 
on  any  series  of  points  A,  B,  C,  D,  E,  etc.,  each  of  which  is  ex- 
actly equal  to  each  other,  but  we  may  push  the  generalization  a 
little  farther. 

Taking  the  entire  population  of  a  country,  or  of  a  continent, 
or  of  the  world,  and  conceiving  it  to  be  made  up  of  a  great  num- 
ber of  units,  either  of  single  individuals  or  of  groups  of  10,  100, 
1,000,  or  1,000,000  individuals,  it  is  plain  that  each  one  of  these 
units  has  potential  traffic  relations  with  every  other  unit.  The 
components  of  each  unit  visit  those  of  the  other  socially  ;  they 
buy  and  sell  from  each  other  ;  they  visit  each  other  in  the  hope 
of  buying  and  selling;  they  produce  more  (this  is  an  invariable 
law)  for  the  especial  purpose  of  supplying  the  necessities  of  others 
with  whom  they  have  or  finally  secure  traffic  relations.  Until 
such  traffic  facilities  exist,  these  relations  are  inchoate,  or  merely 
potential.     As  the  facilities  are  extended  they  become  actual'; 


^ 


716       CNAP.  XXI.— LAW  OF  INCREMENT  OF   TRAFFIC. 

and  they  sliould  tend  to  become  actual,  if  our  reasoning  has 
been  correct,  about  in  proportion  to  the  square  of  the  facilities 
afforded  and  of  the  population  served.  Experience  seems  to 
show  that  they  do  tend  to  increase  about  in  this  ratio,  some  evi- 
dence of  which  fact  is  contained  in  Table  192,  as  also  in  Table 
14,  15,  16,  and  others  referred  to  below  Table  192  ;  but  however 
this  may  be,  that  they  increase  in  very  much  more  than  direct 
ratio  is  beyond  all  question. 

It  is  therefore  unnecessary  to  take  each  individual  town  as 
a  traflSc  unit,  as  we  have  done  heretofore.  We  may  regard 
€ach  individual  person  as  the  traffic  unit,  and  while  it  will  be 
by  no  means  literally  true  that  he  will  have  actual  traffic  rela- 
tions with  all  those  for  whom  the  facilities  exist,  but  only  with 
■every  tenth,  hundredth,  thousandth,  or  millionth  person,  accord- 
ing to  his  character  and  occupation,  yet  practically  the  result  is 
the  same.  His  aggregate  contributions  to  railway  traffic  will 
vary  in  close  accordance  with  the  total  population  connected  with 
him  by  traffic  facilities,  and  his  payments  to  any  particular  line 
will  be  in  direct  proportion  to  that  fraction  of  the  total  of  the 
whole  population  connected  with  him  by  traffic  facilities  which  is 
reached  by  him  over  that  particular  line. 

961,  We  have  thus  only  to  consider  the  points  A,  B,  C,  D,  E^ 
Figs,  233-237,  to  represent  single  individuals  instead  of  towns  or 
other  traffic  points,  and  to  consider  their  number  n  to  be  indefi- 
nitely multiplied,  when  precisely  the  same  process  of  reasoning 
we  have  just  applied  to  towns  leads  to  precisely  the  same  conclu- 
sion as  respects  individuals. 

We  then  have  n{n  — i)  =  «'  [Eqs.  (4)  and  (5)]  almost  exactly; 
whence,  if  7^=  the  actual  tributary  population  on  the  line  and 
p  =^  3.  possible  additional  population,  the  percentage  of  increase 
in  traffic  Z,  all  other  things  being  equal,  will  be, 


(6) 


CffAP.  XXI.— LA  PI'  OF  INCREMENT  OF   TRAFFIC.        yi? 


In  other  words,  if  we  have  1,000,000  tributary  population  and 


can  add  100,000  more,  each  unit  of  which  is  of  the  same  traffic- 
producing  capacity,  the  increase  will  be 

(10 +1)' 

1 —  —1  =  21  per  cent. 

10  ^ 

If  our  original  population  were  500,000,  we  should  have,  all 
other  things  being  equal, 

(5  +  i)' 

— Ti '  =  44  per  cent. 

This  is  really  a  more  correct  way  of  arriving  at  the  theoreti- 
cal effect  of  additional  sources  of  traffic  than  that  used  in  Table 
191,  since  it  takes  each  individual  as  the  unit,  instead  of  a  group 
of  20,000  or  100,000.  It  gives  a  somewhat  smaller  percentage,  but 
the  difference  is  not  great  enough  to  make  a  material  difference 
in  what  are  at  best  merely  illustrative  computations  ;  not  sus- 
ceptible, nor  supposed  to  be  susceptible,  of  exact  application  in 
practice,  except  as  indicating  the  comparative  probable  revenue, 
all  other  things  being  equal,  of  alternate  routes  between  the  same 
termini. 

962.  In  any  actual  instance,  of  course,  all  other  things  would 
be  more  or  less  unequal,  and   hardly  any  of  them  equal,  so  that 
it  would  be  quite  impossible  to  make  any  very  precise  estimates- 
by  the  formula  given.     In  the  first  place,  it  is  impossible  to  more 
than  guess  at  the  true  tributary  population.     That  which  is  ap- 
parently tributary,  from  being  on  the  line,  is  decreased  by  the 
competition  of  other  lines,  so  that  only  a  fraction  of  it  is  really 
tributary  ;  while,  on  the  other  hand,  there  may  be  an  immense 
population  beyond  the  limits  of  the  line  itself  which  is  indirectly 
tributary  to  it  through  the  medium  of  other  lines,  as  in  the  case 
of  the  trunk  lines  from  the  sea-coast  to  the  west.     In  the  second 
place,  a  mere  enumeration  of  heads  is  a  very  rude  index  of  the 
traffic  value  of  those  heads.     A  great  mining  or  manufacturing 
or  commercial  point  will  contribute  vastly  more  traffic  per  head 
than  other  more  inert  communities,  and  a  large  town,  almost  al- 
ways, more  per  head  than  a  small  town. 


mw^. 


I 


( 


7i8 


CHAP.  XXI.— TRUNK  LINES. 


963.  Nevertheless,  when  we  connect  Smithville  with  our  line 
we  get  the  New  York-Smithville  as  well  as  the  Smithville- 
New  York  traffic;  and  the  traffic  of  New  York  is  made  up  only  of 
the  aggregate  of  that  to  thousands  of  Smithvilles,  of  which  we 
get  those  which  we  reach  in  one  way  or  another  by  our  line. 
Thus  the  discrepancy  on  account  of  the  difference  in  the  traffic- 
producing  capacity  of  individuals  is  less  than  might  be  supposed, 
and  Tables  14,  15,  16,  and  191,  with  various  others  in  this  volume, 
show  that  the  law  holds  tolerably  well  when  applied  on  a  large 
enough  scale  to  eliminate  sources  of  irregularity,  while  there  are 
innumerable  examples  of  single  lines  whose  prosperity  or  ad- 
versity can  be  directly  shown  to  imply  the  existence  of  some 
«uch  law. 

These  fundamental  truths  being  granted,  therefore,  it  leads 
very  directly  to  certain  conclusions  as  to  the  proper  manner  of 
laying  out  both  trunk  lines  and  branch  lines  ;  conclusions  which, 
while  they  may  be  difficult  to  apply  so  exactly  as  to  avoid  a  con- 
siderable percentage  of  error,  will  yet  be  so  definite  that  the  radi- 
cal error  of  mistaking  black  for  white,  so  to  speak — taking  that 
for  the  best  course  which  is  rather  the  worst  course, — is  not  likely 
to  occur. 

TRUNK    LINES. 

964.  Trunk  or  main  lines  may  be  roughly  divided  into  two 
classes:  those  which  are,  and  those  which  are  not,  liable  to  be 
subjected  to  close  competition  at  almost  every  important  point. 

Almost  all  lines  in  the  United  States  belong  to  the  former 
class.  Their  only  permanent  protection  against  competition,  in 
most  cases,  is  to  throw  out  a  skirmish-line  of  branches  and  par- 
allel routes  so  as  to  cover  securely  a  considerable  territory;  and 
this  is  one  great  reason  for  the  tendency  in  that  direction  which 
is  so  notable,  and  which  has  already  gone  so  far  that  more  than 
half  the  mileage  of  the  United  States  is  controlled  by  a  dozen 
managements,  with  every  prospect  that  the  tendency  to  consoli- 
dation will  grow  still  stronger.  Table  193  shows  how  far  this 
tendency  has  already  gone.  Another  and  still  stronger  reason, 
however,  directly  results  from  what   has  preceded — that  every 


CHAP.  XXI.— TRUNK  LINES. 


719 


Table  193. 

Length  of  Road  and  Gross  Earnings  of  Fourteen  Great  Systems  of 

Road  in  the  United  States,  1881. 

[Abstracted  from  a  Paper  by  Wm.  P.  Shinn  on  «'  Increased  Efficiency  of  Railways  for 
the  Transportation  of  Freight,"  Trans.  Am.  Soc.  C.  E.,  November,  1882,  with  the  addi- 
tion of  the  Baltimore  &  Ohio,  Atchison,  Topeka  &  Santa  Fe,  and  some  minor  details.] 


New  York  Central  &  Hudson  River. 
Lake  Shore  &  Michigan  Southern  ... 

Canada  Southern 

Michigan  Central 


Total  New  York  Central  System . . 
Ne%v  York,  Lake  Erie  b'  Western. 

Pennsylvania,  Eastern  System 

Western      "      


Total  Pennsylvania , 

Baltimore  &  Ohio,  Eastern  System. 
'*       Western      "     . 


Total  Baltimore  Ss*  Ohio 

Total  Four  Trunk  Lines , 

Per  cent  of  total  United  States. 


Wabash   St.  Louis  &  Pacific 

Chicago,  Burlinerton  &  Quincy 

Chicago,  Rock  Island  &  Pacific... 

Illinois  Central,  Northern  

New  Orleans  line. 


Chicapro&  North-Western 

Chicago,  Milwaukee  &  St.  Paul 

Missouri  Pacific,  Main  System 

Leased  and  controlled  lines. 

Louisville  &  Nashville,  Owned  

Leased  lines 

Louisville,  Cincinnati  &  Lexington 

Nashville.  Chattanooga  &  St.  Louis 

Georgia  Railroad  System 

Atchison,  Topeka  &  Santa  F^ 

Union  Pacific,  Proper 

Lines  in  interest , 

Central  Pacific 

Southern  Pacific *.!!***!  i ! 


Total  Ten  Systems  othsr  than  N.Y. Trunk  Lines. 
Per  cent  of  total  United  States 


Miles. 


993 

403 
950 


3,523 
1,020 


3,041 
2,529 


5,570 


595 
959 


I.5S4 


11,667 
12.35  P-  c. 


1,320 
571 


3,348 

3,160 
1,335 


1,891 
3,276 
4,260 


X,OI2 

4,773 


1.438  I 

434$ 
272 

521 

641 


,5,785 


1,821 
2,449 


3,034 
2,240 


2,874 
1,281 


4,270 


4,155 


36,754 
38.90  p.  C. 


Gross  Earnings. 


$29,322,532 

17,880,000 

3.369,259 

8.8cx>,486 


$44,224,716 
31,058,790 


159,372,277 
20,715,605 


75,283,506 


18,463,877 


Per  Mile  $14,900 


23 -97  p.  c. 


$8,640,957 
19.087,484 


$14,467,790 

21,176.455 
11,956,907 


10,793,105 
»9,334,o72 
17,025,461 


$10,911,650 

1,196,112 
2,256,186 
2,543.032 


$24,258,817 
7,608.936 


$24,094,101 
3,435  945 


27,728,441 

16,906,980 
",584,509 

31,867,753 
27.530.046 


$211,371,510 
Per  Mile  $5,751 
29.14  p.  c. 


"   I 


^:ll 


t 


720 


CHAP.   XXI.— TRUNK  LINES. 


CHAP,   XXI.— TRUNK  LINES. 


721 


Table  193. — Continued. 


• 

Miles. 

Gross  Earnings. 

Total  Fourteen  Great  Systems 

48,431 
51.25  p.  c. 

$385,206,784 
Per  Mile  $7,956 
53"  p.  c. 

Per  cent  of  total  United  States 

Total  of  Minor  Lines  of  the  United  States,  under 
300  to  400  different  managements 

Percent  of  total  United  States 

46,065 
48.7s  P.O. 

«      „., •340,118,335 
Per  Mile  $7,383 
46.89  p.  c. 

Total  of  the  United  States  in  1881,  of  which  earn- 
incTS  were  rei>orted 

94,486 

Per  Mile  $7,677 

Since  1881  there  have  been  many  changes  in  the  details  of  the  above  table,  but  the 
great  sjrstems  given  probably  cover  in  the  aggregate  a  still  larger  proportion  of  the  total 
mileage  of  the  United  States.  There  were  in  1881  a  total  of  104,813  miles  reported  built, 
10,327  miles  of  which  did  not  report  earnings,  being  largely  newly  built  lines. 

addition  to  the  tributary  population  makes  the  revenue  per  head 
from  the  previously  tributary  population  greater.  This  may  not 
often,  perhaps  never,  be  more  than  dimly  felt,  but  that  it  is  the 
true  course  and  justification  for  many  such  extensions  we  cannot 
doubt. 

Nevertheless  there  are  certain  mountainous  or  sparsely  popu- 
lated and  poor  regions,  in  this  and  all  other  countries,  where 
reasonable  freedom  from  competitive  lines  is  assured,  as  in 
Mexico,  the  lines  in  which  afforded  some  instructive  examples  of 
the  right  and  wrong  way  of  laying  out  main  lines. 

966.  Bearing  in  mind  what  we  have  already  seen  as  to  the 
small  expense  of  operating  extra  distance  (par.  197),  the  appreci- 
able additions  to  revenue  which  may  be  expected  to  arise  from 
it  (par.  230),  and  the  small  effect  of  moderate  additions  of  dis- 
tance to  discourage  traffic,  there  can  be  no  question  that  the 
fundamental  rule  for  laying  out  such  lines — deviated  from  only 
for  good  special  reasons — should  be  to  link  together  the  largest 
possible  population,  regardless  of  minor  losses  of  distance,  pro- 
vided    THE    AGGREGATE    POPULATION    PER    MILE    OF    ROAD    is    not 

diminished  (par.  237),  or  even  sometimes  if  it  is.     An  ultimate 


limit,  beyond  which  it  would  certainly  be  unwise  to  go,  and 
hence  which  should  not  be  closely  approached,  is  that  the  in- 
crease per  cent  of  distance  should  not  exceed  the  increase  per 
cent  of  probable  revenue,  according  to  eq.  (6),  par.  961. 

966.  The  most  marked  exception  to  this  rule  is  when  the  dif- 
ference of  distance  becomes  so  great  as  to  seriously  discourage 
traffic,  or  encourage  the  construction  of  a  more  favorably  situ- 
ated competing  line. 

A  further  exception  is  when,  by  passing  midway  between  two 
traffic  centres,  neither  of  which  can  be  reached  readily  by  the 
main  line,  both  may  be  served  fairly  well  by  branches  or  other- 
wise (par.  66). 

Any  marked  difference  in  grades  or  costs  of  construction  may 
of  course  make  a  difference  ^xlh^r  pro  or  con  j  but  entire  disre- 
gard of  the  rule,  by  deliberately  neglecting  intermediate  traffic 
points  for  the  sake  of  through  traffic,  usually  means  financial 
failure. 

967.  Several  instances  of  the  application  of  these  general  rules  may 
be  studied  on  any  map  of  Mexico,  showing  the  existing  railway  lines 
Ihe  most  pronounced  is  the  choice  between  the  route  from  the  City  of 
Mexico  to  the  United  States  {via  the  Mexican  Central  or  the  Mexico 
National  routes),  either  of  which  could  be  chosen  by  the  Central  at  the 
time  the  concessions  were  granted. 

The  longer  line,  passing  through  the  heart  of  Mexico,  and  thence  con- 
nectmg  at  El  Paso  with  the  Atchison.  Topeka  &  Santa  Fe.  was  chosen. 
The  grounds  for  this  choice,  beyond  question,  were  that  (i)  railways  in 
Mexico  were  lo  be  profitable ;  (2)  the  more  railway  controlled  the  more 
aggregate  profit,  even  if  the  less  per  mile ;  (3)  a  long  line  through  the 
heart  of  a  country  must  in  the  long-run  be  the  best  line. 

On  the  other  hand,  the  choice  violated  two  of  the  fundamental  rules 
which  have  been  laid  down.  First,  it  seriously  discouraged  traffic  be- 
tween Mexico  and  the  United  States  by  burdening  that  which  passed 
over  It  with  nearly  500  miles  of  extra  haul :  this  practically  insuring  that 
the  National  line,  when  completed,  would  be.  or  might  easily  make 
•tself.  the  leading  through  line.  Secondly,  it  very  materially  decreased 
the  average  tributary  population  per  mile  over  what  it  would  have  been 
nad  the  Mexican  Central  line  been  followed  as  far  as  Celaya.  in  Central 
Mexico,  and  the  Mexican  National  from  there  north  ;  especially  had  the 


i 


722 


CHAP.   XXI.— TRUNK  LINES. 


CHAP.  XXI.-^TRUNK  LINES. 


towns  of  Silao,  Guanajuato,  and  Leon  been  linked  to  this  main  line  by  a 
branch,  as  they  might  have  been  later. 

Had  the  Mexican  Central  been  built  by  this  line  there  can  be  little 
doubt  that  it  would  be  to-day  (1886)  a  most  flourishing  property,  both 
because  its  investment  would  have  been  smaller  and  its  traffic  larger. 

968.  On  the  other  hand,  leaving  the  flourishing  town  of  Durango  on 
one  side,  although  it  saved  distance  in  what  was  already  a  disastrously 
long  line,  was  probably  an  error,  although  this  cannot  be  asserted  with 
much  posiliveness.  The  loss  of  perhaps  50  or  60  miles  more  would  have 
taken  the  line  through  a  much  better  country,  actual  and  prospective, 
for  nearly  400  miles,  the  country  through  which  the  line  was  actually 
run  having  been  almost  the  poorest  possible ;  while  saving  that  loss  of 
distance  did   not  materially   improve  its  already  bad  case  as  respects 

through  traffic. 

969.  The  National,  for  its  part,  fell  into  an  error  which  has  often 
been  committed  before,  and  never  without  loss— attempting  to  start  a 
new  terminal  port  at  Corpus  Christi,  instead  of  making  for  Galveston 
direct.  Such  projects  for  changing  the  established  course  of  trade  seem 
to  have  a  peculiar  fascination  for  sanguine  projectors,  but  it  is  always  all 
but  certain  that  they  will  end  in  failure. 

The  more  instructive  example  to  be  found  on  the  National  lines,  how- 
ever is  a  striking  instance  of  how,  when  traffic  is  at  best  thin  and  prob- 
ably non-competitive,  connecting  the  largest  possible  population  by  the 
main  line  is  almost  surely  the  wiser  course.  Fig.  239  shows  this  instance, 
the  dotted  line  being  what  had  been  projected,  and  the  full  line  the  route 
finally  chosen  by  the  company  on  the  writer's  recommendation. 

The  full  line  seems  a  most  roundabout  course  for  a  main  line,  espe- 
cially as  the  total  mileage  to  be  constructed  was  not  diminished,  but 
rather  increased.  It  was  to  be  remembered,  however,  first,  that  the 
traffic  was  thin  and  non-competitive;  secondly,  that  the  number  of  trains 
*'could  not  be  great;  thirdly,  that  reasonably  good  facilities  for  continu- 
ous traffic  between  every  one  of  the  many  points  connected  by  the  line 
was  desirable  ;  and,  finally,  that  with  a  traffic  thin  at  best  the  mainte- 
nance and  separate  operation  of  branch  lines  is  very  burdensome.  It  was 
therefore  decided,  as  respects  the  line  from  Morelia  to  Zamora  and  La 
Piedad,  that  it  would  be  better  to  make  the  branch  to  Patzcuaro  a  part 
of  the  main  line,  thus  accomplishing  the  double  end  of  decreasing  the 
aggregate  mileage  to  be  operated  and  maintained,  and  facilitating  Patz- 
cuaro^Zamora  traffic  and  (by  more  trains)  Patzcuaro-Morelia  traffic, 
while  gaining  more  revenue  from  through  traffic  by  not  materially 
heavier  through  rates. 


72Z 

970.  Beyond  La  Barca.  although  the  line  had  alTeady  been  runout 
of  Its  course  from  Patzcuaro  to  the  Pacific,  it  was  decided  to  run  it  still 
farther  north  to  take  in  the  important  city  of  Guadalajara,  the  second 
city  m  Mexico  (about  80.000  inhabitants),  whence  the  line  started  almost 
due  south  for  Colima  and  the  coasts.  This  change  alone  much  more 
than  doubled  the  probable  traffic  per  mile  of  the  road,  and  it  would  have 
been,  from  an  economic  point  of  view,  a  very  great  error  not  to  do  it. 


Fig.  239. 

oni"ff^'^'"yI"  ''"^  '"'°  '''°-°"^  f™"  Guadalajara  to  the  coast,  and 
one  from  Guadalajara  to  Mexico ;  but  all  the  more  it  was  desirable.  The 
Sharply  accentuated  topographical  cond.tions.  which  it  is  impossible  to 
describe  with  more  detail,  made  this  particularly  clear. 

971.  Trunk  lines  open  to  destructive  competition,  and  able 
to  command  only  a  narrow  belt  on  each  side  of  them  as  their 
natural  tributary  territory,  nor  that,  unless  they  afford  almost  as 
good  accommodations  as  it  is  possible  to  give,  can  of  course 


724 


CHAP.  XXI.^TRUNK  LINES, 


CHAP.  XXI. -TRUNK  LINES. 


afford  no  such  sacrifice  as  this.  As  the  subject  is  a  large  and 
complex  one,  the  conditions  of  success  and  failure  may  perhaps 
be  more  usefully  indicated  in  a  small  space  by  a  few  notes  from 
the  history  of  the  actual  trunk  lines,  and  notably  of  the  four 
trunk  Wn&s par  excellence — the  New  York  Central  &  Hudson  River, 
Erie,  Pennsylvania,  and  Baltimore  &  Ohio— than  by  a  more  gen- 
eral discussion, 

972.  The  New  York  Central  is  probably  the  most  striking  example  in 
the  whole  world  of  two  truths:  That  lines  connecting  the  largest  aggre- 
gate of  population  will  be  likely  to  lie  on  the  most  favorable  route  for  easy 
grades,  and  that  easy  grades  give  an  overwhelming  advantage  in  handling 
low-rate  traffic  especially.  As  a  through  line  the  New  York  Central  was 
not  made, — it  grew.  Some  fifteen  different  corporations  built  its  New 
York-Chicago  line,  each  without  a  thought  of  doing  more  than  connect- 
ing its  own  particular  termini.  Consequently  it  did  connect  them  effec- 
tually, and  the  magnificent  string  of  towns  from  which  the  New  York 
Central  has  drawn  its  chief  prosperity  was  the  result. 

Its  intended  rival,  the  West  Shore,  was  built  in  a  very  different  way. 
It  was— unfortunately— planned.  From  attaching  exaggerated  impor- 
tance to  through  traffic  and  to  the  effect  thereon  of  accommodating  way 
traffic,  or  from  other  cause,  several  of  the  most  important  local  points,, 
as  notably  Albany  and  Rochester,  were  left  at  one  side,  and  others 
ill  served,  there  being  hardly  a  competitive  point  on  the  line,  not  even 
its  two  termini,  as  well  served  by  it  as  by  the  Central.  This  may  have 
been  unavoidable.  The  expense  alone  of  doing  otherwise  would  have 
been  enormous,  and  had  the  expense  been  incurred  it  might  not  have 
insured  the  success  of  the  line ;  but  the  fact  that  it  was  not,  foredoomed 
failure— for  the  two  reasons,  that  the  line  which  is  only  half  as  convenient 
as  another  does  not,  therefore,  get  half  as  much  business,  but  none  at  all 
(par.  51  et  al.)\  and  for  the  further  reason  (par.  959),  that  the  value  of  a 
line  is  as  the  square  of  the  population  best  served  by  it. 

973.  From  the  through  business  proper  the  New  York  Central  has 
derived  comparatively  little  benefit.  Its  greater  length  reduces  its  aver- 
age receipts  per  mile  on  competitive  traffic  materially  below  those  of  the 
Pennsylvania,  and  the  magnificent  water-way  which  is  immediately  adja- 
cent to  it  for  the  entire  distance  from  New  York  to  Chicago  has  tended 
powerfully  to  still  further  curtail  its  rates.  But  its  unequalled  grades  (by 
much  the  most  favorable  in  the  world  for  a  line  of  such  length),  and  the 


725 

indirect  benefit  of  its  immense  local  traffic,  which  alone  required  and 
supported  all  the  staff  and  plant  of  a  great  railway,  enabledTts  thigh 
busmess,  vast  as  .twas,  to  be  handled  as  so  much  extra  business  the  onlv 
expense  for  which  was  the  direct  outlay  for  wages  and  fuel  and  a  smaH 
amount  for  wear  and  tear  of  track. 

Of  no  other  trunk  line  was  this  so  nearly  true,  but  the  lower  rate  per 
^^k  Centrlf hir '  'T  f  ^  ^"^(--P^-^ly)  raw  material  on  t^New 
.food    T^  f    '"^  P'^"^""^  ^"^  ^^^"^^  ^h'^h  is  not  always  under- 

Cn  hilh  onTt""\^^'"''^"^^^P^"^^^^^  ^^^^'P^^  ^^  -^  ha's  always 
been  high  on  it.  as  shown  more  clearly  in  Table  37,  page  1 10,  viz. : 


New  York  Central. 
Erie 

Pennsylvania,    .    . 
Baltimore  &  Ohio, 


1876-80. 

61.3 

70.0 

557 
53-9 


-AVERAGE- 


1881-85. 
67.9 
69.7 

56.0 


This  contrast  is  immutably  fixed  by  tlie  nature  of  the  traffic  and  th^ 
operatmg  conditions,  and  gives  no  indication  of  relative  efficiency  of 
operation,  as  has  often  been  carelessly  assumed.  emciency  of 

^JJX  ^'^"'"7  '"  ""  P^'""'^^''  °'  °P--«n8  expenses  which  is  visible 
above  m  the  figures  for  every  one  of  the  three  lines  but  the  Erie  is  due  <:in,ni„ 
tothe  enormous  reduction  in  rates  in  recent  years,  the  later  Tei  g  at "  "'  a 
cause  and  effect  of  the  still  more  enormous  increase  in  volume  of  traffic  The 
astoundmg  and  almost  incredible  figures  for  this  change  are  shown  in  Table  lo. 
an  graphically  in  Fig.  .40.  The  history  of  the  worfd  affords  no  parl^^^l  t^^  " 
andu,soneof  the  strongest  proofs  that  we  have  not  erred  far  in  our  colclu 
sions  in  the  first  part  of  this  chapter.  conclu- 

V   Tn  "^"^i  P^.^f  ^^^^ANIA  is  in  many  respects  a  contrast  to  the  Ne«r 
York  Central.     L,ke  the  latter,  it  grew,  rather  than  was  made,  as  a  Ne" 

West  t'piXdlT''  T"'  'r-  ''™^'^"'^'  *°  ■'■•'"^  '-<«=  f™- 1"! 

west  to  Philadelphia  only,  ,t  chanced  to  lie  in  the  most  favorable  Dosi 

.on  for  a  short  low-grade  line  between  New  Vork  and  the  Wes     "^he 

.rresistible  tendency  of  events,  and  of  its  situation,  linked  with  ita  Pe^t 

sylvan  la-New  York  line  on  the  East,  and  a  branching  network  of  Hnes" 

hrough  the  West.     In  comparing  it  with  the  New  vfrk  Central  one  !s 

■mmediately  struck   by  the  contrast   in   this  respect  which    it    poLv 

^ffords.  and  while  much  of  this  may  well  be  due.'and  no  dou^  is' to  a 

ZC-:Zltl''  r"°r'  ^''""'"""  °'  ^"^  "^"^Sers,  an  underlying  r^a! 
son  for  it-of  which,  perhaps,  no  one  was  conscious-is  that  the  Pennsyl- 


;;i 


726 


CHAP.  XXI.— TRUNK  LINES. 


Table  194. 

Increase  of   Traffic  and  Decrease  in  Rates  on  Various  Groups  of 

American  Lines,  1865-1885. 

[The  last  part  of  this  table  is  shown  graphically  in  Fig.  240.] 


Seven  Trunk 
Lines. 

Six  Chicago 

Roads. 

Twenty-one  Leading  Lines. 

Year. 

Ton- 
miles. 

^'=    ^ 
1,000,000.) 

Rate. 
Cents. 

Ton- 
miles. 
(I  = 
1,000,000.) 

Rate. 
Cents. 

I  —  1,000,000. 

Freight 
Earnings. 

91000.) 

Rate. 
Cents. 

Tons. 

Ton- 
miles. 

1865  ... 

1.654 

2.900 

a.  546 
2.306 

1.951 
1.715 

5»3 

3.642 

22 

2,370 

$69,825 

2.945 

1866.... 
1867  — 

i868.... 
1869... 

2,044 
2,258 

2,651 
3.159 

893 
1,054 

3-459 
3-»75 

3.154 
3.036 

a8 
30 

35 
39 

2,981 

3,223 

3.743 
4.408 

77,003 
75,381 

80,141 
87.426 

2.582 
2.338 

3.140 
1-983 

1870  . . 

3.744 

1.585 

1,234 

2.423 

39 

5.IH 

88.488 

1.731 

1871 

187a 

1873... 
1874.... 

4.341 
5.»8i 

5.782 
5.879 

1.478 
1-475 
1.470 
1-342 

1,233 
1,337 

».749 
1,851 

2.509 

2.583 

2.188 
2.160 

50 
59 

67 
65 

5.937 
6,973 

7.885 
8,020 

8,380 

97,186 
112,408 

127,045 
108,598 

1.636 
1.612 

1. 611 
1-354 

1875   ... 

S.937 

1. 161 

1.904 

1.979 

63 

107.657 

1.284 

1876.... 
1877.... 

1878.... 
1879  ... 

6,739 
6,536 

8,853 

10,T20 

.983 
.971 

.807 

•725 

1.994 
a,2ii 

2,823 
3.470 

1.877 
1.664 

1.476 
1.280 

69 
73 

9,072 
9.131 

10,433 

»3.033 

102,009 
100,804 

105,973 
114,255 

1.124 
1.103 

1. 015 

0.876 

1880  ... 

XO.544 

.840 

4.544 

1.266 

106 

14.085 

139,331 

0.988 

x88i.... 
1883.... 

1883... 
1884.   .. 

11,659 
11,189 

11,141 
10.719 

.759 
.665 

.842 
.740 

4,435 
5,04» 

5,768 
5.940 

1.420 
1-364 

1.308 
1.251 

126 
134 
14a 
144 

16,074 
»6,075 

17.307 
17.501 

18,837 

146,699 
147,719 

167.564 
153.735 

0.912 
0.918 

0.968 
0.878 

1885  ... 

".331 

.636 

6.287 

1.200 

151 

144,562 

0.767 

This  table  is  from  data  compiled  by  Mr.  Henry  V.  Poor.  The  seven  trunk  lines  are 
the  Pennsylvania ;  Pittsburg,  Fort  Wayne  &  Chicago ;  New  York  Central ;  Lake  Shore; 
Michigan  Central ;  Boston  &  Albany  ;  and  New  York,  Lake  Erie  &  Western.  The  six 
Chicago  lines  are  the  Illinois  Central ;  Chicago  &  Alton ;  Chicago  &  Rock  Island ; 
Chicago,  Burlington  &  Quincy ;  Chicago  &  Northwestern ;  Chicago,  Milwaukee  &  St. 
Paul. 

These  thirteen  roads,  with  eight  others  of  most  prominence,  are  included  in  the  last 
part  of  the  table,  from  which  Fig.  240  was  constructed. 


vania  had  more  to  gain  by  extending  itself  in  all  directions,  and  more  to 
lose  by  not  doing  so.  Additional  traffic  we  have  seen  (par.  41)  to  be 
that  on  which  railways  grow  rich.  With  the  greatest  city  of  the  country 
only  ninety  miles  off,  it  was  mdispensable,  to  secure  the  utmost  traffic 
from  it,  to  reach  it  by  its  own  lines,  even  with  a  friendly  independent 
connection  as  an  alternative.     The  futility  of  terminating  a  line  at  any 


CHAP.  XXI. -TRUNK  LINES. 


727 


other  than  the  largest  available  city  was  never  better  illustrated,  unless 
by  the  experience  of  the  Erie  at  Dunkirk  on  a  smaller  scale.     Perhaps 


Fig.  241  is  as  good  an  object-lesson  as  could  be  found  as  to  the  folly  of 
such  attempts,  even  when  circumstances  seem  to  especially  favor  what 
sanguine  projectors  look  on  as  a  "  fair  divide"  of  an  enormous  traffic. 


1 


728 


CHAP.  XXI.— TRUNK  LINES. 


CHAP.  XXL— TRUNK  LINES. 


976.  A  larger  reason,  which  includes  the  first,  was  that  the  Pennsyl- 
vania  was    so    situated 


729 


12s 


Fig.  941. — NoRiHWKSTERN  Grain  Reckipts  at  Various  lead- 
ing Shipping  Points,  1876-1885. 


as  to  form  a  very  short 
line  between  almost  all 
points  on  the  West  and 
the  sea-coast.  This  in- 
sured good  average  rates 
per  mile,  while  the  abun- 
dance of  coal  and  iron 
on  the  line,  and  the 
large  amount  of  favor- 
able grades  insured  low 
operating  expenses.  The 
Pennsylvania  had  much 
to  gain,  therefore,  from 
handling  additional 
through  traffic  OVER  ITS 
OWN  LINES,  according 
to  the  law  laid  down  in 
par.  211 — that  the  only 
conditions  under  which 
a  line  could  reap  the 
full  benefit  of  being  a 
short  line  was  that  it 
should  reach  all  its  im- 
portant traffic  points  by 
its  own  lines.  The  Penn- 
sylvania was  such  a  short 
line ;  it  proceeded  to 
satisfy  the  other  half  of 
the  true,  and  too  little 
considered,     conditions 


[One  nf  many  illustrations  of  the  prrsistency  with  which    O*    prosperity,   aS   it  WaS 
..affic  flows  to  leading  and  well-established  centres,  as  com- 
pared with  the  irregularity  and  uncertainty  of  traffic  at  minor 


traffic  flows  to  leading  and  well-established  centres,  as  com-    j^g   natural    policy  tO  do. 


points]  Until  it  did   so   it  was, 

by  its  existence  and  facilities,  making  the  fortunes  of  other  lines  in- 
stead of  its  own. 

Moreover,  the  additional  through  traffic,  which  it  could  secure  by 
controlling  its  connections,  was  a  great  object  to  it,  for  it  made,  and 
must  always  continue  to  make,  a  comparatively  large  profit  on  it,  while 


to  the  New  York  Central  it  was  a  small  object,  because  it  made  a  small 
profit  out  of  it.  The  New  York  Central's  chief  reliance  has  been  on  its 
iocal  trafiic ;  its  through  rates  per  mile  being  necessarily  low  at  best 
even  on  that  traffic  so  situated  as  to  come  to  it  most  naturally  while  its 
expenses  were  higher  because  of  dear  fuel.  Had  it  gone  much  out  of 
Its  way  to  seek  more  through  traffic,  its  average  fates  per  mile  would  have 
been  lower  yet.  and  un remunerative.     Therefore  it  has  not  done  so. 

977.  In  part,  this  likewise  explains  why  the  unfortunate  Erie  has 
never  tended  to  ramify  throughout  the  West ;  but  the  Erie  is  an  example  of 
a  line  which  has  succeeded  in  spite  of  this  disadvantage,  for  four  reasons  • 
^  I.  By  terminating  at  the  greatest  city  of  the  East,  and  (after  correct- 
ing the  error  of  attempting  to  make  a  new  great  city  at  Dunkirk)  at  the 
chief  traffic  point  at  the  eastern  end  of  the  great  lakes,  making  two  ad- 
mirable termini. 

2.  By  its  skilful  location,  most  of  its  line  being  on  very  low  grades 
mdeed.  although  it  has  some  high  summits  and  bad  sections. 

3.  By  its  local  coal  traffic  and  cheap  supply  of  fuel. 

4.  By  its  large  and  growing  local  traffic— less  than  the  New  York  Cen- 
trals.  but  larger  than  the  Pennsylvania's,  and  until  very  recently  little 
subject  to  competition. 

These  gave  it  great  powers  of  offence  against  the  New  York  Central 
and  It  has  been  able  to  command  at  all  times  a  fair  proportion  of  the 
traffic  wh.ch  lines  in  the  Central  interest  brought  to  Buffalo.  But  the 
Erie  s  prosperity  has  been  injured  by  three  causes  quite  as  potent  • 

I.  Of  ail  the  great  Eastern  cities,  the  Erie  reached  advantageously 
^nly  ONE,  whereas  the  New  York  Central  reached  two.  New  York  and 
Boston  (in  fact,  all  New  England  and  a  large  part  of  the  Canada  trade 
has  been  almost  monopolized  by  the  Central),  and  the  Pennsylvania 
reached  four;  the  two  greatest  directly.  New  York  and  Philadelphia 
and  Boston.  Baltimore,  and  Washington  fairly  well.  This  has  been  the 
pnmary  difficulty  with  the  Erie.  "  To  him  that  hath  shall  be  given  "  It 
might  pay  the  Pennsylvania  well  to  control  a  line  to  Smithville  in  order 
to  secure  thereby  its  traffic  with  the  whole  Atlantic  coast,  when  it  would 
not  pay  the  Erie  at  all  to  own  a  line  to  it  which  would  secure  onlv  its  New 

The  Smithville-Pittsburg  traffic,  the  Smithville-Boston  traffic,  and  the 
bm.thville-jonesburg  traffic  naturally  gravitated  to  the  line  which  com- 
manded Its  other  traffic  East;  and  so  the  owners  of  lines  in  the  West 
were  naturally  drawn  most  to  that  line  which  offered  the  most  widely 


\\ 


K 


rT" 


730 


CHAP.  XXI.^TRUNK  LINES. 


CHAP.  XXI.— BRANCH  LINES. 


11 


«IK 

il 


ramifying  connections,  and  could  both  give  and  ask  better  terms.  Hence 
it  has  happened —  * 

2.  The  Erie  has  never  been  able  to  secure  good  Western  connec- 
tions.  The  only  serious  attempt  in  that  line,  until  1881,  was  the  old  At- 
lantic &  Great  Western,  one  of  the  most  ill-judged  enterprises  which  has 
ever  been  constructed  in  tjiis  country,  whose  failure  was  foredoomed  from 
the  beginning,  as  pointed  out  in  par.  215  et  seq.  We  may  be  tolerably  as-^ 
sured  that  the  Erie  never  will  have  a  great  system  of  connecting  lines,. 
for  it  is  not  planned  to  secure  them.  In  this  respect  the  history  of  the 
road  is  full  of  instruction. 

3.  The  Erie  has  been  peculiarly  unfortunate  in  its  past  management — 
in  part  from  lack  of  comprehension  by  its  foreign  owners  of  its  necessi- 
ties and  conditions. 

978.  The  Baltimore  &  Ohio  is  somewhat  of  a  contrary  example — 
of  a  line  whose  judicious  and  consistent  management  has  given  great 
financial  strength  to  a  property  under  many  disadvantages.  It  has 
obeyed  the  irresistible  tendency  of  the  times  by  extending  its  lines  X.o 
Chicago  in  the  West  (as  well  as  to  the  Ohio  River  tier  of  cities)  and  ta 
Philadelphia  and  New  York  on  the  East.  The  effect  of  the  latter  it  is 
as  yet  (1886)  impossible  to  foresee;  but  unless  the  laws  of  railway  pros- 
perity which  prevail  elsewhere  are  to  fail  in  its  case,  it  will  result  in  a 
very  great  addition  to  its  traffic,  giving  it  what  it  has  never  had  before — 
what  may  be  called  a  continental  traffic. 

For  the  Baltimore  &  Ohio,  as  it  stood  up  to  about  1880,  was  merely 
an  example  of  the  financial  strength  which  may  be  secured  by  locating 
between  considerable  local  sources  of  natural  traffic,  and  holding  strictly 
to  them.  Between  Baltimore  and  Washington  on  the  East  and  Pitts- 
burg, Cincinnati,  Louisville,  and  St.  Louis  on  the  West,  the  Baltimore  & 
Ohio  was  the  natural  channel  of  communication,  and  as  good  a  one  as 
could  be  secured.  A  large  coal  traffic  was  also  assured  to  it.  On  this  it 
prospered,  avoiding  dissipation  of  its  means  on  many  branches  and  con- 
nections. Nevertheless,  it  was  economically  impossible  that  it  should  fail 
for  long  to  reach  out  to  the  other  large  cities  mentioned,  and  to  transfer 
itself  from  a  local  line  to  a  national  one. 

Had  the  Pennsylvania  chosen  to  restrict  itself  to  its  main  line  between 
Pittsburg  and  Philadelphia,  with  a  few  only  of  the  most  necessary 
branches,  it  also  would  have  been,  and  might  have  indefinitely  continued 
to  be,  a  prosperous  local  line  of  the  kind  that  the  Baltimore  &  Ohio  was. 
It  might  even  have  earned  as  good  or  better  dividends  than  now,  but  its 
cost  and  value,  and  its  earning  capacity  likewise,  would   have  been  far 


73  r 


less,  and  its  aggregate  profits  vastly  less.     It  was  therefore  not  to  be  ex- 
pected, nor  for  the  public  interest,  that  it  should  pursue  this  policy. 

979.  In  the  history  of  these  four  trunk  lines,  could  we  afford 
space  to  consider  it  in  detail,  we  have  warning  of  almost  every 
possible  danger  which  can  arise  in  the  laying  out  of  trunk  lines 
—meaning  by  the  latter  term  not  necessarily  lines  of  enormous 
traffic  (see  par.  981),  but  lines  the  main  part  of  whose  traffic  is 
complete  in  itself,  so  that  they  are  not  mere  branches  or  feeders 
of  other  lines.  We  may  summarize  a  few  of  the  more  important 
conditions  of  success  in  such  lines  as  follows: 

1.  They  must  reach  by  their  own  lines  the  largest  traffic- 
point  at  each  end  which  is  at  all  within  reach  by  an  extension  of 
20  or  30  per  cent  of  their  length,  and  there  must  stand  on  equal 
terms  with  their  connections  as  respects  benefits  and  injuries  to-  . 
be  given  and  received.  Failing  to  do  this  is  pretty  sure  to  result 
in  great  loss,  and  generally  in  insolvency. 

2.  They  must  reach  without  fail  every  considerable  inter- 
mediate traffic  point  along  their  line  which  can  be  reached  by 
any  reasonable  detour  or  even  sacrifice  of  grades,  their  prosper- 
ity being  about  as  the  square  of  the  tributary  population. 

3.  They  can  in  no  case  attempt  to  create  new  channels  of 
trade,  as  by  attempting  to  make  a  seaport  out  of  some  neglected 
roadstead,  without  the  greatest  risk  of  failure.  The  attempts  ia 
this  direction  have  been  many  ;  the  successes  as  yet  none. 

4.  Nearly  or  quite  half  of  their  traffic  must  practically  begin, 
and  end  on  their  own  lines,  either  because  it  goes  no  farther,  or 
because  it  is  delivered  at  some  great  competitive  distributing 
point. 

5.  It  is  of  little  avail  to  run  a  line  even  from  a  great  city  to 
nowhere.  The  apex  to  the  pyramid  in  Fig.  238  is  eloquent  and 
truthful  in  this  respect.  Without  a  good  traffic-point  at  each 
end  of  a  line  the  conditions  for  great  prosperity  are  not  present. 

BRANCH    LINES. 

980.  That  branches  are  in  the  main  profitable  investments  is^ 
evident  from  their  very  rapid  rate  of  increase,  which  is  largest, 


732 


CHAP.  XXI.— BRANCH  LINES. 


up  to  a  certain  point  at  least,  on  the  most  prosperous  lines.  That 
they  are  rarely  very  profitable  when  considered  by  themselves, 
and  apart  from  the  main  line,  and  as  a  rule  do  little  more  than 
pay  operating  expenses,  is  abundantly  shown  by  the  reports  of 
almost  every  line  which  has  branches  and  reports  their  traffic  in 
detail.  This  fact  is  so  clear  and  so  generally  admitted,  that  it 
hardly  needs  statistics  to  prove  it.  As  a  rule,  the  earnings  per 
mile  of  branches  range  only  from  a  fifth  to  a  tenth  of  the 
earnings  of  the  main  stems. 

981.  The  only  considerable  exceptions  to  this  rule  are  branches 
which  are  in  reality  main  lines,  having  a  very  considerable  traf- 
fic which  is  complete  in  itself.  A  striking  example  of  this  kind 
of  branch  is  what  is  knov^rn  as  the  Mahoning  Division  or  Cleve- 

•  land  Branch  of  the  New  York,  Pennsylvania  &  Ohio  Railroad, 
which  runs  diagonally  across  the  main  line  from  Cleveland  to 
Youngstown.  This  nominal  *' branch"  was  really  a  subordinate 
main  line,  built  by  a  separate  company  and  projected  on  rational 
principles,  according  to  par.  979.  It  had  and  has  a  very  consider- 
able traffic,  both  freight  and  passenger,  which  is  complete  in 
itself.  On  the  other  hand,  the  nominal  "main  line"  is  in  reality 
a  mere  branch,  violating  conspicuously  every  one  of  the  condi- 
tions for  the  success  of  main  lines  specified  in  par.  979.  It  is 
not  surprising,  therefore,  that  the  "  main  line"  was  a  financial 
failure  and  the  "  branch"  a  financial  success,  which  has  largely 
helped  to  support  the  main  line  even  after  paying  a  very  heavy 
rental  (10  per  cent  dividends  per  annum)  to  the  lessor  company. 

982.  The  reason  for  the  continued  and  rapid  building  of 
branches  in  spite  of  their  apparent  unproductiveness  is  simply 
this  :  They  contribute  traffic  to  the  main  line  which,  as  it  is 
merely  an  increment,  costs  always  comparatively  little  to  move, 
and  often  nothing  at  all.  The  company,  therefore,  receives  from 
its  contributed  traffic  rates  for  a  haul  of  perhaps  500  miles  at  a 
cost  for  hauling  due  to  only  100  or  200  miles.  This  follows 
directly  from  what  we  have  seen  in  Chapter  XV.,  par.  181,  and 
elsewhere.  Rudely  speaking,  if  we  call  the  average  cost  per  tor? 
or  passenger-mile  100,  we  may  say  : 


CHAP.  XXL— BRANCH  LLNES.  ^33 

Average  cost  per  unit  of  traffic  = 100 

Extra  passengers,  singly,  cost o  -|- 

**  "  in  car-loads  cost 51030 

"  "  in  train-loads  cost 50 

f^xtra  freight  in  small  lots  costs  often  in  both  directions  and  usually 

in  one  direction , 0  + 

**  •*      in  car-loads 51020 

*•  "  in  train-loads  (and  all  car-loads  must  ordinarily  be  con- 
sidered to  be  made  up  into  extra  trains  in  the  direc- 
tion of  heaviest  traffic)  not  over 60 

Not  unfrequently  when  a  large  part  of  the  traffic  of  a  branch 
j^oes  over  the  main  line  in  the  direction  of  favoring  grades  it  is 
Handled  over  the  main  line  at  no  appreciable  extra  cost  by  simply 
tilling  up  trains,  and  the  branch  is  then  enormously  profitable. 

To  these  direct  and  evident  advantages  from  a  branch  is  to  be 
added  the  vivifying  effect  of  increasing  the  tributary  population 
from  the  causes  discussed  in  the  first  part  of  this  chapter,  the 
prosperity  of  the  line  increasing  in  something  like  the  square  of 
the  tributary  population. 

983.  It  is  not  to  be  wondered  at,  therefore,  that  branches  and 
extensions  are  much  sought  for  by  prosperous  companies,  even 
in  regions  where  there  is  not  the  likelihood  of  rapid  increase  of 
traffic  which  prevails  throughout  the  United  States.  Neither  is  it 
to  be  wond^red  at  that  the  seeking  for  them  is  often  overdone, 
so  that  the  branches  become  a  burden  which  threatens  to  swamp 
the  main  line,  and  often  does  so.  For  there  is  this  to  be  said 
against  branches  :  Their  traffic  is  usually  thin,  while  they  cost  as 
much  or  more  to  build  and  not  much  less  to  keep  up  than  the 
main  line.  Therefore  it  is  easy  to  lose  all  that  is  gained  on  the 
main  line  by  the  extra  cost  of  handling  the  traffic  on  branches 
and  paying  their  rentals  ;  although  it  still  remains  universally 
true,  that  branches  are  far  more  profitable  than  appears  on  the 
face  of  their  returns,  separately  considered. 

984.  These  facts  make  it  easy  to  see  what  should  be  the  gov- 
erning rule  in  laying  out  branches.  The  one  universal  rule,  to 
be  deviated  from  only  when  special  reasons  to  the  contrary  ap- 
pear, is  this  :  Strike  the  main   line   as  soon  as  possible.     In 


734 


CHAP.  XXL— BRANCH  LINES, 


laying  out  a  branch  to  A  from  the  main  line  ED,  Fig.  241  (which 
represents  to  scale  an  actual  instance),  B  is  in  all  ordinary  cases 
^.  the  point  to  strike  the  main  line,  if  possible,  even  at 

\- — T"^  some  disadvantage  in  grades  and  construction.     It 
\)        is  not  correct  to  compare  the  entire  line  ABCD  with 
"C\  the    alternate   ACD,     Were  we   building  a  line  to 

>r  handle  a  main-line  traffic  between  A  and  Z>,  that  would 
Fig.  241'  be  the  proper  course  to  pursue  ;  but  with  a  branch- 
line  traffic,  when  we  have  gotten  it  to  the  main  line  we  may 
say,  for  preliminary  and  approximate  purposes,  that  we  shall 
handle  it  thereafter  for  nothing.  If  the  branch  traffic  be  nearly 
all  toward  D  and  the  grades  favor  it,  this  will  be  almost  literally 
true.  Therefore  the  true  question  is  :  How  will  this  traffic  be 
moved  to  the  main  line  most  cheaply  and  advantageously — via 
AB  or  via  BCl  In  nine  cases  out  of  ten  AB  will  be  the  best,  for 
these  reasons : 

985.  Branch-line  traffic  is  light  and  fragmentary.  Grades 
and  curves  then  become  minor  considerations  within  pretty  wide 
limits,  especially  when  one,  two,  or  three  engines  must  be  kept 
on  the  branch  anyway.  On  the  other  hand,  the  extra  cost  of 
■keeping  up  the  track  on  AC  instead  of  AB  is  so  much  dead  loss. 

Any  traffic  AE  is  seriously  burdened  by  the  additional  dis- 
tance via  ACE  over  ABE^  while  the  gain  to  the  traffic  AD  is  but 
trifling. 

Passenger  traffic  is  almost  invariably  better  served  if  deliv- 
ered on  the  main  line  with  the  shortest  possible  haul. 

It  is  therefore  bad  practice  to  lengthen  out  branches  to  get 
■cheap  construction  and  good  grades,  even  when  the  difference 
favors  most  of  the  traffic  of  the  branch,  unless  the  extension  is 
justified  by  the  cardinal  rule  laid  down  :  By  which  route  is  the 
traffic  delivered  on  the  main  line  at  any  point,  most  cheaply 
and  advantageously,  regardless  of  where  ? 

986<  To  the  preceding  is  to  be  added  another  still  more  im- 
portant and  sometimes  conflicting  rule  :  Strike  the  main  line  at 
A  considerable  town,  if  possible.  If  there  be  a  town  of  some 
size  at  either  B  or  C,  Fig.  241',  that  will  be  the  point  to  termi- 


CHAP,  XXL— BRANCH  LLNES.  735 

nate  the  branch  at,  or  to  consider  it  to  terminate  in  comparing 
the  alternate  roiites,  for  the  traffic  of  the  branch  will  be  very  apt 
to  be  delivered  at  this  town  even  if  the  branch  strikes  the  main 
line  elsewhere,  if  it  does  not  add  more  than  20  per  cent  to  the 
haul. 

The  purely  local  traffic  of  two  neighboring  towns,  A  and  B 
or  A  and  6*,  will  ordinarily  be  found  a  very  welcome  addition  to 
the  traffic  contributed  to  the  main  line  by  the  branch,  and  it 
depends  greatly  on  facilities.  If  a  train  has  to  be  taken  from  B 
to  C  and  then  another  from  C  to  -^  to  get  from  A  to  B^  the  A-B 
traffic  will  be  practically  killed.  Only  the  necessary  travel  (par. 
45)  will  remain. 

987.  The  preceding  has  been  on  the  assumption  that  the 
branch  is  to  reach  a  point  A.     When  the  purpose  of  the  branch 

Fig.  342. 

is  not  to  reach  any  particular  point,  but  to  develop  a  tract  of 
territory,  the  conditions  are  of  course  somewhat  charged,  but 
even  then  the  same  general  principles  apply.  It  will  as  a  rule 
be  more  economical,  and  more  convenient  to  the  traffic,  to  con- 
centrate it  upon  the  main  line  as  soon  as  possible.     Therefore  it 

— ^^ 


Fig.  243. 


is  not  as  a  rule  good  practice,  even  when  the  purpose  of  the 
branch  is  to  develop  a  long  strip  of  parallel  territory  which  has 
traffic  relations  mostly  in  one  direction,  C,  Fig.  242,  to  construct 
branches  along  parallel  lines.     The  method  outlined  in  Fig.  243 


736 


CHAP.  XXL— BRANCH  LINES. 


CHAP.  XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS.  72,7 


is  far  more  likely  to  accomplish  its  purpose  advantageously,  even 
when  branches  like  DEF  become  necessary;  the  governing  rules 
being,  first,  to  link  together  neighboring  towns  having  natural 
traffic  relations  as  directly  as  possible,  and  secondly,  to  reach  the 
main  line  quickly. 

988.  This  policy  is  the  correct  one,  not  only  because  it  handles 
a  given  traffic  most  economically,  but  because  it  tends  to  unify 
the  district  served  by  the  railway  and  aggrandize  points  on  its 
main  line.  The  two  lines  AC  and  DC,  Fig.  242,  are  practically 
two  separate  roads  having  no  interrelation  with  each  otlier 
whatever.  A  less  amount  of  road  in  Fig.  243  gives  equal  traffic 
facilities  from  the  district  AB  to  C  at  less  cost  to  the  railway,  and 
likewise  promotes  traffic  relations  with  other  points  on  the  main 
line  and  to  the  south  of  it. 

When  the  traffic  of  the  branch  is  equally  divided  between 
East  and  West,  or  nearly  so,  as  respects  destination  on  the  maia 

line,  then  Fig.  244  gives  what 
is  abstractly  by  much  the  best 
Q  system  for  laying  out  branches, 
other  things  being  equal.  Other 
things  rarely  are  exactly  equal, 
and  hence  considerable  devia- 
tions from  this  plan  are  oftea 
required  in  the  laying  out  of  such  branches,  but  in  all  cases 
branch  traffic  needs  to  be  quite  differently  considered  from  what 
it  would  be  if  we  were  laying  out  a  main  line  to  the  same  point. 

The  writer  is  compelled  to  omit  a  number  pf  concrete  examples  of  the  lay- 
ing out  of  branches,  especially  a  most  interesting  one  having  reference  to  the 
Pacific  branch  of  the  Mexican  Central  Railway,  ia  order  to  keep  this  volume 
within  more  reasonable  size. 


i 


7^^ 


Fig.  944. 


CHAPTER  XXII. 

LIGHT  -RAILS   AND   LIGHT    RAILWAYS. 

989.  A  FACT  evident  enough  in  the  existing  railway  system  of 
this  country,  and  indeed  of  the  world,  is  that,  taking  it  as  a 
whole,  distinctively  light  railways  do  not  prosper  nor  multiply. 
The  apparent  field  for  them  is  great — many  times  greater  than  for 
railways  of  tho  ordinary  type.  The  need  for  them  is  keenly  felt 
in  many  regions  where  it  would  appear  as  if  cheap  light  lines 
would  answer  every  requirement  which  the  traffic  justifies.  Such 
lines  can  admittedly  be  built,  and  in  many  cases  have  been  built, 
both  of  standard  and  narrow  gauge,  for  but  little  more  than  the 
cost  of  a  good  turnpike  ;  some  of  them  even  following  the  turn- 
pike, using  low  speed,  light  rails,  light  rolling-stock,  sharp  curves, 
and  little  or  no  grading  beyond  a  mere  smoothing  of  the  sur- 
face. 

Yet  it  is  a  significant  fact  that  out  of  the  125,000  miles  of  rail- 
way in  the  United  States  (1885)  very  little  of  it  is  of  this  charac- 
ter, or  anything  closely  resembling  it.  Absolutely  there  is  a 
large  amount,  no  doubt  ;  but  comparatively  there  is  very  little, 
and  that  little  shows  a  constant  and  strong  tendency  to  approxi- 
mate to  the  general  standard.  In  spite  of  enormous  differences 
in  traffic  there  may  still  be  said  to  be  a  certain  average  standard 
to  which  the  vast  majority  of  the  roads  approximately  conform, 
or  begin  to  do  so  almost  as  soon  as  the  track  is  laid.  Between 
the  12,000  to  14,000  miles  of  trunk  lines  or  sections  thereof, 
which  make  nearly  half  the  earnings  and  carry  far  more  than 
half  the  traffic  of  the  country,  and  the  113,000  to  115,000  miles 
which  manage  to  live  on  the  rest  of  it,  or  on  less  than  one  tenth 
as  heavy  an  average  traffic,  there  are  indeed  considerable  differ- 
ences of  condition;  yet  the  resemblances — in  rails,  in  ties,  in  bal- 
47 


i 


738  a/AP.  XXII.-LICHT  RAILS  AND  LICIIT  RAILWAYS. 


um 


( 


last  in  rolling-stock,  in  alignment-are  still  more  striking,  prov- 
ing almost  to  demonstration  that  the  law  (to  which  there  are  of 
course  exceptions)  is  that  distinctively  light  railways  do  not 
prosper,  or  if  they  prosper,  do  not  stay  light.  We  need  not 
search  far  to  find  some  strong  reasons  why  this  should  be  so, 
and  it  is  well  that  every  one  should  do  so  who  is  concerned  in 
projecting  a  light  line  before  finally  deciding  on  its  details  of 
construction  ;  not  because  so  doing  will  necessarily  induce  him 
to  abandon  his  intention,-very  light  lines  are  often  justifiably 
built  and  are  the  only  alternative  to  none  at  all,— but  because  it 
is  always  desirable  that  the  consequences  of  an  intended  course 
of  action  should  be  fully  understood  in  advance. 

990  The  first  and  greatest  question  in  connection  with  alight 
railway  is,  What  weight  of  rails  shall  be  chosen?  This  is  so  for 
two  reasons  :  First,  because  the  rail  is  the  largest  single  item  of 
expense  on  such  a  line,  and  secondly,  because  on  the  weight  of 
rail  hinges  the  character  of  the  rolling-stock,  the  ties,  the  ballast, 
and  so  to  a  greater  or  less  extent  almost  every  other  detail  of  the 
line.  The  rail  question  is  therefore  a  very  fundamental  one, 
which  we  may  well  consider  with  some  care. 

Cutting  down  the  rail  section  is  almost  the  first  point  of  at- 
tack  for  a  certain  large  class  of  economists,  much  as  cutting  ten 
percent  off  salaries  is  liable  to  be  at  a  later  period  in  the  history 
of  a  railway  There  is  probably  no  other  way  in  which  anything 
like  as  large  a  saving  can  be  effected  with  so  little  demand  upon 
the  time  or  thought  or  skill  of  the  manager  ;  nor  does  it  admit 
of  doubt  that  either  or  both  of  these  economies  may  at  times  be 
both  expedient  and  necessary.  Nevertheless,  they  would  not 
we  may  be  certain,  be  resorted  to  nearly  so  often  as  they  are  if 
the  full  extent  of  the  sacrifice  made  were  realized. 

991  That  it  is  not  more  fully  realized  as  to  rails  is  probably 
due  in\he  main  to  a  not  unnatural  impression  that  in  buying  rails 
what  one  wants  is  steel  :  That  if  light  and  heavy  sections  are 
the  same  price  per  ton,  buying  a  30-lb.  section  instead  of  a  60-lb. 
is  like  a  poor  and  hungry  man  buying  a  one-pound  loaf  at  five 
cents  instead  of  a  two-pound  loaf  at  ten  cents. 


CHAP.   XXII.-LIGHT  RAILS  AND  LIGHT  RAILWAYS.   739 


Tins  is  not  at  all  the  case.     In  buying  rails  we  are  not  buying 
steel  ;  at  least  we  do  not  care  to  buy  it.     We  are  buying  three  im- 
ponderable  qualities:  (i)  stiffness,  (2)  strength,  (3)  durability 
If  we  get  our  money's  worth  of  these  qualities,  it  is  a  matter  of 
complete  indifference  (except  the  future  scrap  value  of  the  steel 
which  a  poor,  light  traffic  road  cannot  afford  to  give  mucli  thought 
to)  whether  we  get  much  or  little  of  steel.     If  we  do  not  get  our 
money's  worth  of  what  7ve  want,  our  bargain  is  just  as  bad,  how- 
ever much  steel  we  get. 

992.  To  determine  whether  we  do  or  not,  one  must,  unfortu- 
nately,  use  an  intelligence  somewhat  higher  than  that  of  a  hay- 
scale.     Any  absolute  measure  of  the  qualities  mentioned  is  es- 
pec.ally  difficult.     Thus,  it  may  be  hardly  necessary  to  say  here 
that  to  estimate  exactly  our  stiffness  and  strength  we  must  de 
termine  the  position    in  the  rail   section,  Fig.   245,  of  two  little 
points  which    lie   at  a  distance  called  the  radius  of  gyration 
from  the  centre  of  the  rail  (meaning  simply  the  points 
where,  if  all  the  steel  in  base  and  head  were  concen- 
trated, it  would  have  the  same  power  to  resist  gyration  , 
i.e.,  bending,  as  it  now  has)  and  we  must  then  make  a   "^, 
number  of  other  assumptions  in  regard   to  the  character  of  The 
load  and  support  which  we  well  know  are  not  only  doubtful   but 
will  not   be  even  approximately  true  in  practice,  unless  bv  ac- 
cident. 

But  for  comparative  purposes  all  this  is  unnecessarv  The 
support  given  to  the  rail  from  below  by  the  road-bed  and  ties  may 
be  assumed  the  same  for  any  section  of  rail,  whatever  it  may  be 
absolutely.  We  may  assume  that  any  two  or  more  sections  re- 
quiring to  be  compared  will  be  practically  -  similar"  to  each 
other.  I.e.,  with  the  same  proportion  of  base  to  height,  etc  etc 
so  that  Fig.  245  may,  by  simply  varying  the  scale,  be'taken  to 
represent  a  section  of  any  weight  from  10  to  100  lbs.  per  yard 
and  yet  be  tolerably  well  designed  even  for  these  extremes  * 
^    established    mathematical    laws  we  also   know  that  the 

xCwT^^^^     designed  in  having  a   head  flaring  outward  "artheboVoin^^t 
inat  IS  a  detail  we  need  not  enter  into. 


A 


»••»*" 


w 


740  C//AP.   XXIT.— LIGHT  RAILS  AND  LIGHT  RAILWAYS, 


weight  will,  under  these  assumptions,  vary  as  breadth  X  height, 
and  that  the  stiffness  will  vary  as  breadth  X  cube  of  height.  That 
is  to  say,  if  we  multiply  every  dimension  by  two,  we  increase  the 
weight  of  the  section  by  2  X2  =  4,  but  the  stiffness  by  2  X2'  or 
2  X  8  =  16  or  2*;  in  other  words,  tiie  stiffness  in  that  case  varies 
as  the  fourth  power  of  the  increase  in  linear  dimensions,  whereas 
the  weight  varies  only  as  the  square. 

993,  An  algebraic  demonstration  of  the  simplest  character, 
which  it  is  unnecessary  to  give  here,  would  prove  this  result  to 
be  in  accordance  with  a  general  law — that  the  stiffness  in  a 

RAIL   VARIES   AS   THE   SQUARE   OF     ITS    WEIGHT    PER   YARD.       If     We 

increase  the  weight 


10  percent, 


20  per  cent, 


30  per  cent, 


we  shall  increase  the  stiffness  to 


1. 10  =  1. 21, 
or  21  per  cent, 


1.20*  =  1.44, 
or  44  per  cent, 


1.30*  =  1.6'^j 
or  69  per  cent. 


Mere  formulae  have  a  hazy,  indefinite  sound,  which,  it  is  evi- 
dent from  what  we  see  around  us  (for  these  general  facts  are  welP 
enough  known),  do  not  produce  much  impression  on  the  mind  r 
but  let  us  reduce  them,  in  the  accompanying  Table  195,  to  the 
plain,    practical   basis   of    how  much    stiffness  we  get  for  a 
DOLLAR  with  light  and  heavy  rails,  and  we  shall  have  some  more 
forcible,   because  more  readily  comprehensible,  evidence  as  to- 
why  light  rails  are   sooner  or  later  avoided   as  the  plague  by  all 
railways  ;  admitting  the  evident  fact,  that  for  light  lines  especi- 
ally stiffness   is  not  only  by  much  the  most  important  quality  a 
rail  can  have,  but  (as  we  shall  see  more  fully)  by  much  the  cheap- 
est stability  to  be  had  in  the  market— far  cheaper  than  tamping- 
bar  stability,  which  roads  of  heavier  traffic  can  afford  to  rely  on 
more  extensively.     In  Table  195  a  so-lb.  rail  is  taken  as  the  unit 
of   comparison,  as   being  about  the  maximum  for   distinctively- 
light  railways  and  the  minimum  for  those  of  ordinary  type,  and 
the  cost  of  rails  is  taken  at  the  even  figure  of  $30  per  ton. 


CHAP.  XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS.  741 


Table  195. 
Comparative  Amount  anp  Cost  of  Stiffness  in  Light  and  Heavy  Rails. 


Weipht 
of  Rails. 

Tons 

Cost 
Per  Mile 

Comparative 

Cost 
Per  Unit 

Comparative 
Value 

Lbs. 

Per  Mile. 

at  $30 
Per  Ton. 

Stiffness. 

of 

Received 

Per  Yard. 

Stiffness. 

for  $1. 

10 

16 

I480 

.04 

$12,000 

20  cts. 

15 

24 

720 

.09 

8,000 

30  cts. 

20 

32 

960 

.16 

6,000 

40  cts. 

25 

40 

1,200 

.25 

4,Soo 

50  cts. 

30 

48 

1,440 

.36 

4,000 

60  cts. 

35 

56 

1.680 

.49 

3.429 

70  cts. 

40 

64 

1,920 

.64 

3.000 

80  cts. 

45 

72 

2,160 

.81 

2,667 

90  cts. 

60 

80 

2,400 

1.00 

2,400 

$1.00 

55 

88 

2,640 

I. 21 

2.182 

1. 10 

60 

96 

2,880 

1.44 

2,000 

1.20 

65 

104 

3.120 

1.69 

1,846 

1.30 

70 

112 

3.360 

1.96 

1,714 

1.40 

75 

120 

3.600 

2.25 

1,600 

1.50 

80 

128 

3.840 

2.56 

1,500 

1.60 

Tons  of  rail  per  mile  taken  at  1.6  tons  per  lb.  per  yard,  allowing  for  a  certain  mini- 
mum of  side  track.     Main  track  only  requires  \^  or  1.571  tons  per  pound  per  yard. 

Comparative  stiffness  (4th  column)  is  as  the  square  of  the  weight  per  yard,  50  lbs. 
being  taken  as  the  limit  of  comparison.  Cost  per  unit  of  stiffness  (5th  column)  is  given 
fcy  dividing  column  3  by  column  4.  Comparative  value  received  for  $1  (last  column)  is 
given  by  dividing  column  5  by  $2400. 


994,  This  table  should  be  carefully  studied.  It  will  be  seen 
from  it  that  the  lighter  the  original  section  of  a  railroad,  the 
more  it  loses  by  using  a  light  section,  because  the  more  would 
be  its  proportionate  gain  from  a  given  increase  in  weight  of  sec- 
tion. The  sacrifice  of  value  in  buying  light  sections  is  precisely 
the  same  as  if  in  buying  rails  we  were,  in  fact  as  well  as  in  form, 
buying  steel  instead  of  stiffness,  and  were  to  choose  light  sec- 
tions in  spite  of  the  following  market  quotations: 

Per  ton. 
Steel  in  20-lb.  sections, ^75  00 

30    "  "  50   GO 

40  "  "  37  50 

50  30  00 

60 "       "       25  00 

70   "  "  .       .' 21    43 

80   "  "  18    75 


742    CHAP.    XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS, 


#1^ 


Or,  again,  our  loss  is  the  same  as  if  we  were  offered  a  certain 
amount  of  steel  in  25-lb.  sections  at  $30  per  ton,  but  were  told 
that  if  we  would  take  twice  as  many  tons  in  the  form  of  50-lb. 
sections  we  could  have  the  remainder  at  $10  per  ton.  That  is 
precisely  what  we  are  told  in  effect,  as  respects  the  quality  we 
are  really  buying — stiffness— when  we  are  offered  rails  of  such 
sections  at  a  uniform  price  per  ton. 

995.  The  ultimate  strength  of  rails  is  a  less  im.portant 
quality  than  the  stiffness,  because  it  is  never  expected  to  be 
called  fully  into  use.  Nevertheless,  it  often  is  so  called  into  use 
and  even  exceeded,  especially  as  the  rail  wears  out,  and  it  is 
therefore  an  important  quality.  The  strength  is  less  affected  by 
the  weight  of  the  rail  than  the  stiffness;  for,  referring  to  Fig.  245 
once  more,  the  strength  varies  only  as  the  square  of  the  height, 
whereas  the  stiffness  varies  as  the  cube,  both  varying  directly  as 
the  width.     Therefore,  in  a  similar  way  to  that   employed  for 

Table  196. 
Comparative  Amount  and  Cost  of  Strength  in  Light  and  Heavy  Rails. 


Weight 

Cost  Per  Mile 

Cost 

Comparative 
Value 

of  Rails. 

at  S10 

Comparative 

Per  Unit 

Lbs. 

Per  Ton. 

Strength. 

of 

Received 

Per  Yard. 

Strength. 

for  $1. 

10 

I480 

.089 

I5.365 

44.  7  CtS. 

15 

720 

.164 

4.380 

54-8    * 

20 

960 

.253 

3.796 

63.2    • 

25 

1,200 

•354 

3.717 

70.7    ' 

30 

1,440 

•465 

3.091 

77.6    • 

35 

1,680 

.586 

2,870 

83.6    • 

40 

1.920 

.716 

2,684 

89.4    • 

45 

2,160 

.854 

i.^'\o 

94.8    • 

50 

2,400 

1.000 

3,400 

100.0    • 

55 

2,640 

I  154 

2,288 

104.9    ' 

60 

2.880 

1. 314 

2. 191 

109.5   ♦ 

65 

3.120 

1.482 

2,105 

114. 0    ' 

70 

3.360 

1.656 

2.028 

118. 3     ' 

75 

3.600 

1.838 

1.959 

122.5     ' 

80 

3.840 

2.024 

1,897 

126.5     * 

The  different  columns  are  determined  in  substantially  the  same  manner  as  in  Table 
195,  except  that  the  third  column  is  as  the  9  power  of  the  weight  per  yard,  taking  50-lb. 
rails  as  the  unit  of  comparison. 


CHAP.   XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS.    743 

determining  stiffness,  we  may  determine  that  the  strength  varies 
as  the  square  root  of  the  cube  (or  ^  power)  of  the  weight,  and  thus 
obtain  Table  196.     This  table  also  should  be  carefully  studied. 

The  loss  of  strength  obtained  with  light  sections  will  be  seen 
from  Table  196  to  be  far  less  striking  than  the  loss  of  stiffness. 
Nevertheless,  it  is  as  if  strength  were  a  ponderable  element,  and 
we  bought  it  in  spite  of  the  following  prices  per  ton: 

Per  ton. 

Rails  of  2o-lb.  section ^7  c© 

"      30  "        "           !    .*  38  60 

**      40"        «           3230 

5^                           30  00 

o<^                             27  40 

7°                          25  30 

°^  23    70 

If  steel  were  quoted  at  these  prices  per  ton,  it  is  a  tolerably 
safe  hypothesis  that  light  rail-sections  would  not  be  in  much 
favor;  yet  this  is  an  unduly  favorable  showing  even  for  the  item 
of  strength,  for  if  we  were  to  compute  the  comparative  strength 
after  the  sections  have  received  a  certain  fixed  amount  of  wear, 
we  should  find  the  apparent  disadvantage  of  light  sections  as 
given  above  very  much  increased. 

996.  It  is  a  little  difficult  to  determine  a  standard  by  which 
to  measure  durability,  because,  as  a  rule,  light  and  heavy  sec- 
tions are  chosen  for  very  different  duties,  i.e.,  are  approximately 
proportioned,  and  necessarily  must  be,  to  the  kind  of  locomo- 
tives running  over  them,  so  that  no  rational  comparison  can  be 
made  between  the  durability  in  a  10-  or  20-Ib.  section  and  that 
in  a  70-  or  8o-lb.  section,  as  there  can  be  in  the  items  of  stiffness 
and  strength.  What  we  can  do,  however,  is  to  compare  each 
section  with  one  5  or  10  lbs.  heavier,  since  there  is  a  rational 
and  practical  choice  between  such  sections,  for  any  one  given 
service. 

Taking  a  rude  yet  tolerably  approximate  average  of  rails  as 
they  are  now  designed  and  chosen,  we  may  say  (i)  that  half  the 
total  weight  is  in  the  head,  and  (2)  that  half,  or  nearly  half,  of 


744   CHAP,  XXII.— LIGHT  RAILS  AND  LIGHT  RAIL  WA  YS. 

the  metal  in  the  head  (or  i  of  the'whole  weight  of  the  rail)  is 
expected  to  be  worn  away  before  the  rail  is  finally  condemned 
as  unsafe,  although  it  rriay  be  earlier  removed  to  a  less  trying 
location.  That  is  to  say,  a  40-lb.  rail  has  10  lbs.  of  wear  in  it, 
and  a  50-lb.,  12^  lbs.,  making  their  weight  when  finally  con- 
demned 30  and  37i  lbs.  respectively. 

997.  But  when  comparing  two  \dJ\\'s>  for  atiy  one  given  service  it  is 
obvious  that  this  is  an  unfair  basis  of  comparison,  since,  what- 
ever the  original  weight  per  yard,  a  rail  for  any  one  given 
service  may  be  so  designed  as  to  utilize  most  of  any  additional 
weiglit  in  wear,  leaving  the  weiglits  of  the  worn-out  rails  when 
scrapped  nearly  the  same.  This  is,  of  course,  not  fully  possible 
without  using  very  ugly  and  distorted  original  sections,  but  it  is 
at  least  a  moderate  statement  that,  even  if  any  two  rails  of  dif- 
ferent weights  are  designed  precisely  "similar"  to  each  other  (as, 
say.  Fig.  245),  so  that  they  have  the  same  proportion  of  waste 
metal  (as  respects  wear)  in  the  base,  yet  the  head  can  in  all 
cases,  in  any  one  given  service,  be  worn  down  to  an  equal  ulti- 
mate weight  before  condemnation,  so  that  a  40-lb.  and  50-lb. 
rail  would  compare  as  follows: 


40-lb.  rail,  . 
50-lb.  rail,  . 


•Whhn  Nrw.— >  , When  Worn  Out. 

ead.  Base.  Head.  Base. 


Head.  

20  lbs.     20  lbs. 
25  lbs.     25  lbs. 


Head.  Base.  Total. 

10  lbs.     20  lbs.        30  lbs. 
10  lbs.     25  lbs.         35  lbs. 


A  50-lb.  rail  worn  down  to  35  lbs.  may  fairly  be  said  to  be  at 
least  as  strong  and  safe  as  a  40-lb.  rail  worn  down  to  30  lbs., 
althougii  that  is  rather  an  extreme  illustration  as  respects  the 
absolute  amount  of  wear  for  either  of  the  rails  specified;  but  by 
proper  design  it  is  realizable  in  sections  sufficiently  strong  for 
their  duty. 

998.  If,  however,  we  are  practising  the  last  degree  of  economy 
in  first  cost,  clioosing  the  very  lightest  section  which  is  con- 
sistent with  the  duty  laid  upon  it,  as  we  have  already  admitted 
is  sometimes  expedient,  it  is  obvious  that  we  cannot  count  on 
any  such  rate  of  wear  as  that.  Wearing  off  half  the  head  means 
reducing  its  ultimate  strength  by  something  like  45  per  cent,  and 


CHAP.   XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS.   745 


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746   CJ/AP.    XXII.— LIGHT  RAILS  AND  LIGHT  RAIL  WA  YS. 

its  stiffness  by  65  to  70  per  cent  (making  merely  a  rough  estimate- 
of  the  new  **  moments  of  inertia"  and  "radius  of  gyration" 
necessary  to  determine  it  exactly).  When  we  are  selecting  a 
rail  as  light  as  we  dare,  we  have  no  such  margin  as  that;  yet  we 
must  assume  some  margin  for  wear,  for  however  light  a  section 
may  be,  it  cannot  be  expected  to  become  unserviceable  as  soon- 
as  the  top  is  fairly  polished.  We  may  assume,  perhaps,  that,  in 
such  cases,  a  wear  equal  to  one  fifth  of  the  metal  in  the  head 
is  more  or  less  consciously  contemplated  and  actually  realized^ 
With  these  premises,  we  may  determine  in  Table  197  how  mucb 
durability  we  get  for  a  dollar  with  light  and  heavy  sections,  and 
it  will  be  seen  that — of  all  the  three  qualities  we  are  buying — 
the  worst  sacrifice  by  far  is  in  buying  durability  in  light  sec- 
tions. It  is  as  if  when  buying  rails  we  were  buying  steel  in- 
stead of  durability,  and  chose  the  light  sections  in  the  face  of 
the  following  market  quotations  of  steel: 

Per  ton. 

Steel  in  20-lb.  sections $30  00 

Additional  lots  (spot  cash  for  future  deliver)',  as  needed,  at  end 

of  —  years) 2  75 

Steel  in  40-lb.  sections, 30  oa 

Additional  lots, 2  31 

Steel  in  60-lb.  sections, 30  co- 
Additional  lots, I  76 

Of  course  this  enormous  difference  is  due  not  so  much  to  the 
extraordinary  cheapness  of  the  durability  in  the  heavier  sections 
as  to  the  extraordinary  dearness  of  the  durability  in  the  lighter 
sections.  Still,  if  we  assume  that  we  get  our  money's  worth  out 
of  the  light  sections,  the  comparison  is  a  fair  one.  By  varying, 
the  assumed  rates  of  wear,  the  numerical  comparison  will  be 
modified  accordingly,  but  in  no  probable  case  enough  to  make 
the  moral  materially  different. 

999.  Of  course,  too,  it  is  to  be  remembered  that  durability  is 
a  quality  for  future  delivery  (for  light-traffic  roads,  perhaps,  in 
a  very  distant  future),  which  we  pay  down  for  now,  in  cash.  It 
is  therefore  onlv  the  present  worth  of  this  future  value  which 
we  ought  to  consider.     Still,  this  applies  only  to  the  durability. 


CHAP.    XXIL— LIGHT  RAILS  AND  LIGHT  RAILWAYS.    J^J 

The  strength  and  stiffness  we  have  use  for  from  the  very  day  the 
rails  are  laid;  and  even  the  present  worth  of  the  extra  durability 
at  the  largest  probable  rate  of  interest  and  the  longest  probable 
life  of  light  rails  is  cheap  indeed  at  the  price  paid  for  it,  as  will 
appear  from  Table  18,  page  ?>2,  or  more  directly  from  the  follow- 
ing Table  198,  which  explains  itself,  and  will  probably  make  it 
very  clear  that  whether  a  new  project  as  a  whole  will  pay  or 
not,  it  is  almost  sure  to  return  a  heavy  profit  on  the  additional 
capital  invested,  obtained  at  any  probable  cost,  to  buy  reasonably^ 
heavy  rail-sections,  for  the  sake  of  their  durability  alone. 

Table  198. 

Years  of  Wear  which  a  Light  Rail-Section  must  Outlast  before  thk 
Durability  obtainable  by  adding  Five  Lbs.  Per  Yard  to  it  will 
BECOME  A  Losing  Bargain,  costing  more  than  that  of  the  LiGHr 
Section.* 


Weight  of 

Light  Section. 

Lbs.  Per  Yard. 


Present  Cost  of  Capital. 


5  per  cent. 


30 
30 
40 
50 
60 

70 
80 


Years. 
450 
49-1 
52.0 


55-5 
58.1 

60.3 

62.4 


10  per  cent. 


Years. 

23.0 

25.2 

26.6 

28.4 

29.7 

30.9 

31.9 


15  per  cent. 


20  F>er  cent. 


Years. 

Years. 

15-7 

12.0 

17.2 

13.1 

18. 1 
19.4 
20.6 

139 

14.8 

15-5 

21. 1 

16. 1 

21.8 

16.7 

♦  For  the  ultimate  value,  U,  of  a  certain  sum/  invested  at  compound  interest  for  «  years  at 
»  per  cent,  wc  have 

:/  =  /(. +  »-)": 
^•bence  log  £/  =  log  /  +  log  (i  +  r)  x  «, 


and 


log  (1  -I-  r) 


Letting  the  numerator  (1)  of  the  vulgar  fractions  in  column  9  of  Table  197  =  p  (the  log  of 
which  is  o  and  may  be  dropped),  the  denominator  of  the  same  fractions  will  =  U,  and  we  have 

log  n  =  log  of  log  U  -  log  of  log  (1  -I-  r). 


1000.  In  these  facts  we  have  reasons  enough,  and  to  spare, 
why  all  roads  should  tend,  as  they  do  tend,  to  use  what  project- 
ors of  new  roads  call  a  "  heavy  '  rail,  and  think  they  can't  afford. 
It  is  because,  for  a  poor  road  as  well  as  a  rich  one,  the  best  is. 


■1  1 


■J 


i 


I 


748    CJIAP.   XXIL— LIGHT  RAILS  AND  LIGHT  RAILWAYS. 

THE  CHEAPEST,  and  a  poor  road,  even  more  than  a  rich  one,  must 
have  the  cheapest  to  live  at  all.  It  is  because,  with  railways  as 
with  men,  ''the  destruction  of  the  poor  is  their  poverty,"  in  that 
there  are  not  as  many  cents  in  a  poor  man's  dollar  as  in  a  rich 
one's,  because  of  the  bad  bargains  which  his  poverty  drives  him 
to — or  he  thinks  it  does.  While  it  may  still  be  right  to  buy  the 
light  sections,  if  we  must  have  something  and  cannot  pay  more^ 
it  should  at  least  be  realized  how  great  a  sacrifice  is  made,  in 
order  to  make  sure  that  there  is  no  other  direction  in  which  a 
less  costly  economy  can  be  exercised. 

Of  course,  as  has  been  already  stated,  there  is  another  side  to 
this  question — a  certain  legitimate  and  advisable  use  of  light 
rails.  If  a  man  needs  but  three  yards  of  cloth  to  make  a  coat, 
and  only  needs  one  coat,  there  is  no  particular  economy  in 
his  buying  four  yards,  simply  because  he  can  get  it  cheap;  and 
then,  besides,  there  is  always  the  open  question  whether  his  great- 
est need  is  for  a  coat  or  a  pair  of  breeches.  That  part  of  the  ques- 
tion we  may  now  consider.  We  have  merely  found  so  far  that 
if  a  man  is  going  to  buy  a  coat,  there  is  a  fearful  loss  which  a 
poor  man  cannot  afford  in  buying  one  which  is  too  small  to  fit 
and  too  flimsy  to  wear.  Of  all  directions  for  economy,  cutting 
down  the  rail-section  is  the  most  costly  in  the  end. 

1001.  If  attempted  economies  in  all  other  directions  were 
equally  disastrous,  we  should  be  led  directly  to  the  conclusion 
that  it  was  not  worth  while  to  build  light  railways,  and  that  they 
could  never  reasonably  be  expected  to  prosper;  but  such  a  con- 
clusion must  be,  in  part  at  least,  fallacious;  for  there  is  evident 
need  at  many  points  for  just  such  lines,  which,  when  built,  do 
prosper,  or  at  least  answer  the  requirements.  Hence  there  must 
be  certain  directions  in  which,  within  certain  limits,  it  is  expe- 
dient to  economize  in  their  construction,  and  there  are,  in  fact, 
many  directions  where  economy  does  little  harm.  If  we  exam- 
ine in  detail  the  cost  of  even  a  moderately  important  line,  we 
shall  find  that  an  enormous  proportion  of  it  is  for  items  which  a 
light,  cheap  railway  either  has  no  use  for  at  all,  or  can  dispense 
with  at  slight  inconvenience,  in  part  or  whole,  or  can  postpone  at  , 
moderate  sacrifice  to  some  indefinite  date  in  the  future. 


CHAP.    XXIL— LIGHT  RAILS  AND  LIGHT  RAILWAYS.    749 

1002.  Terminal  facilities,  for  instance,  are  an  immense  item 
in  the  investment  in  large  railwa)^s.  In  the  Buffalo  (N.  Y.)  yards 
alone  there  are  650  miles  of  track  (Table  201),  representing  an  in- 
vestment of  millions.  Station  and  other  buildings  are  other 
large  items,  which  may  be  made  small  on  a  light  road;  but  the 
chief  of  all  directions  in  which  a  rigid  yet  intelligent  economy- 
may  be  exercised  to  reduce  largely  the  construction  account  with- 
out undue  effect  upon  earning  capacity  is  in  the  construction  of 
the  road  to  sub-grade. 

1003.  This  is  best  seen  by  considering  how  much  (or  rather 
how  little)  the  cost  of  5  lbs.  per  yard  extra  weight  in  the  rail, 
which  We  may  take  at  the  even  figure  of  $30  per  ton,  or  $240  per 
mile,  will  do  to  construct  the  road  to  sub-grade.  We  have  seen 
how  very  advantageous  is  the  effect  of  this  expenditure  upon  the 
rail-section.  If  expended  on  grading  and  masonry,  the  same 
amount  will  only  do  the  following: 

Cubic  Yards.. 

Earthwork,  at  20  cents  per  cubic  yard 1,200 

Equal  to  a  continuous  fill  5  in.  deep,  or  a  cut  10  ft.  deep  and 

100  ft.  long. 
Rock  cutting,  at  $1.50  per  cubic  yard i6a 

Equal  to  a  cut  100  ft.  long  and  2.3  ft.  deep. 
Culvert  masonry,  at  $5  per  cubic  yard 48. 

Or  one  small  box  culvert. 
Bridge  masonry,  at  $10  per  cubic  yard only  24 

Far  more  than  these  quantities  can  usually  be  saved  by  aban- 
doning the  attempt  to  fit  the  line  for  high  speed  and  long  trains, 
and  judiciously  economizing  in  these  three  ways  :  (i)  By  using 
sharp  curvature;  (2)  by  using  trestling  in  place  of  masonry  and 
heavy  earthwork;  (3)  by  moderate  undulations  of  grade;  to  which 
may  be  added  (4)  sacrifice  of  distance  to  obtain  easy  work,  and 
especially  to  reach  towns. 

1004.  Whatever  conclusion  may  be  just  as  to  the  proper  stand- 
ard OF  CURVATURE  for  Hnes  of  fair  traffic,  it  is  certain  that  for  a 
road  to  which  the  last  degree  of  economy  in  first  cost  is  essen- 
tial, and  which  does  not  expect  more  than  a  very  light  traffic,  the 
intelligent  use  of  sharp  curvature  offers  one  of  the  simplest,  most 


750   CHAP.   XXII.^LIGHT  RAILS  AND  LIGHT  RAILWAYS, 

effective,  and  most  expedient  methods  of  economizing  in  first 
cost.  We  have  seen  tliat  since  the  introduction  of  steel  rails  and 
air-brakes  both  the  operating  cost  and  the  danger  of  sharp  curva- 
ture have  been  greatly  diminished.  The  New  York  elevated  rail- 
ways run  800  or  more  trains  of  four  cars  each  per  day  around  the 
63°  curves  (shown  in  Figs.  201-2)  with  perfect  ease  and  with  only 
a  moderate  slackening  of  speed.  Another  much-used  curve  of 
50  ft.  radius  is  described  on  page  326.  In  Table  116  full  details 
are  given  of  other  sharp  curves  in  use  on  standard-gauge  lines, 
ranging  from  410  to  175  ft.  radius,  over  many  of  which  a  very 
heavy  traffic  passes.  While  these  extremes  are  to  be  deprecated 
{nor  are  they  often  required),  they  do  make  it  an  absurdity  to 
say  that  a  cheap  light-traffic  railroad  may  not  use  almost  any 
curvature  which  the  nature  of  its  route  calls  for  in  order  to  re- 
duce first  cost,  whatever  its  gauge. 

In  a  country  offering  any  difficulty,  the  reduction  which  can 
be  effected  in  this  way  is  very  large  indeed,  and  it  will  in  gen- 
eral be  found  that  no  excessive  reduction  of  radius  is  needed  to 
give  a  line  closely  approximating  to  a  surface  line,  and  fitting  so 
well  that  any  further  reduction  of  radius  will  save  but  little 
(par.  883).  This  disadvantage  is  far  less  than  that  of  light  rails 
in  almost  every  instance. 

1005.  Moreover,  if  the  profile  of  almost  any  line  be  studied,  it 
will  be  found  that  the  expenditures  are  largely  concentrated 
AT  SINGLE  POINTS.  Four  or  five  cuts  in  a  mile,  eight  or  ten  miles  in 
a  hundred,  are  what  bring  up  the  average;  so  that  in  seeking  the 
last  degree  of  economy  at  these  critical  points  the  line  as  a  whole 
is  not,  after  all,  so  seriously  modified  as  would  be  imagined,  A 
further  advantage,  or  rather  a  bright  side  to  the  disadvantage  of 
so  economizing  by  sharp  curvature  is  that  at  many  points  the 
works  may  assume  a  mere  temporary  character  for  present  ne- 
cessities, while  being  adapted  for  ready  improvement  in  the  fu- 
ture, when  and  if  means  exist  for  doing  so.  In  this  way  the  ne- 
cessities of  both  the  present  and  future  are  better  provided  for 
than  if  a  compromise  line  were  chosen  in  the  beginning  which 
did  not  fully  insure  either  present  cheapness  or  future  excellence. 
Par.  283  gives  a  notable  instance. 


CHAP,  XXII.—LIGHT  RAILS  AND  LIGHT  RAILWAYS.    75 1 


1006.  Here  the  question  of  gauge  naturally  comes  up.  Among 
the  many  advantages  which  have  been  so  loosely  claimed  for  the 
narrow-gauge  system,  perhaps  none  has  been  so  insisted  on,  or 
so  affected  the  popular  imagination,  as  this  one  of  being  able  to 
use  sharp  curves  readily  which  were  all  but  impracticable  with 
the  standard  gauge. 

A  few  years  ago,  when  the  first  edition  of  this  treatise  was  is- 
sued, no  discussion  of  the  question  of  light  railways  could  have 
been  adequate  without  entering  pretty  fully  into  \.\i^  pros  and 
cons  of  the  gauge  question.  This  is  no  longer  necessary.  The 
irresistible  logic  of  events  has  practically  settled  the  question, 
and  the  belief  in  the  narrow-gauge  as  an  expedient  and  defensi- 
ble system  of  construction,  which  was  from  the  beginning 
founded  chiefly  on  illusion  and  delusion,  is  rapidly  passing  away, 
and  all  but  gone.  We  may  therefore  merely  summarize  briefl'y 
file  leading  points  of  the  question. 

As  respects  curvature,  we  have  already  seen  (pars.  335-6)  that 
while  the  gain  in  curve  resistance  from  a  narrowing  of  gauge 
only,  with  no  other  change,  is  very  slight,  yet  when  the  wheel- 
base  is  reduced  correspondingly  the  curve  resistance  is  probably 
diminished  about  in  proportion  to  the  gauge.  As  this  is  what  is 
usually  done  in  practice,  we  may  consider  it  from  that  point  of 
view. 

1007.  But  the  question  then  arises:  What  is  saved  thereby  ?  If 
It  be  to  increase  the  hauling  capacity  of  engines,  a  very  slight  ad- 
ditional curve  compensation  will  neutralize  the  extra  resistance 
of  the  wider  gauge,  and  we  have  already  seen  (par.  290)  that  any 
radius  which  is  likely  to  be  desired  is  readily  practicable  foV 
properly  designed  standard-gauge  engines.  If' it  be  to  save  the 
extra  wear  and  tear  and  loss  of  power,  a  small  reduction  in  an 
Item  the  whole  of  which  is  so  small  (Table  115,  page  322)  is  not 
worth  any^considerable  sacrifice,  nor  can  it  be  taken  for  granted 
(nor  is  it  probable)  that  there  is  any  such  reduction. 

1008.  As  respects  rolling-stock,  there  cannot  be  a  question 
that  there  is  absolutely  no  practical  advantage  in  the  narrower 
gauge.    Any  reputable  locomotive-builder  will  contract  to  build 


I 


752    CJ/AP.   XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS, 

• • — — — -♦ ■ 

engines  of  the  same  weight  and  power  for  either  gauge,  which 
will  traverse  the  same  curves,  for. the  same  price.  The  standard- 
gauge  engine,  in  fact,  will  or  can  have  enough  shorter  wheel- 
base,  because  of  its  greater  width,  to  make  it  take  curves  a  little 
better — a  very  important  point  which  narrow-gauge  advocates 
and  opponents  alike  have  almost  wholly  lost  sight  of. 

The  same  is  essentially  true  of  the  cars.  The  car-bodies  may 
be  exactly  the  same,  and  the  trifling  loss  from  the  extra  width  of 
trucks,  if  it  were  worth  discussing  at  all,  may  be  fully  made  up 
by  a  slight  increase  in  the  weight  and  capacity  of  the  car-body,, 
while  car-bodies  of  the  ordinary  size  and  capacity  can  go  safely 
over  any  structures  or  track  which  will  carry  a  light  locomotive 
— whether  standard-gauge  or  narrow-gauge — and  carry  as  large 
a  proportion  of  paying  load  as  is  customary  in  narrow-gauge 
cars. 

1009.  The  bridges  and  trestles  are,  of  course,  not  affected  hf 
the  width  of  the  gauge,  if  rolling-stock  of  the  same  weight  and 
width  pass  over  them;  besides  which,  we  shall  shortly  see  evi- 
dence (par.  1039)  that  the  cost  of  bridges  is  but  very  little  affected 
by  the  load  per  lineal  foot  they  are  built  to  carry,  so  that  there 
is  little  real  inducement  to  build  such  structures  to  carry  less  than 
the  common  loads. 

The  earthwork  and  masonry  is  affected  only  by  whatever  dif- 
ference there  may  be  in  the  width  of  the  road-bed,  which  cannot 
properly  be  more  than  the  difference  of  gauge.  The  ties,  we  shall 
soon  see  (par.  1056),  may  be  made  somewhat  shorter,  or  about 
three  quarters  of  the  usual  width,  but  only  at  the  expense  of  de- 
creasing the  stability  of  the  track  and  increasing  the  labor  re- 
quired. 

Fencing,  right  of  way,  buildings,  frogs,  switches,  side-tracks, 
shops,  etc.,  etc.,  are  not  affected  at  all,  if  the  standard  of  excel- 
lence and  weight  of  rolling-stock  be  the  same. 

1010.  There  remains,  therefore,  as  the  net  gain  from  the  nar- 
rower gauge,  only  the  slight  saving  in  grading  and  ties,  which 
may  amount  to  one  to  four  per  cent  of  the  total  cost  of  the  line. 

On  the  other  hand,  there  are  several  very  serious  losses.    The 


CHAP.   XXII.-LIGHT  RAILS  AND  LIGHT  RAILWAYS   753 

one  which  is  alone  of  decisive  importance  is  the  great  loss  from 
not  being  able  to  exciiange  traffic  in  bulk,  but  having  to  trans- 
ship all  freight  and  passengers.  The  loss  from  this  is  far  more 
than  its  direct  cost.  The  resulting  inconvenience,  delay,  and 
damage  to  freight  drives  away  much  traffic. 

The  cost  of  maintaining  track  to  a  given  standard  of  excel- 
lence is  likewise  greater,  the  cost  for  track-labor  being  in  about 
inverse  proportion  to  the  length  of  the  ties.  The  less  bearing 
area  of  the  ties  on  the  ballast  increases  this  disadvantage  ma- 
terially. ^ 

The  maintenance  of  rolling-stock  is  decidedly  more  costly  in 
proportion  to  work  done,  and  the  train  resistance  higher,  because 
of  the  smaller  wheels.  The  speed  is  necessarily  lower,'  and  the 
passenger  cars  less  comfortable. 

Tiiese  facts  are  now  admitted  by  all  intelligent  managers, 
whether  of  broad  or  narrow  gauge,  and  the  reconstruction  of 
narrow  to  standard-gauge  is  now  going  on  with  great  rapidity, 
Several  thousand  miles  of  narrow-gauge  lines  have  already  been 
changed,  and  it  is  plainly  only  a  matter  of  a  few  years  when  prac- 
tically all  the  remaining  lines  will  be  changed 

1011.  It  is  often  apologetically  admitted  by  those  otherwise 
opposed  to  the  narrow-gauge  that  for  certain  mountainous  re- 
gions  it  is  best  adapted.  This  likewise  is  an  error,  except  for 
such  few  lines  as  are  not  likely  to  either  have  or  desire  traffic 
relations  with  other  roads. 

An  example  is  the  great  system  of  narrow-gauge  lines  in 
Colorado.  The  Denver  &  Rio  Grande  was  projected  in  the 
early  days  of  the  narrow-gauge  movement,  and  did  much  to 
extend  it,  if  indeed  it  may  not  be  said  to  have  been  the  origin  of 
It,  as  it  certainly  was  the  source  of  its  temporary  strength.  It 
>s  by  much  the  most  considerable  narrow-gauge  system  in  the 
world,  and  for  many  years  was  a  great  financial  success;  nor  are 
Its  later  troubles  to  be  ascribed  primarily  to  its  gauge,  but  to 
bad  judgment  in  extensions  and  other  expenditures. 

Nevertheless,  the  success  of  this  line  had  little  or  nothing  to 
do  with  its  gauge,  but  was  due   rather  to  the  fact  that  it  was 
48 


% 


754   C//AP.    XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS. 


cheaply  built,  and  was  assured  a  monopoly  of  a  remunerative 
and  growing  traffic  at  very  higli  rates— rates  from  three  to 
eight  limes  higher  than  were  usual  on  lines  farther  east.  The 
disadvantages  of  a  break  of  gauge  were  likewise  reduced  to  the 
minimum  by  its  location.  Its  narrow-gauge  system  was  com- 
plete in  itself,  and  connected  with  standard-gauge  tracks  at  but 
a  few  points,  where  transshipment  was  often  no  disadvantage. 

Yet  even  under  these  circumstances — the  most  favorable  under 
which  any  large  narrow-gauge  lines  have  ever  been  placed — the 
disadvantages  of  the  gauge  have  proved  so  serious  that  it  is 
now  (1887)  only  the  lack  of  means  which  prevents  the  immediate 
widening  of  the  gauge  on  all  the  more  important  lines.  To  do 
this  involves  little  expense.  The  ties  are  rather  short  for  the 
purpose;  but  the  20°  and  24°  curves  can,  in  the  first  place,  be 
passed  without  difficulty  by  the  standard-gauge  engines,  and,  in 
the  second  place,  the  cost  of  reconstructing  such  curves  as  are 
objectionable,  while  it  may  be  a  considerable  absolute  sum,  will 
be  a  very  trifling  one  in  proportion  to  the  total  investment,  and 
probably  far  less  than  the  present  yearly  loss  from  the  narrower 
gauge. 

1012.  The  use  of  a  narrower  gauge  to  cheapen  construction 
has  been  proved  by  actual  experience,  therefore,  to  be  in  all  cases 
inexpedient  for  any  road  handling  a  general  traffic,  or' having 
any  reasonable  chance  of  wishing  to  exchange  traffic  with  other 
lines. 

1013.  Returning  to  the  more  hopeful  directions  for  economy: 
the  free  use  of  wooden  trestling  and  the  practical  abandon- 
ment of  the  (immediate)  use  of  masonry  is  another  legitimate 
and  wise  device  for  reducing  first  cost. 

There  are  not  a  few  engineers  who  decry  the  use  of  wooden 
trestles,  nor  can  it  be  denied  that  they  are  often  ill  and  danger- 
ously built,  and  then  neglected  so  long  that  they  become  a  fre- 
quent source  of  accident.  But  when  properly  built  and  properly 
kept  up,  they  furnish  a  safe  and  cheap  method  of  avoiding  or 
postponing  the  more  costly  features  of  construction,  so  that, 
even  for  roads  of  considerable  traffic,  it  is  far  wiser  to  preach 


CHAP.    XXII-LIGHT  RAILS  AND  LIGHT  RAILWAYS.    755 

the  gospel  of  sound  construction  than  to  decry  their  existence 
Fortunately,  under  existing  conditions  in  America,  most  of  the 
localities  where  very  light  railways  only  can  be  supported  are 
near  enough  to  local  timber  supply  to  obtain  pine,  hemlock  or 
other   suitable    trestling  timber   at    very  low  prices;  and   with 
split  stringers,  and  split  sills  and  caps,  it  is  easilv  possible  (with- 
out going  into  fuller  details,  which  would  be  inappropriate  in 
this  volume)  to  erect  substantial  structures,  without  mortises   in 
which   each   individual  stick  is   renewable   in   detail,  and   which 
will  be  as  safe  for  the  passage  of  trains  as  any  bridge,  so  long  as 
they  are  properly  maintained.     The  great  majority  of  the  trestles 
now  erected  in  this  country,  however,  are  ill-designed,  especiallv 
as  respects  the  floors. 

1014.  At  somewhere  from  10  to  15  feet  of  height  of  fill  such  a 
structure  becomes  cheaper  in  first  cost  than  even  a  plain  earth  fill- 
and  when,  in  addition  to  the  fill,  there  would  have  to  be  a  ma- 
sonry structure,  or  when,  if  it  were  not  for  the  trestle,  the  grade 
would  have  to  be  dropped  or  the  line   swung  in  so  as  to  give  a 
rock  cut  (or  even  a  heavy  earth  cut)  at  each  end  of  it,  the  trestle 
becomes  very  much  cheaper,  and  its  free  use  affords  us  a  solid 
and  safe  roadway  for  immediate  use  which  can  be  continued  in 
the  same  form   indefinitely,  if  poverty  requires  it,  or  which  can 
be  advantageously  and  economically  replaced   by  more  perma- 
nent structures  at  any  time,  using  trains  to  make  the  fills  and 
supply  the  stone, 

1015.  It  is  also  allowable  to  use  wooden  box  culverts  to  be 
replaced  in  time,  as  they  begin  to  decay,  by  iron  pipes  placed 
inside  of  them.  Many  great  roads  where  stone  is  scarce  build 
these  in  place  of  open  culverts  or  trestles  as  a  regular  practice 
and  much  can  be  said  for  it.  No  road,  of  course,  would  use 
wood  for  box  culverts  when  stone  could  be  obtained  at  reason- 
able cost. 

1016.  The  use  of  moderate  undulations  on  gradients  affords 
^nother  means  by  which  the  first  cost  of  a  line  mav  often  be 
largely  reduced,  and  we  have  seen  (par.  397)  that  if  the  track  be 
good  enough  to  stand  a  certain  moderate  increase  of  speed  at 


756   CHAP,   XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS, 


special  points,  it  involves  no  injury  to  the  hauling  capacity  of 
engines.  The  limits  within  which  momentum  can  be  relied  on 
in  this  manner  has  been  already  considered  (par.  441)  and  may, 
when  economy  is  urgent,  be  closely  approached,  as  in  the  in- 
stance of  par.  832,  because,  should  such  undulations  prove  seri- 
ously objectionable,  they  may  be  taken  out  at  any  time.  This 
is  certainly  a  far  wiser  way  of  economizing  than  cutting  down 
the  rail  so  light  that  it  will  barely  carry  the  engine,  as  is  often 
done. 

1017.  Finally,  one  remaining  device  will  complete  all  that  is 
possible,  or  probably  necessary,  in  the  way  of  reducing  the  first 
cost  of  the  road-bed.  A  great  deal  of  money  is  spent  by  many 
roads  which  can  ill  afford  the  luxury  in  getting  a  short  line.  In 
the  light  of  the  facts  brought  out  in  Chap.  VII,  it  is  unquestion- 
able that,  how^ever  it  may  be  with  roads  of  large  or  of  fair  traffic^ 
a  cheap  light-traffic  railway  which  spends  money  to  get  a  short 
line  is  burning  its  candle  at  both  ends,  ai»d  the  engineer  of  such 
a  line  cannot  too  carefully  remember  that,  although  on  the  one 
hand  its  length  may  be  the  ruin  of  it,  because  it  has  to  operate 
it.  vet  on  the  other  hand  it  is  its  salvation,  because  its  revenue 
depends  on  it. 

1018.  Especially  is  this  true  when,  in  choosing  the  easiest 
line  regardless  of  distance,  we  not  only  obtain  an  easier  line  to 
construct,  but  one  which  will  take  us  nearer  to  the  various 
SOURCES  OF  TRAFFIC.  Howcvcr  it  may  be  with  lines  of  larger 
traffic,  a  poor  railway  certainly  cannot  afford  to  pass  by  on  the 
other  side  even  quite  small  traffic  points  which,  by  going  nearer 
to  them,  will  add  a  little  more  traffic  to  the  slender  aggregate; 
not  only  because  every  little  helps,  but  because  the  revenue  per 
head  of  that  population  is  also  smaller,  as  we  have  seen  in  the 
preceding  chapter. 

1019.  The  truths  which  have  been  stated  are  not  to  be  taken 
*'  neat,"  nor  recklessly  twisted  to  mean  more  than  has  been  said; 
as,  for  instance,  that  it  is  ever  expedient  to  lengthen  a  line  merely 
for  the  sake  of  lengthening  it,  or  that  it  is  not  worth  while  to  try 
to  avoid  curvature,  or  that  wooden   trestles  are  as  good  as  per- 


CHAP.   XXII.-LIGHT  RAILS  AND  LIGHT  RAIL  WA  YS.    757 


manent  works.  It  has  been  merely  intended  to  show  that,  for  a 
road  which  must  practise  the  last  degree  of  economy  and  which 
has  little  more  than  a  turnpike  traffic,  the  construction  of  the 
ROAD  TO  SUB-GRADE  is  the  proper  place,  and  the  most  hopeful 
place,  for  J' cutting  to  the  bone,"  because  an  amount  sufficient 
to  give  a  decently  solid  superstructure  can  usually  be  saved  out 
^f  the  first  construction  with  far  less  risk  of  injury  and  loss 
This   IS  apparent  from  Table  199,  showing  the  percentages  of 

Table  199. 

-Showing  the  Percentage  of  Cost  to  Sub-Grade  on  Various  Items  of 
Construction  on  Various  Lines. 


Length,  miles 

Total  cost  per  mile.. . 
Clearing 


I. 


trading,    |  ^^''^h. 


Masonry,  ] 
Bridging 


Rock . . . 
Culverts. 
Bridge.. 


Trestling,  etc. 
Fencing,  etc. . 
Tunnel 


60 
Is. 073 

2.1 
71.0 

•  •   •   • 


14.3 
12.6 


11. 


100 
$7. 490 

•  •  •   • 

61. g 

•  •    •    » 

6.1 

13.7 
2.0 

II. 7 
4.6 


III. 


14-5 
I18.260 

0.2 

51.0 

7- 
II, 

13- 
I. 

9- 


5 
.0 

5 
2 
I 


IV. 


100. o 


100. o 


6.5 


100.  o 


46 

118.920 
2.0 

35.1 


5.8 

12.4 
31.8 
12.9 


V. 


100. o 


^  15 

$83,854 

•   •   •    • 

25.7 
50.3 

5-4 
9.8 

1-5 


7.3 


100. o 


Character  of  Lines  : 


stone- work, 
many  structures. 


^\r    T  ,M,f  c.    /  j^ .  very  numerous  structures. 

V'  n.S  .f^h         ^l-ading:,  two  costly  bridges  only  ;  much  hijjh  trestling- 
V.  One  of  the  costliest  sections  of  mountain  line  in  the  Unitid  Stated 

AwJ^A     7' u '"^^  ""''  ""^  ^""'^"''  "^^'  ^^^^'"^"  ^°^^'  ^-^'•^'  hundred  miles  lon^  was 
divided  as  follows,  mcluding  all  items,  and  not  those  to  sub-grade  only  : 


Engineering  ^j^* 

Grading,  including  tunneilW!!.'."!.*""  2,6 

"ridge  masonry \f^ 

Culvert  masonry \ 

Temporary  trestling  j  ^ 

Superstructure,  bridges  and  trestles  .■.".'.■  45 
«allast.  and  settling  of  embankments. . .  ,7 
^ressmg  up  road-bed  after  winter.  i  7 

K'ght  of  way.  fencing,  cattle-guards  and      ' 

road -crossings ._ 

-Kails  and  track-laying,  complete".*.!.*.*  .*.".■  179 


Cross-ties  (very  small) '^\^' 

Engine-houses,    shops,   stations,    water 

supply,  pumps,  etc g  „ 

Locomotives  and  cars  iq^ 

Interest  on  bonds  to  opening e  8 

Discount  on  bonds 7,.     f° 

Taxes  to  opening '^'' 

Office  expenses,  salaries,  etc.',*  "t*© 'o^n-      ' 

ingof  line ^ 

Incidental  to  opening  of  line .......'.  03 

Total  to  opening  of  line 


100. o 


per  iw 


758    C^AP.   XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS, 


CHAP,   XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS.   759 


th*^  cost  to  sub-grade  of  various  items  on  different  railroads,  all 
of  them  of  comparatively  light  (although  not  the  lightest)  traffic, 
and  varying  in  character  of  work  from  moderately  light  to  the 
very  heaviest.  The  prices  on  all  of  them  were  from  25  to  40  per 
cent  higher  than  now  (1886)  obtain,  under  favorable  conditions; 
but  in  each  case  alike  it  will  be  seen  how  much  less  injury  a  sav- 
ing of  $240  per  mile  in  some 'or  all  of  the  items  given  would 
probably  have  done  to  the  road  than  if  5  lbs.  per  yard  were  cut 
off  the  rail-section. 

1020.  Nothing  has  been  said  so  far  about  gradients,  because 
a  very  light  traffic  road  cannot  afford  to  spend  money  to  obtain 
more  favorable  gradients  than  careful  study  of  the  country  will 
afford  at  the  minimum  cost,  which  (par.  894)  will  generally  be 
quite  reasonably  favorable.  At  any  rate,  while  the  temptation 
for  the  locating  engineer  to  magnify  his  office  may  be  great, 
until  provision  has  first  been  made  for  a  reasonably  substantial 
and  well-maintained  track,  it  may  be  taken  as  a  tolerably  safe 
general  rule,  that  the  same  amount  of  money  expended  on  track 
will  add  far  more  to  the  hauling  capacity  of  the  line  than  if  ex- 
pended to  reduce  gradients. 

1021.  Cutting  the  work  down  in  the  various  ways  suggested, 
with  due  care  to  do  the  minimum  of  injury  to  its  efficiency,  $3000 
to  $5000  per  mile  may  be  made  to  grade  a  very  light  railway 
through  tolerably  broken  country,  and  this,  of  course,  under  fa- 
vorable circumstances,  may  be  reduced  much  lower.  For  such 
lines,  intelligently  planned,  there  is  and  will  probably  always  be 
a  very  wide  field.  The  trouble  is  that  the  economy  is  too  often 
given  a  wrong  direction,  and  the  item  which  is  ordinarily  the 
first  attacked — the  rail-section — is  one  of  the  last  of  all  to  attempt 
to  economize  in. 

1022.  This  may,  perhaps,  be  made  still  clearer  if  we  revert  to  the  rail 
question  for  a  moment  to  consider  a  little  more  exactly  the  RELATIONS 
OF  RAIL  TO  TRACK-LABOR.  Where  is  money  for  improving  track  best 
expended— in  increasing  the  rail-section  or  in  more  track-labor  ?  The 
stiffer  the  rail  the  less  perfect  need  be  the  supports  of  the  road-bed  for 
equal  excellence ;  but  it  is  sometimes  claimed  that  this  needed  support 


can  be  more  cheaply  obtained  by  putting  a  little  more  work  into  the  sur- 
facing, especially  when  extreme  economy  in  first  cost  seems  necessary. 
It  hardly  needs  more  than  a  few  contrasting  figures  to  see  that  this  is 
more  an  impression  than  a  well-founded  belief. 

1023.  To  increase  the  weight  of  rail  10  lbs.  per  yard  requires,  in  round 
numbers,  16  tons  per  mile,  costing,  at  the  even  figure  of  $30  per  ton,  $480 
per  mile,  the  interest  on  which  is, 


At  5  per  cent, 
$24.00. 


At  ID  per  cent, 
148,00. 


At  20  per  cent, 
).oo. 


Equal  to  a  cost  in  cents  per  train-mile,  assuming  various  numbers  of 
trains  per  day  each  way,  of 

. Cents  PER  Train-Milr , 

At  5  p.  c.  At  10  p.  c.  At  20  p.  c. 

I  train  per  day 3.29  6.58  13.16 

104  329  6.58 

*°  0.33  0.66  1.32 

^^  o-i6  0.33  0.66 

1024.  The  common  expenditure  on  raising  and  surfacing,  ballast,  etc., 
IS  about  10  cents  per  train-mile,  as  an  average,  and  from  that  to  15  on 8 
cents  per  train-mile  on  roads  of  very  light  traffic ;  and  contrasting  this 
sum  with  the  figures  above,  we  see  at  once  that  on  a  road  of  any  consid- 
erable traffic,  which  is  a  kind  of  road  we  are  not  now  considering,  the 
stability  gained  by  adding  10  lbs.  per  yard  to  the  weight  of  a  rail  would 
give  far  more  for  the  money  invested,  at  any  probable  rate  of  interest, 
than  the  expenditure  of  an  equivalent  sum  annually  on  additional  track- 
labor  for  lining  and  surfacing.  On  a  road  running  20  trains  per  day. 
even  if  it  cannot  get  money  at  less  than  10  per  cent,  the  interest  charge 
of  $48  per  year  per  mile  amounts  to  but  0.33  cents  per  train-mile.  There- 
fore the  extra  5  lbs.  per  yard  has  only  to  save  less  than  3^  per  cent  of 
track-labor  to  be  a  paying  investment.  It  is  unquestionable  that  far 
more  than  that  might  be  saved,  and  yet  maintain  equal  condition,  even 
when  the  rail  was  a  tolerably  heavy  one. 

1025.  As  respects  the  extreme  of  light-traffic  roads,  especially  those 
built  at  great  cost  for  capital,  it  must  be  admitted  that  the  case  is  not  so 
clear  as  that.  In  fact,  for  the  extreme  of  thin  traffic  and  scant  capital, 
say  one  train  per  day  and  20  per  cent  cost  of  capital,  it  seems  at  first  sight 
clear  that  it  will  not  pay  to  increase  the  rail-section  beyond  what  safety 
requires,  as  the  cost  of  interest  on  even  5  lbs.  per  yard  extra  weight  of 
rail  will  in  that  case  be  6.58  cents  per  train-mile. 


■ 


76o   CHAP.   XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS. 


■^f  ' 


! 


1026.  But,  premising  that  this  extreme  case  can  but  rarely  be  ap- 
proached in  practice,— because  (i)  there  are  few  even  of  the  lightest-traffic 
roads  which  do  not  run  more  than  one  train  each  way  per  day;  and  (2) 
few  roads  are  so  poor  that,  if  the  case  is  properly  presented,  they  cannot 
raise  a  moderate  ar/iil// Zona/  capital  for  betterments  which,  whatever  the 
profit  on  the  enterprise  as  a  whole,  will  return  20  per  cent  profit  on  their 
own  separate  cost, — it  may  be  reasonably  maintained  from  the  result  of 
experience  that  even  in  this  extreme  case  the  extra  weight  of  rail  is  the 
best  use  which  can  be  made  of  the  money.     The  very  least  which  can 
possibly  be  spent  on  mere  track-surfacing  and  maintenance  (par.  124)  to 
keep  it  in  fairly  safe  condition  for  the  passage  of  one  train  per  day,  is 
from  $100  to  $125  per  mile,  with  $80  to  $100  additional  for  ties,  or,  say, 
$200  in  all,  excluding  perhaps  $100  more  for  yards  and  miscellaneous. 
The  cost  of  the  5  lbs.  per  yard  extra  weight,  even  at  20  per  cent  interest 
on  capital,  is  only  $48  per  year,  for  which  slight  increase  of  one  fifth  or 
one  sixth  in  the  interest  charge  on  rails  we  have  just  seen  (Tables  195, 
196,  197)  that  we  obtain  an  average  increase,  in  a  very  light  rail,  of  fully 
50  per  cent  in  the  three  elements  of  strength,  stiffness,  and  durability. 
Granting  a  road  to  be  so  poor  that  no  increase  whatever  in  total  charges 
can  be  borne  for  any  betterment,  however  great,  beyond  absolute  neces- 
sities, is  it  certain  that  so  great  a  difference  in  the  stability  of  the  rail 
will  not  enable  one  fourth  of  the  otherwise  minimum  track  expenditure 
to  be  saved,  while  yet  leaving  the  track  as  safe  and  good  as  before  ?     It 
is  fairly  even  balance,  indeed,  under  tliis  extreme  supposition.     Unless 
the  rails  were  very  light  indeed,  it  probably  would  not  pay  to  increase 
their  weight;  but  it  is  difficult  to  escape  from  the  conclusion  that  under 
any  ordinary  conditions,  with  the  lightest  traffic,  it  plainly  will  pay  to 
use  a  tolerably  heavy  rail  before  relying  on  track-labor  to  make  up  by 
better  surfacing  for  its  deficiency  of  strength,  simply  to  save  a  slight  ad- 
ditional investment  of  capital. 

1027.  If  so,  then  as  the  traffic  increases  up  to  a  comfortable  average, 
as  to  six  or  eight  or  ten  trains  each  way  per  day.  there  becomes  plainly 
an  immense  economy  in  using  heavy  rails  to  save  track-labor,  so  much 
so  as  to  indicate  strongly  that  the  very  curious  similarity  in  weight  of 
rails  used  on  all  roads  in  this  country  above  the  poorest  class,  despite  the 
great  difference  in  volume  of  traffic,  is  due,  not  so  much  to  the  use  of  too 
heavy  rails  on  light-traffic  roads,  as  the  use  of  far  too  light  rails  for  true 
economy  on  our  more  important  lines,  as,  for  instance.  60-  or  65-lb.  rails 
on  trunk  lines  which  would  be  acting  more  wisely  to  use  80-  or  90-  or 
loo-lb.  rails.     The  difference  is,  however,  that  such  lines  are  rich  enough 


CHAT.    XXII.— LIGHT  RAILS  AND  LIGHT  RAILWAYS.    761 

•to  stand  the  resulting  loss,  whereas  a  poor  road  which  permits  its  poverty 
to  destroy  it  by  buying  an  over-light  rail,  cannot.  Some  of  our  more 
prosperous  lines  have  recently  begun  to  break  through  this  rule  by  using 
what  are  now  called  very  heavy  rails,  but  the  exceptions  are  not  yet  so 
numerous  as  to  do  more  than  prove  the  rule.  It  is  in  every  way  prob- 
able that  within  a  few  years  8o-lb.  or  90-lb.  rails  will  be  the  rule  and 
lighter  rails  the  exception.  The  inertia  from  past  precedents,  which 
have  come  down  to  us  from  the  days  when  rails  were  several  times  more 
costly  than  now,  will  in  time  be  overcome. 

1028.   We  are,  therefore,  again  and    more   strongly  driven   to 

the  conclusion,  that  the  one  thing  on  which  it  is  dangerous  to 

economize  is  the  item  which  is  often  cut  down  first  of  all— the 

weight  of  rail.     On  the  other  hand,  we  are  led  to  these  conclu- 

^sions  as  respects  the  details  of  alignment: 

1.  As  respects  the  minor  details,  distance,  curvature,  and  rise 
and  fall,  their  effects  to  increase  expenses  are  at  best  small,  and 
when  the  traffic  is  very  light  become  very  small.  They  are, 
therefore,  one  of  the  first  directions  in  which  close  economy  is 
warrantable  for  very  light  roads. 

2.  In  less  degree  the  same  is  true  of  ruling  grades.  Much 
increase  of  expenditure  to  obtain  lower  grades  than  a  careful 
study  of  the  ground  shows  to  be  possible  at  a  minimum  expense 
is  not  warrantable. 

3-  Both  the  above  conclusions  are  especially  true  when  the 
objectionable  details  may  be  readily  corrected  later,  when  and  if 
the  traffic  warrants  it. 

4.  Temporary  wooden  structures  to  decrease  the  immediate 
outlay  are  the  next  most  judicious  direction  for  economy. 

5.  Economies  which  decrease  the  stability  of  the  permanent 
way  are  the  most  objectionable  of  all. 

6.  Sources  of  local  traffic  which  can  be  reached  by  any  rea- 
sonable sacrifice  should  in  no  case  be  neglected. 


• 


ii 

4 
ft 


762    CJ/AP.   XXIIL—THE  ECONOMY  OF  CONSTRUCTION. 


CHAP.   XXI I  I. —  THE  ECONOMY  OF  CONSTRUCTION.    y6^ 


CHAPTER  XXIII 

THE   ECONOMY    OF    CONSTRUCTION. 

1029.  We  must  necessarily  assume,  in  considering  the  /r^r 
and  cons  of  many  of  the  details  of  construction  (as  in  par.  13), 
that,  the  construction  of  the  road  once  entered  on,  a  little  more 
or  less  money  will  not  be  a  serious  question,  but  that  means  will 
always  be  forthcoming,  at  some  rate  of  interest  or  other,  if  only 
it  can  be  shown  that  the  additional  investment  will  be  profit- 
able. 

But  while  this  is  so  far  true  in  a  small  way  that  it  is  the 
only  proper  guide  for  planning  the  details  of  a  line,  yet  it  is 
undeniable  that,  when  extended  to  larger  questions,  affecting 
considerable  sums  of  mone}'^,  it  does  not  in  all  cases,  nor  in  many 
very  prominent  cases,  correspond  with  the  facts;  which  are 
rather  that  a  certain  gross  sum  only  is  available,  and  when 
that  is  exhausted,  if  it  has  not  been  so  expended  as  to  com- 
plete all  the  more  essential  details  of  the  line,  the  company  be- 
comes bankrupt,  and  the  line  passes  into  other  hands — perhaps 
for  lack  of  only  a  small  fraction  of  the  sum  which  has  been  al- 
ready lavishly  expended. 

So  many  prominent  instances  of  this  have  happened,  that  it  is 
no  more  than  common  prudence  to  assume  that  there  is  immi- 
nent danger  of  it  in  the  case  of  every  new  line,  to  the  extent  of 
guarding  against  it  so  far  as  is  legitimately  possible. 

1030.  This  is  the  more  true  because  of  the  fact  alluded  to  on 
page  34,  that  money  for  new  lines  of  importance  or  for  extensive 
additions  to  old  lines  can,  as  a  rule,  only  be  raised  in  "good 
times."  "  Good  times"  are  times  of  high  prices,  as  Fig.  246  il- 
lustrates very  forcibly,  and  are  naturally  followed  within  two  or 
three  years  by  ''  bad  times."     By  that  time  the  new  line  is  per- 


haps nearly  built,  and  needs  its  last  instalment  of  money,  which 
latter  is  often  a  sum  which  it  was  not  expected  to  need,  and 
which  was  even  refused  when   offered,  for  fear  of  letting  in  toa 


Fig   246.-PRICES  OF  English   Iron   and  Steel  Rails  (shown  by  Shaded   Lines)  and  of 
American  Steel  Rails,  Refined  Bar  Iron,  and  No.  i  Pig  Iron,  from  1855  to  1886. 

many  "on  the  ground -floor"— and  this  money  very  often  indeed 
has  to  be  raised  at  great  disadvantage,  if  raised  at  all. 

Unfortunately,  the  order  of  time  in  which  the  various  expen- 
ditures are  incurred  is  such  as  to  rather  increase  this  danger. 
Many  of  the  most  essential  expenditures  come  last  of  all,  and 
many  of  those  which  may  be  most  harmlessly  curtailed  or  post- 
poned come  first. 

The  locating  engineer  is  in  particular  danger  of  overloading 
his  company  in  this  way,  because,  from  the  order  of  time  in 
which  his  work  is  done,  he  in  effect  hypothecates  a  large  part  of 
Its  funds  to  meet  expenses  which  are  not  fully  defrayed  until 
near  the  very  end  of  construction.  Prudence  indicates,  there- 
fore, that  whenever  there  is  even  the  slightest  doubt  of  securing 
the  money  necessary,  the  work  should,  from  the  first  (par.   7)^ 


■li 


% 


It 


764   C//AP.    XX///.—  TJ/E  ECONOMY  OF  CONSTRUCTION. 

be  conducted  on  the  assumption  that  only  a  given  minimum 
sum  will  be  certainly  available,  and  that  from  it  enough  should 
be  reserved  to  cover  the  most  necessary  items  at  least.  The 
question  then  arises  :  In  what  direction  will  close  economy  do 
least  harm  ? 

So  far  as  it  goes,  the  preceding  chapter  is  an  answer  to  this 
question,  for  the  economies  least  harmful  to  a  light  road  are 
likely  to  be  also  least  harmful  to  a  line  of  fair  to  large  prospective 
traffic.  It  is,  however,  not  a  complete  nor  entirely  pertinent  an- 
swer. 

1031.  Perhaps  the  first  of  all  directions  in  which  economy  should 
be  sought,  or  rather  the  last  one  in  which  expense  should  be  in- 
curred, is  in  the  building  or  purchase  of  branches  during  the 
period  of  original  construction.  There  are  exceptions  to  this 
rule,  as  there  are  to  all  rules  ;  but  as  a  rule,  a  point  so  important 
tliat  a  branch  to  it  cannot  be  legitimately  postponed  until  the 
main  line  is  finished,  is  so  important  that  the  main  line  should 
be  carried  through  it.  Only  in  the  event  that  all  other  expenses 
are  certainly  provided  for,  should  the  construction  of  main  line 
and  branches  be  undertaken  simultaneously. 

To  give  only  a  single  example  of  the  importance  of  this  rule,  the  Canada 
Southern  Railway  Company,  while  it  was  building  its  main  line  to  Chicago, 
■carried  on  simultaneously  the  construction  of  the  St.  Clair  branch,  62  miles, 
and  an  extension  into  Michigan  from  St.  Clair;  the  Toledo  and  Detroit  branch, 
52  miles;  and  also  involved  itself  in  expenses  to  control  an  existing  line  to  Ni- 
agara Falls.  Had  the  money  which  went  into  these  desirable  but  subordinate 
lines  been  concentrated  on  its  main  line,  the  latter  would  probably  have  been 
completed  to  Chicago,  and  would  then,  probably,  have  secured  enough  traffic 
to  have  saved  its  projectors  from  the  almost  total  loss  which  the  panic  of  1873 
brought  upon  them,  in  spite  of  certain  unfavorable  circumstances. 

1032.  Allied  to  the  question  of  building  branches  is  that  of 
double-tracking  during  original  construction.  If  there  is  any 
reasonable  doubt  of  securing  funds  to  carry  through  the  entire 
enterprise  successfully,  opening  a  single  track  only  at  first  is  cer- 
tainly the  next  most  reasonable  method  for  a  temporary  econ- 
omy, to  insure  that  the  means  on  hand  shall  not  give  out  before 
the  line  is  in  working  order,  and  on  a  business  footing.     If  it  be 


CHAP.    XXIII.— THE  ECONOMY  OF  CONSTRUCTION.    76^ 

reasonably  certain  that  a  double  track  will  be  needed  in  the  near 
future,  all  masonry  structures  may  be  built  at  once  for  double 
track,  which  will  involve  but  a  small  addition  to  the  total  cost  of 
the  road— ordinarily  not  over  five  per  cent,  and  often  much  less 
If  It  appear  still  more  certain  that  a  double  track  will  be  speed- 
ily needed,  even  the  grading  may  be  done  in  the  first  instance 
for  double  track,  and  grading  and  masonry  together  will  not  or- 
dinarily increase  the  immediate  capital  required  more  than  la 
to  15  per  cent. 

But  as  both  the  grading  and  masonry  for  double  track  can 
ordinarily  be  done  to  somewhat  better  advantage,  on  the  whole 
after  the  track  is  laid  than  before,  the  expediency  of  doing  even 
this  much  immediate  work  to  provide  for  the  future  is  question-^ 
able,  unless  the  financial  condition  of  the  line  is  very  strong-  and 
tiie  following  items  for  double  tracking,  at  least,  can  always  be 
postponed  to  advantage  till  the  line  is  opened,— even  if  it  is  fully 
expected    to    immediately  proceed    with    double    tracking,  and 
funds  for  if  appear  to  be  certain,— viz.,  the  bridging,  ties,'rails 
and  ballasting.  ^ 

1033.  In  IRON  bridging  there  is  not,  contrary  to  what  is  gen- 
erally imagined,  any  economy  worth  taking  the  slightest  chance 
for,   in    building  double-track    bridges    instead   of   two    parallel 
single-track   bridges.     The   weight  of  a  double-track  bridge  is. 
increased  about  90   per  cent  over  a  single-track  bridge  of  the 
same  span,  and  for  the  same  live  load ;  and  although  the  cost  of 
the  structure  is  not  increased   in  quite  the  same  proportion,  yet 
when  we  take  into  consideration  (i)  even  a  year  or  two's  interest 
at  ordinary  cost  of  capital ;  and  (2)  the  depreciation  and  possi- 
ble great  need   of  the   invested   capital  in   the  dark  days  of  the 
hrst  operation,  the  petty  saving  is  not  to  be  considered  in  com- 
pan  son. 

There  is  also  a  certain  considerable  operating  advantage  in 
'Wing  independent  bridge-spans  for  each   track,  although  the 
single  structure  is  unquestionably  the  most  pleasing  to  the  eye 
An  accident  to  one  structure  leaves  the  other  one  available. 

The  superstructure  of  the  double  track  complete,  on  a  line 


I;- 


'j(^  CHAP.   XXIII.— THE  ECONOMY  OF  CONSTRUCTION, 

requiring  double  track,  will  ordinarily  cost  $10,000  per  mile — a 
sum  which  has  repeatedly  made  all  the  difference  between  suc- 
cess and  failure. 

If  any  line  could  be  justified  by  the  nature  of  its  expected  traffic  in 
laying  a  double  track  at  once,  it  was  the  West  Shore  Railroad,  but  had 
this  policy  been  adopted  by  that  line  in  respect  to  the  double  track  and 
some  similar  matters,  it  would  probably  have  saved  it  from  bankruptcy. 

1034.  In  Fig.  247  is  given  a  diagram  prepared  by  the  writer  from  va- 
rious data,  but  chiefly  from  formula  for  estimating  the  weight  of  bridges 
given  in  a  valuable  paper  by  Geo.  H.  Pegram,  C.E.,  a  bridge  engineer  of 
large  experience  (Trans.  Am.  Soc.  C.  E.  1885),  which  shows  graphically 
several  things  of  importance  in  respect  to  bridges. 

It  shows,  first,  how  nearly  a  double-track  bridge  comes  to  being 
double  the  weight;  secondly,  how  little  saving  is  effected  by  building 
bridges  to  carry  light  loads;  thirdly,  the  point  at  which  the  saving 
effected  by  using  steel  instead  of  iron  becomes  important;  SL.nd, fourthly, 
the  comparative  weight  of  various  spans  by  inspection. 

If  the  truths  which  the  eye  readily  grasps  from  this  diagram  were 
more  generally  understood  and  acted  on,  there  would  probably  be  less 
bad  practice  in  railway-bridge  construction. 

1035.  The  third  least  objectionable  direction  for  economy  is 
the  bold  adoption  of  temporary  lines  where  permanent  works 
of  great  cost  will  otherwise  be  required;  meaning  by  "tempo- 
rary lines"  not  those  intended  merely  for  construction  purposes 
or  for  use  until  the  permanent  works  can  be  completed,  but  lines 
good  enough  for  several  years'  use  at  least  without  any  great 
loss,  leaving  the  better  permanent  line  to  be  constructed  only 
when  it  is  certain  that  the  traffic  justifies  and  requires  it,  and 
means  are  available.  Considerable  amounts  of  distance,  curva- 
ture, and  rise  and  fall  will  not  cause  a  dangerous  loss  in  opera- 
tion for  a  few  years,  if  used  only  on  the  rougher  sections  as  a 
substitute  for  more  costly  works  later,  and  will  enable  the  im- 
mediate outlay  on  the  usually  short  sections  (par.  1005),  where  the 
most  costly  works  are  concentrated,  to  be  very  materially  reduced 
in  many  cases,  as  well  as  enable  the  line  to  be  opened  before  an 
impending  crash  comes.  The  same  is  true  in  less  degree  of  the 
use  of  TEMPORARY  PUSHER  GRADES  of  an  objectionable  character, 
but  not  so  bad  as  to  prevent  the  handling  of  through-trains. 


THE  ECONOMY  OF  CONSTRUCTION. 


767 


This  diagram  shows  the  shipping  weight  of  iron,  including  an  all- 
iron  floor,  except  ties  and  guard-rails.  The  narrow-gauge  bridges  are 
for  quite  light  engines,  as  shown  in  Fig.  248.  The  slight  effect  of 
rolling  load  to  increase  weight  is  perhaps  more  strikingly  shown  in 

.^    Table  200.     The  formulae  on  which  it  was  constructed  are  given  near 

"rp"   '^^  ^"<^  of  the  last  chapter. 


Fig.  247  — Diagram  of  thb  Compara- 
TiVF  Weights  of  Iron  in  Fridges 
OF  Varioits  Spans  and  for  Varioi's 
Rolling  Loads  shown  in  Fig.  248. 

(See  also  Table  200.) 
[The  base  of  the  diaffram  for  spans 

of  less  than  200  feet  is  at  the  side.J 


n 


51 


■ 


768    CHAP.   XXIIL—THE  ECONOMY  OF  CONSTRUCTION. 


1036.  The  fourth  least  objectionable  economy,  but  one  which,, 
like  the  preceding,  from  its  coming  among  the  first  in  order  of 
time,  is  apt  to  be  one  of  the  last  practised,  is  the  adoption  as  a 
standard,  for  the  entire  line,  of  a  systematic  economy  (in' money, 
but  not  in  time  or  care)  in  respect  to  the  minor  details  of  align- 
ment. The  pros  and  cons  of  this  question  have  been  discussed 
so  fully  in  the  preceding  chapter  that  we  need  not  further  en- 
large upon  it. 

In  these  five  ways  (with  which  perhaps  the  use  of  timber 
STRUCTURES,  such  as  are  shown  in  Fig.  249,  might  make  a  jixth) 
a  very  large  economy  may  be  practised  which  will  almost  assure 
that  any  project  with  any  merit  whatever  will  be  so  little  bur- 
dened by  its  capital  account  that  it  will  be  able  to  live  on  what  it 
can  get  to  live  on,  even  if,  as  it  usually  is,  it  is  far  below  its  ex- 
pectations. 

1037.  Beginning  now  at  the  other  end  of  the  question,  the 
most  objectionable  of  all  ways  of  economizing  is  much  the  com- 
monest of  all,  for  reasons  already  sufficiently  discussed  in  Chap. 
III.,  omitting  to  go  into,  as  well  as  to,  the  terminal  cities,  and 
other  important  traffic  points  on  the  line.  This  error  very  largely 
arises  from  the  fact  that  it  is  an  expenditure  which  comes  late  in 
the  history  of  construction,  or  can  be  made  to  do  so. 

Probably  the  next  most  serious  injury  which  can  happen  to  a 
line  is  neglect  to  secure  best  possible  ruling  grades,  but  this 
more  often  happens  from  a  lack  of  care  and  skill  than  from  a  de- 
sire to  economize,  since  the  expenditure  is  incurred  early  in  the 
history  of  construction  and  the  importance  of  favorable  grades  is 
more  generally  understood  than  the  best  manner  of  securing  them. 

1038.  Barring  this  error,  the  next  worst  form  of  economy 
which  can  afflict  a  line  is  what  is  more  emphatically  than  ele- 
gantly called  a  "cheap  and  nasty"  style  of  construction:    Light 

RAILS,  POOR  TIES,  THIN  BALLAST,  NARROW  ROAD-BEDS,  POOR  MA- 
SONRY, and  LIGHT  BRIDGES.  These  defects  really  save  but  little 
money,  while  the  expense  and  the  bad  name  which  has  resulted 
from  them  have  sapped  the  life  of  many  a  line.  It  is  far  better 
to  economize  closely  in  all  the  details  of  location  but  the  grades,. 


CHAP.   XXIII. -THE  ECONOMY  OF  CONSTRUCTION.   ;6^ 


:m 


and  sometimes  even  in  the  grades  themselves,  than  to  do  this. 
The  difference  between  a  thoroughly  adequate  and  solid  road- 
bed, and  a'  mferior  a  one  as  it  will  seem  possible  to  tolerate,  will 


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9rrT  T  T?  ^■ 

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Fig.  m8.-Enc.nb  Loads  used  in  Computing  th»  Ws.chts  for  F,g.  ,„. 

Sv  ^™°7i''r  f'°°°  '°  ^^°°°  P"  ""^^  ^"'^  °"  ^"--k  at  all 
eavy  ,t  .s  not  d.fhcult  to  save  that  sum  by  economizing  in  loca- 

t.on  us.ng  temporary  but  solid  wooden  structures,  and  theothe- 

expedients  noted  above.     These  latter  economies  will  not  add 

49 


t;©   chap.   XXIII.— the  ECONOATY  OF  CONSTRUCTION. 


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C^^A   XXIII, 


■THE  ECONOMY  OF  CONSTRUCTION.   7/1 

materially  to  expenses  during  the  first  ten  or  fifteen  years  on 
operation,  whereas  a  poor  and  flimsy  superstructure  entails  a 
large  and  constant  addition  to  maintenance  expenses 

1039.  The  loss  which  results  from  light  bridges*  is  propor- 
tionately  quite  as  great  as  from  light  rails,  as  is  made  evi- 
dent  enough,  without  further  discussion,  from  Figs  247-8  and 
Table  200.  The  proportionate  loss  from  poor  masonry  is  even 
greater  it  is  far  better  to  put  up  temporary  wooden  structures 
altogether,  than  to  put  up  such  flimsy  masonry  as  is  often  built 
That  so  very  large  a  part  of  the  masonry  put  up  on  new  Ameri^ 

Table  200, 

Comparative  Weight  and  Cost  of  Bridges,  taking   Bridges  of  "T" 
(Typical  Consolidation)  Type,  Fig.  249,  as  Unit. 


Class  of  Load. 
(Fig.  249.) 


Minor  Spans  of— 


30  ft. 


T. 
C. 

M. 


100 
98.74 
97-73 


50  ft. 


Soft. 


100 

98.05 
96.47 


100 
97-IO 
94-56 


104  ft. 


150  ft. 


100 

96.33 

93.16 


N. 


(Uniform  at  75.00). 


100 
94.98 
90-75 


20lj4j  ft. 


100 
94.00 
88.61 


Larger  Spans , 


T. 
C 


201^  ft. 


100 
93-34 


320  Feet. 


Iron. 


100 
91. II 


Steel. 


100 
89 -55 


420  Feet. 


Iron. 


lOO 

88.77 


Steel. 


100 
89-55 


516  Feet, 


Iron. 


100 
88.21 


Steel. 


100 

89-55 


^rc^I^Ltr^^  n  °"'  ''  M,  "^'^"'^  '^''  *^'  '^^  °f  ^°'""S  ^«^d  «"  --i^ht  of  bridges  is 
small,  and  the  followmg  will  perhaps  more  fully  show  how  petty  is  the  economy  . 


For  engines  weighing  (tons) 
Y"^  'n  the  proportion  of 


•0?in  th.*  '°*'*  behind  engine,  per  fi^'t  of'(Ibs.) 
•^r  in  the  proportion  of ' 


I 


"kB 


772    CHAP.   XXIIL—THE  ECONOMY  OF  CONSTRUCTION. 


Table  200. — Continued. 


Giving  a  loss  percent  in  rolling  load  over  the  strongest 
type  of  bridge  of 


The  saving  per  cent  in  weight  (not  cost)  of  bridge  is 
otily  -  for  spans  of i 


Per  Cent. 


Engine, 
Cars, 

30  ft. 

50" 

80  " 
104  " 
150  " 
io\\^  ft. 


6.3 
14.6 
1.26 

1.95 
2.90 

367 
5.02 
6.00 


Per  Cent. 


19. 

27 

3. 

3 
5 
6 


9 

o 

27 
53 

44 

84. 


9.25 
11-39 


Beyond  these  spans  the  comparative  difference  becomes  g^-eater,  so  that  we  have  for 
the  difference  between  a  rolling  lt)ad  of  the  *'  typical  "  and  ordinary  Consolidation  type 
(neglecting  the  Mogul  type)  the  following  : 


Iron. 

Steel. 

ft. 

6.66 

.  •  •  • 

It 

8.89 

10.45 

i( 

10.23 

10.45 

tt 

11. 79 

10.45 

Thus  even  the  largest  spans  do  not  increase  in  weight  as  fast  as  they  increase  in- 
capacity, and  on  the  shorter  and  more  common  spans  an  increase  of  only  3  to  6  per  cent 
in  weight  gives  15  to  25  per  cent  increase  in  carrying  capacity. 


can  lines  should  give  out  within  a  few  years,  as  it  does,  either 
because  the  foundations  were  inadequate  or  were  not  properly 
protected  against  wash,  or  the  stone  poor,  or  laid  dry,  or  the 
spans  inadequate,  reflects  little  credit  on  engineers. 

1040.  A  still  less  reasonable  and  creditable  mode  of  economy 
is  CUTTING  DOWN  THE  ROAD-BED,  especially  in  cuts.  The  saving 
is  but  trifling,  and  tlie  effect  on  maintenance  expenses  very  un- 
favorable, since  it  forbids  proper  ditching,  impedes  access  of  the 
sun  to  the  road-bed,  and  makes  difficult  to  apply  a  proper  coat  of 
ballast  and  leave  any  ditch  at  all.  The  narrowest  road-bed  in 
earth  should  be  20  ft.,  especially  in  light  work,  or  on  light  grades 
having  many  long  low  cuts  on  them,  which  latter  are  very  difficult 
to  drain.  In  fills,  a  15-ft.  or  i6-ft.  road-bed  is  none  too  wide,  and 
will  rarely  be  found  to  be  much  wider  than  is  necessary  to  hold 
the  ballast  when  the  track  is  laid. 

1041.  Cutting  down  the  coat  of  ballast  is  likewise  one  of  the 
most  costly  economies  in  which  a  road  can  engage.  Sometimes 
it  is  necessary,  because  ballast  is  not  readily  available,  and  tO" 
some  extent  good  ditching  may  be  substituted  for  it,  but  econ- 
omy requires  that  both  ditching  and  ballast  should  be  good. 


^-^-^^^^^^^^-T^^C^^V^^^  OP  CONSTRUCTION    77^ 

It  was  a  saying  of  the  late  Charles  Colli^i^^^i^ented  chi7 

two  feet  of  ditcli  is  worth  one  foot  of  ballast,"  and  this  has  a 

foundation  of  truth  at  least,  as  was  shown  by  the  results  of  fre^ 

hltth'en^VrSd'^-^'^  '"^  '''''     ''  ^^^  ^^^si^^^^^l^ 

d  Tmount  of  to  ""      n  "'"  '''''^'  "^^  "^"  ^^"^^^^  ^  li- 
lted amount  of  money  Will  accomplish  more  good  if  spent  for 

<litchmg  than  for  ballasting,  and  there  is  a  ceftain  absurd"  V  in 

putting  on  a  thick  coat  of  clean  ballast  in  a  cut  where    he  dfch 

-g  IS  so  imperfect  that  there  can  hardly  be  said  to  be  any     Nef 

TnsM^^bTr  T  ;""*  '^"^"  ''  '  ^^^^"^  "^^^  -  many'iin^s  of 
conside.ab.e  traffic,  if  not  on  most  lines  not  of  the  first  rank  and 

plied  by  improved  modern  appliances,  and  how  greatlv  it  would 
decrease  wear  and  tear  and  maintenance  expense^s,  botl  of  track 
^nd  of  rolling-stock,  as  well  as  sometimes  increase  bv  a  car  or 

All  expenses  connected  with  loading 

Loading  and  delivering  on  road-bed. 'iomi're'iaui.V.V.V.V.'.'.'io  ''''  ^^^'  '''''^^'^^ 

*'    "     "    '•    i«'    ?o ;;  ;; -••••is  ^  »   - 

.5"       20 "  *•   *' 

means  on  »  f\^'^P'"«  °'"  "'  '"e  way  of  all  regular  trains."  What  that 
fc  clekrin.  ,r'  7^-  "'  ""^'^"^""^  ""— •  «i>h  all  the  necessary  delays 
^aitnTfo r  .h       ,  r'""'"  ^'■'^''  °'""  ^^«"'-'  "-'"''  time/'  and  fo 

4  doub  n^  al  trX"  'T  ''''•  '^  ^"  '"°'""'"^  P™P°"-"  °'  '-'  '-^  P- 


I 


774      CHAP.  XXIII.— THE  ECONOMY  OF  CONSTRUCTION. 


m\ 


m 


Nevertheless,  this  limitation  of  privileges  is  natural  enough  and  well  enough 
as  a  matter  of  permanent  rule.  A  ballast  train  cannot  be  anything  else  than  an 
irregular  train,  and  cannot  safely  be  given  any  rights  whatever,  except  by  spe- 
cial order  ;  but  therein  lies  the  difficulty.  Trains  are,  as  a  matter  of  fact, 
almost  all  run  by  special  order,  and  when  giving  such  order,  it  rests  entirely 
with  the  discretion  of  the  dispatcher,  within  wide  limits,  to  favor  one  train  or 
another  as  he  sees  fit.  This  discretion,  however,  is  rarely  exercised  to  prevent 
delays  of  ballast  trains,  which  cost  money,  rather  than  delays  of  regular  trains, 
which  do  not  directly  cost  money;  but  the  ballast  train  gets  from  the  dispatcher, 
improperly  and  unwisely,  much  the  same  kind  of  treatment  that  it  necessarily 
and  properly  has  in  the  printed  rules  and  lime-tables. 

Now  a  regular  freight  train  is  earning  perhaps  $1.50  per  mile  run  and  cost- 
ing $1,  but  it  will  earn  no  less  and  cost  no  more  (barring  a  slight  loss  of  fuel) 
for  being  a  quarter  or  half  an  hour  more  or  less  upon  its  trips.  On  the  other 
hand,  the  total  expenses  for  running  a  steam-excavator  with  perhaps  three  or 
four  engines  at  work  to  handle  the  cars,  are  from  $100  to  $150  per  day.  A 
delay  to  any  one  of  these  trains  is  to  a  considerable  extent  a  delay  to  all  and  to 
the  excavator  as  well,  and  a  delay  of  three  hours  per  day  to  these  trains  (which 
is  about  a  minimum)  means  the  loss  of  $1200  to  $1500  per  month. 

Under  these  circumstances  what  ought  to  be  done,  if  true  economy  is  to  be 
considered,  is  to  prepare  something  like  a  regular  schedule  for  the  movement 
of  these  trains,  from  day  to  day  and  from  week  to  week,  for  the  use  of  the  dis- 
patcher ;  to  provide  as  good  facilities  as  possible  for  communicating  orders  to 
them,  and  to  require  that,  whenever  and  wherever  it  is  possible  without  too 
great  delay,  the  gravel  trains  shall  be  favored  at  the  expense  of  the  ordinary 
freight  train. 

1043.  Supposing  the  delays  to  gravel  trains  to  have  been  re- 
duced to  a  minimum,  there  are  few  expenditures  so  directly 
profitable  as  to  procure  a  steam-excavator  and  ballast  plows, 
and  keep  two  or  three  trains  at  work  for  a  good  part  of  several 
seasons  increasing  the  depth  of  ballast.  Half  a  cubic  yard  per 
cross-tie  will  raise  the  track  some  8  in.,  and  where  the  road-bed 
is  wet  and  the  haul  not  too  great,  this  would  not  be  so  very  bad 
an  investment,  simply  as  a  preservative  of  cross-ties. 

An  additional  economy  for  this  kind  of  work  on  many  lines,, 
and  one  deserving  of  more  frequent  use,  is  the  hauling  <  side- 
dump  cars  loaded  with  ballast  on  regular  trains,  especially  way 
freight,  whenever,  as  is  frequently  the  case,  eight  or  ten  addi- 
tional cars  can  be  hauled  over  a  portion  of  the  division  as  well 
as  not,  owing  to  more  favorable  gradients.     Many  types  of  cars 


CHAP.  XXriT.-THB  ECONOMY  OF  CONSTRUCTION.      77S 
suitable  for  this  purpose  exist  which  are  readily  dun,ped  by  one 

n.nr^  ^"'  °^  '^^  ^"^  ^°'''  P'""^  ^°  economize  in,  but  for- 
tunately not  a  common  one,  is  in  the  cross-ties.  Th;  number 
of  these  cannot  be  too  great  for  economy,  until  they  become  so 

ttele-lh  If  rraTre^- ;--  T,"  ^^  ^  -""'  ^ 

crease  the  t,e  support,  as  may  be  speedily  shown. 

Some  "rop^^Jti^n^'V^^  "°"""'  ^'^  """''"^  ""'^-  ">«  '^s. 
each  of  these  must  be 
used  to  maintain  a  sta- 
ble track,  but  in  pro- 
portion as  the  stabil- 
ity from   one  of  them 

less  track  labor      U        ^  '         ''  '"''  "^  ™^-^  "^^  '«^=  ''^^  -^ 
iess  track-labor.     If  we  have  more  or  better  ties,  we  may  use  a 


Fig.  250. 


Fig.  251. 

The  different  modes  of  yielding,  outlined  in  Figs     S  and  !  r' 
which  occur  more  or  less  on  all  trark  ,^,    k  ^  ^  ' 

and  will  arise  from   H   fi  '  ^"^  ^^  assumed  to  arise, 

will  ause,  f.om  deficiencies  in  any  one  of  these  three  re 


1  1 


'J'J^      CHAP.  XXIII.^THE  ECONOMY  OF  CONSTRUCTION. 

quirements,  either  the  rails  or  ties  or  tamping,  and  may  be 
cured,  in  part  or  whole,  by  spending  more  money  on  either  one 
of  them.  Assuming  as  a  standard  of  comparison  a  6x8  in.  tie  8 
ft.  long,  spaced  2  ft.  apart,  or  2640  per  mile,  the  following  com- 
binations of  spacing  and  width  will  afford  an  equal  bearing-sur- 
face of  ties  on  the  road-bed  and  of  rails,  but  will  be  seen  to 
afford  a  very  unequal  support  to  the  rail  : 

Ties  per  mile 2,640       3,000  3,168  3,520 

Distance  apart,  centre  to  centre 24  in.  21.12  in.  20       in.  18  in. 

Average  width  of  face Sin.  7.04  in.  6.67  in.     6  in. 

Clear  space,  tie  to  tie 16  in.  14.08  in.  13.33  in.  12  in. 

Comparative  stiffness  of  same  rail  for 

each  span i.oo        1.47  1.73  2.37 

Comparative  weight  of  rail  to  give  same 

stiffness i.ooo  0.825  0.761  0.650 

The  method  of  determining  the  comparative  stiffness  and 
comparative  weight  of  rail  in  the  last  two  lines  is  the  same  as 
used  in  par.  992  for  rails,  and  need  not  be  repeated.  Whether 
we  compute  the  comparative  stiffness  of  the  rails  for  spans  from 
centre  to  centre  of  ties,  or  for  one  clear  span  between  ties,  or  for 
spans  omitting  one  tie,  as  in  Fig.  250,  the  result  is  the  same,  al- 
though the  absolute  stiffness  will  of  course  vary  greatly. 

1045.  Taking  the  extremes  of  the  table  above,  we  see  that  the 
addition  of  880  ties,  or  one  third  increase,  gives  so  much  addi- 
tional support  to  the  rail  that  (assuming  the  support  to  each  tie 
to  be  the  same)  a  rail  only  two  thirds  as  heavy  will  distribute 
the  load  as  well  from  tie  to  tie.  Not  forgetting  that  stiffness  is 
only  one  of  the  three  qualities  in  a  rail  which  are  gained  by  in- 
creasing its  weight,  this  great  difference  still  indicates  that  in- 
creasing the  number  of  ties  to  the  extent  of  practical  possibility 
(their  dimensions  remaining  the  same)  adds  much  more  to  the 
aggregate  stiffness  of  the  track  than  the  same  amount  spent  on 
rails ;  as  thus: 

The  cost  of  880  more  cross-ties  per  mile,  more  than  doubling 
the  stiffness  of  the  same  rail,  amounts — 

At  25  cents,  to  $220  =    7.14  tons  rails  at  $30  =  4.5  lbs.  per  yard. 
"  30     "        "    264=    8.80    "       "        "      =5.5    "      "      " 
"  40     '-        "    352  =  11.73    "       "        "      =7.3    "      '*      " 
"  50     "        "    440=14.67    ••       "        "      =9.1. * 


1.51 
2.12 


35  lbs. 
I.oo 


1.27 
1-57 


50  lbs. 
I.oo 


1. 19 
1.40 


CHAP.  XXrn.-THE  ECONOMY  OF  COl^STRUCTION.      777 

Comparing  this  with   the  figures  in  Table  196,  giving  the 

comparauve  st.ffness  of  light  and  heavy  rails,  we  have  the  fol! 

ow.ng  companson  for  various  light  rails-for  which  rails  ol 

the  comparison  is  at  all  close:  ^ 

Original  weight  of  rail,  .    .  <,^  i^ 

Stiffness  in  do.  taken  as ^^  ^"• 

Addmg  4.5  lbs.  per  yard  (=  cost  of'  880  'ties 
at  25  cents  each,  as  above)  makes  stiff- 
ness       

Adding  9.1  lbs.  per"yard'(=  cost' of'  880  'ties 

at  50  cents  each)  makes  stiffness    . 
Whereas  the  same   sum   spent  on  ties  inl 

creases  the  stiffness,  as  above,  to     .     .     . 

deciralYS-  ''^1'^'''°"  °^  -  '-g^  -  ""-bar  of'iies,  without 
deceasing  the.r  wdth.  can   rarely  be  practicable,  and  while  the 
companson  ,s  not  strictly  exact  for  other  reasons,  this  does  indi 
cate  clearly  the  genera,  fact,  that  increasing  the'numberoffes 
iilitv't  "  — enience  is  a  cheaper  way  of  increasing      a! 

bd.ty  than  .ncreasmg  the  rail-section,  even  for  very  light  rails 
On  the  other  hand  the  total  stability  which  is  obta'^nab  ^  from 
t.es  IS  I.m.ted  by  the  number  which  it  is  possible  to  use.  so  that 
what  these  figures  in  fact  indicate  is  that,  in  endeavoring  to  ge 
he  utmost  stab.hty  at  .he  least  cost,  the  first  essential  it  to  use 
t>es  as  free  y  as  ,s  possible,  and  the  next  essential  is  to  decide 

mT  T.  :  oh:,  "  I  r'  """-^'^-P-^  -  -PP-y  the  deficU 
1047.  The  physical  hmit  to  the  increase  in  number  of  ties  of 

The  r7,  K,     1:'  """''''  "  P^^^'^'y  ^«°°  P^--  ■":'-;  but  if  as  t 
Xhe  fi,-st  table  above,  we  consider  the  width  of  the    ies  to  be  di 

w£  use  ,:oc  r  '""'  '  """'"  °'  ^^'^  '"  '""^  United  States 
wh.ch  use  3,00  to  3300  narrow  ties  per  mile  with  very  satisfac- 
tory results.  Remembering  that  the  stiffness  of  a  rail  decreases 
as  the  cube  of  the  span,  it  is  obvious  that  by  dividing  up  the 
beanng-surface  among  a  greater  number  of  ties,  so  thaf  Z  Ig! 
gregate  area  remains  the  same,  we  measurably  obtain  two  desi^. 
able  ends  at  once-we  give  much  more  effectual  support  to  a 
w  aU  .a.l,  and  we  in  general  reduce,  instead  of  increasinl  the 
total  cost  of  t,es,  since  the  cost  of  ties  will  usuallv  increase  fester 


i 


ii 


27^      CHAP.  XXIII.— THE  ECONOMY  OF  CONSTRUCTION. 

than  the  required  minimum  face.  As,  therefore,  the  necessary 
space  between  ties  varies  approximately  with  the  width  of  face, 
and  is  about  twice  the  face  (so  that  full-width  ties  cannot  be 
used  with  very  narrow  spacing),  the  utmost  economy  would  seem 
to  require  that  narrow  ties  spaced  close  together  should  be  given 
a  decided  preference  at  the  same  cost  for  ties  per  mile  when  a 
light  rail  is  to  be  supported,  and  there  are  few  rails  indeed  in 
this  country  which  cannot  be  said  to  be  light  in  proportion  to 
the  duty  imposed  on  them.  It  could  not  rationally  be  expected^ 
indeed,  that  6-in.  ties  spaced  i8  in.  apart,  instead  of  8-in.  ties- 
spaced  24  in,  apart,  would  increase  the  stiffness  of  a  light  rail 
from  1. 00  to  2.37,  as  the  figures  above  indicate;  yet  we  may 
justly  conclude  that  it  will  be  increased  very  greatly,  with  a  pos- 
sible decrease  in  the  total  cost  of  ties  as  well,  where  the  supply 
of  large  timber  is  small.  In  not  a  few  localities  ties  of  5-  or  6-in. 
face  can  be  had  for  but  little  more  than  half  the  cost  of  ties  with 
8-in.  face. 

1048.  A  great  error  is  often  committed  in  making  ties  too 
thin.  A  cross-tie  is  an  inverted  cantilever.  In  Fig.  251  we  have 
a  tie  yielding,  as  they  all  do,  more  or  less  under  a  load;  and  by 
inverting  Fig.  251  it  will  be  seen  that  we  may  consider  the  tie 
as  a  cantilever  beam,  supported  upon  two  piers  (the  rails)  and 
loaded  with  a  more  or  less  uniformly  distributed  load.  If  the 
tie  were  perfectly  stiff,  it  would  be  an  evenly  distributed  load, 
and  the  pressure  of  the  tie  upon  the  soil  would  be  uniform  for 
every  square  inch  of  its  bearing-surface.  If  the  tie  be  very  thin, 
the  conditions  of  the  exaggerated  sketch  will  literally  obtain. 
The  middle  and  ends  of  the  tie  will  then  be  able  to  transmit  but 
little  pressure  to  the  ballast,  and  (since  the  total  pressure  trans- 
mitted must  in  any  case  be  the  same)  an  excessive  and  destruc- 
tive pressure  will  be  thrown  upon  the  road-bed  directly  under 
the  rails,  causing  rapid  deterioration  therein.  This  may  be 
shown  by  the  load-diagram  below  Fig.  251.  Let  us  suppose 
that  a  tie  be  so  thin,  or  the  nature  of  the  support  so  unyielding, 
that  the  load  per  square  inch  directly  under  the  rail  is  three  timeT 
as  great  as  at  the  ends  and  in  the  middle,  as  shown  by  the  full 


CHAP.  XXIII-THE  ECONOMY  OF  CONSTRUCTION.      779. 

line  in  the  diagram  below  Fig.  25i^a  very  co^n  differen"^. 
If  not,  indeed,  one  almost  universally  exceeded  in  occasional  in- 
stances,  even  on  a  very  good  track.  An  increase  of  stiffness 
which  would  double  the  load  on  these  lightly  loaded  extremities 
would  produce,  as  will  be  seen  from  the  diagram,  an  absolutely 
uniform  distribution  of  pressure,  and  although  this  can  never  be 
fully  realized,  yet  it  is  plain  that  it  may  be  approached 

1049.  Now  the  stiffness  of  any  beam,  however  supported   or 
oaded   IS  in  proportion  to  the  cube  of  its  depth  (or  thickness  of 
tie)  and  of  its  lengths  between  supports  (or  the  gauge)      Anv 
attempt  to  compute  from  these  facts  the  absolute  requirements, 
or  distribution  of  load,  with  a  given  tie  or  gauge,  would  be  pre- 
posterous.     There  is  no  absolute  requirement,  since,  however 
well  maintained  the  track,  occasional  ties  are  badlvor  unequallv 
supported;  and  since  the  load  is  far  more  than  sufficient  to  break 
any  tie  in  two  at  the  middle  if  only  supported  at  that  point  (a 
dead  load  of  14,000  lbs.  per  wheel  would  probablv  break  such 
ties  the  first  time  it  was  imposed),  it  is  for  these  maximum  de- 
mands,  and  not  the  average,  that  we  must  provide.     Therefore 
speaking  comparatively  only,  and   taking  a  tie  6  in.  thick  as  the' 
basis  of  comparison,  we  have  the  following: 


Thickness. 

5  in. 

6  " 

7  " 

8  " 


Comparative 
Stiffness. 

0.58 

I. GO 

1.59 

2.37 


Thickness  of  Narrow  (3  ft.)  gauge  Tie  of- 


Equal  Stiffness. 
3.18  in. 
3.82   " 

4.46   " 
5.10  " 


Equal  Strength. 

4-30  in. 

5.16    " 
6.02     " 


From  this  it  is  clear  that  although  the  nominal  bearing-sur- 
face of  a  tie  IS  not  increased  by  increasing  its  thickness,  yet  that 
the  effective  bearing-surface  is  likely  to  be  very  materially  in- 
creased by  a  very  moderate  increase  of  thickness.  By  increasing 
the  thickness  from  5  to  6  in.,  we  nearly  double  the  stiffness  •  bv 
increasing  it  from  6  to  7  in.,  we  increase  the  stiffness  50' per 
cent,  giving  the  effect  outlined  below  Fig.  251,  in  which  the  full 
iine  shows  the  assumed  distribution  of  pressure  with  a  tie  6  in 
thick,  and  the  dotted  line  the  effect  on  the  latter  of  thickening^ 


-,^^nk.A 


78o      CHAP.  XXIII,— THE  ECONOMY  OF  CONSTRUCTION-. 


the  tie  i   in.     Economizing  in  the  thickness  of  ties,  therefore, 
would  seem  to  be  one  of  the  poorest  ways  of  saving  money. 

1050.  This  is  more  fully  seen  by  comparing  the  effect  of  differ- 
ence of  length.  It  cannot  be  attempted  to  consider  the  matter 
in  detail,  but  a  tie  which  is  under  fair  conditions  to  permanently 
fulfil  its  office  of  distributing  the  load  may  be  considered  to 
curve  into  the  three  circular  arcs  shown  in  Fig.  251,  from  which 
it  will  be  apparent  that,  under  whatever  assumptions  as  to  the 
curve  of  flexure,  there  is  a  clear  limit  to  the  useful  increase  of 
length  in  ties  at  a  point  considerably  within  a  length  of  twice 
the  gauge,//'.  If  the  tie  be  made  longer,  as,  for  instance,  ex- 
tended to//',  or,  still  worse,  to^  ^',  either  the  extra  length  will 
carry  little  or  no  load  (which  is  most  likely),  or,  if  the  support 
nearer  the  rail  has  given  way  so  as  to  throw  load  upon  it,  it  will 
be  very  liable  to  break  the  tie. 

If  the  tie  be  made  shorter,  the  load  thrown  on  the  middle  of 
the  tie  will  be  disproportionately  increased  until,  if  we  conceive 
the  tie  cut  off  close  to  the  outside  edge  of  the  rail,  the  load  per 
square  inch  will,  in  the  first  place,  be  very  greatly  increased, 
and,  in  the  second  place,  the  strength  of  that  portion  of  the  tie 
between  the  rails,  considered  as  a  beam,  is  diminished  by  about 
one  half  and  its  stiffness  about  seven  eighths;  because  the  effective 
span  of  the  beam  has,  by  cutting  off  the  projecting  ends,  been 
almost  doubled,  i.e.,  increased  from  b  b\  Fig.  251,  iocc'. 

1051.  For  the  most  efficient  service  from  ties,  therefore,  we 
have  a  certain  quite  narrow  limit  of  length,  the  minimum  being 
about  7i  ft.,  and  the  maximum  about  8^  to  9  ft.,  for  the  ordinary 
gauge  of  4.71  ft.  It  is  clear  from  the  above  that  any  increase  of 
length  above  8  ft.  gives  a  far  less  effectual  way  of  disposing  a 
given  quantity  of  wood  (to  obtain  an  approximately  uniform 
pressure  on  the  ballast,  and  so  keep  down  the  maximum),  than 
to  increase  the  thickness,  provided  the  nature  of  the  timber  per- 
mits it.  The  apparent  gain  of  bearing-surface  by  increasing  the 
length  of  ties  from  8  ft.  to  9  ft.,  and  the  apparent  absence  of  gain 
in  bearing-surface  by  increasing  the  thickness  from  6  in.  to  7  in., 
will  be  seen  to  be  precisely  the  reverse  of  the  true  conditions, 


CHAP.  XXm.-THE  ECONOMY  OF  CONSTRUCTION.      JU 

and  we  may  well  believe  that  this  deceptivT^trast  hn<=  h 
the  chief  cause  for  such  awkward  combination    as  ansl^r  .ft" 
t.e  w.th  only  6  in.  thickness,  which  prevails  with  6  i  pe.-  cent  of 
the  ties  in  the  United  States.  ^  °^ 

Neglecting  the  widths,  as  an  indeterminate  element  not  defi 
nitely  fixed,  the  percentages  for  the  entire  United  States  of  t£ 
various  lengths  and  thicknesses  of  ties  in  use  is  as  follows 
Lengths,     .     .     8  ft.      8  ft.  6  in.      9  ft.         ,0  ft      Total 
Percentages,.     63.5         .7.6  8..,         o+'       To.o 

6|  in. 


Thickness, 
Percentages, 


6  in. 
54.4 


7  in. 
41.4 


8  in. 
0.4 


lOO.O 


erneTbv  thT'  ^:".^"°"^  ^-^^  -  P^"-  and  perhaps  chiefly,  gov- 
at  least,  we  may  safely  assume,  from  mistaken  views  as  to  wh.t 
.s,  abstractly  considered,  the  best  proportion  for  a"      T^^bes 
dimensions  for  a  tie  are  about  7  in   thick   8  U  /,     ,  . 

7  to  9  in.  face.  ,  '      "•  ^  '"'  '°"S'  a"^ 

1052.   There  is  another  side  to  the  question  of  masonrv  struc 
ures  which  may  be  briefly  noted.     While  a  structure,  if  bui     at' 
a  1,  should  be  well  and  solidly  built,  it  does  not  follow  tha    be 
cause  a  certain  proportion  of  the  structures  of  a  line  Ivlntuallv 
wash  out  that  they  were  therefore  ill-designed.      "  The  „!  "l 
end  of  a  tutor,"  say  the  Autocrat  of  the  Brfakfast-Table  "'  s  To 
die  of  starvation.     It  is  only  a  question  of  time  just  as  with  ,h 
burning  of  colleee  librar;«  "   <;„  ■  ■"  ""  ""^ 

«nc«  »-""egeiibraiies.      So  in  a  certain  narrow  and  limited 

sense  we  may  say  that  the  natural  end  of  a  culvert  and  evTn  of 
".any  bridges,  is  to  perish  in  some  excessive  flood  tL  Ixceo 
t'onal  storms  which  come  but  once  or  twice  in  .  /  .  ^' 
ardlybe  fully  provided  for,  for  tl.rreas  r  at"  t  is"iSt": 
build  any  large  number  of  structures  with  such  an  ample  2  '^ 
of  safety  as  to  insure  that  many  of  them  will  not  eventualirwfsh 

chance7"S  ml"/'''  ''f"  '""'  ^""^  """'-'  ^'°™^  -h-b 
anced  to  fall  most  severely  on  some  of  the  Boston  roads  which 

a.e  about  the  oldest  roads  in  this  c6untry,  having  beeVb:ilt 


782      CHAP.  XXIIl.^TIIE  ECONOMY  OF  CONSTRUCTION'. 


8 


from  40  to  50  years,  and  had  rarely  suffered  much  from  floods 
and  washouts  heretofore.  As  a  consequence  structures  were 
washed  out  in  considerable  numbers  (on  the  Old  Colony  there 
were  40  washouts),  many  of  which  were  "supposed  to  be  strong 
enough  to  resist  any  current,"  and  had  succeeded  in  doing  so 
for  half  a  century. 

1053.  Such  occurrences  will  and  ought  to  make  engineers 
cautious;  but  we  may  remember,  on  the  other  hand,  that  to  have 
insured  that  these  structures  should  not  have  washed  out,  their 
original  size  and  cost  would  have  had  to  be  nearly  if  not  quite 
doubled,  and  a  simple  computation  in  compound  interest  will 
show  that  had  this  been  done  in  the  first  instance  the  additional 
investment  would  have  amounted  at  6  per  cent  to  19.50  times 
the  actual  first  cost.  It  follows  that  in  1835  even  a  certainty  of 
saving  the  cost  of  duplicating  the  original  structure  in  1886  would 
have  warranted  barely  5  per  cent  additional  expenditure.  It  is 
true  that  the  bare  cost  of  renewal  does  not  cover  the  whole  loss, 
for  there  is  a  loss  from  delay  and  danger  of  accident  incurred 
by  the  washout  in  addition  thereto  ;  but  on  the  other  hand,  to 
guard  against  all  the  contingencies  which  might  arise  in  1886,  it 
would  have  been  necessary  in  1835  to  have  about  doubled  the 
■cost  of  all  the  structures,  since  all  may  be  assumed  to  have  been 
laid  out  with  equal  care,  and  it  could  not  have  been  foreseen 
which  would  be  most  tried  thereafter. 

All  of  which  goes  to  show  that  when  structures  have  been 
skilfully  laid  out  to  stand  the  ordinary  contingencies  of  20  or  30 
years  it  is  about  all  that  is  either  practicable  or  justifiable,  and 
that  the  remarkable  storms  which  come  only  once  or  twice  in  a 
century  are  not  in  fact,  and  hardly  can  be,  successfully  guarded 
against.  This  is  especially  true  because  the  worst  effects  of  even 
the  greatest  storms  are  localized  within  quite  narrow  limits. 
The  storms  referred  to  were  not  by  any  means  the  worst  for  50 
years,  except  at  a  few  spots.  But  those  structures  which  washed 
out  chanced  to  be  at  those  spots,  while  the  really  greater  storms 
which  have  washed  out  others  in  past  years  did  not  chance  to 
fall  so  severely  on  these. 


CHAP.  XXIII.— THE  ECONOMY  OF  CONSTRUCTION,      ^83 

1054.  Tiie  same  is,  in  substance,  true  of  inundations  of  rail- 
way lines.     Every  year  we  hear  of  miles  of  line  of  important 
roads  being  under  water,  and  every  year  it  is,  to  a  considerable 
extent,  in  different   localities.     It  is  a  tolerably  safe  prediction 
that  within  reasonable 
and  justifiable  limits 
of  expenditure  no  rail- 
way   can    be    carried 
for  any  long  distance 
through  that  place  of 
all  places  foreconomi- 
■cal  operation,  a  river 
valley,  without   being 
at  some  time  and  at 
some  point  under  wat- 
er.     The     conclusion 
that  whenever  this  oc- 
curs it  is  evidence  of 
bad  engineering  is  not 
justified.      There   are 
lines    in    all    parts  of 
the  country  which  are 
overflowed  for  consid- 
erable distances  every 
three  or  four  years  for 
a  few  days,  and  find 
it    cheaper   to    suffer 
the  evil   than  to  cor- 
rect    it.       Prominent 
examples   among   in- 
numerable   others    is 

the  main  line  of  the  Pennsylvania  Railroad  in  Trenton    N  J 
various  points  on  the  Erie,  Philadelphia  &  Erie,  and  Baltimore 
&  Ohio,  and  various  roads  in  the  vicinity  of  Buffalo,  N.  Y. 

Without  going  to  the  length  of  saying  that  this'is  ordinarily 
justifiable,  which  would  be  going  too  far,  it  is  an  entirely  safe 


Fic.  259.— Annual  Rainfall  in  Inches  at  Lake 
CocHiTUATE,  Mass.,  1852-1883. 


I 


1 


784 


CHAP,  XXIII.^THE  ECONOMY  OF  CONSTRUCTION, 


CHAP.  XXIV.-IMPROVEMENT  OF  OtD  LINES. 


Statement  that  when  the  works  endangered  by  such  overflow  are 
not  of  a  very  costly  character,  it  is  far  better  to  risk  the  chances 
of  overflow  and  damage  at  a  few  points  every  eight  or  ten  or 
fifteen  years,  and  often  still  more  frequently,  than  to  sacrifice 
the  advantage  of  easy  gradients  and  light  first  cost  to  avoid  the 
risk,  especially  as  it  is  often  impossible  to  avoid  it  without  aban- 
doning  the  valley  altogether.  This  latter  has  been  done  in  not 
a  few  instances,  and  by  no  means  to  the  advantage  of  the  prop- 
erty, although  of  course  there  are  many  valleys  which  are  so. 
frequently  subject  to  excessive  floods  as  to  make  them  unfit  for 
any  permanent  railway  line. 

1055.  Very  great  fluctuations  in  rainfall  occur  in  successive 
years,  as  shown  in  Fig.  252,  which  likewise  strongly  indicates 
that  there  are  periods  of  great  or  small  rainfall  of  ten  or  fifteen 
years'  duration.  It  by  no  means  follows,  however,  that  the  years 
of  greatest  rainfall  are  the  years  of  greatest  floods,  but  rather 
the  contrary. 


785 


CHAPTER  XXIV. 

THE   IMPROVEMENT    OF   OLD    LINES. 

1056.  It  should  follow  from  what  wp  h-,„->   ,i       j 
respect  to  the  errors  which  ..ay  be  committed  ■„'."?''  ""  '" 
^f  new  lines,  that  many  existing  lines  buTf\  ^^'"^  °"' 

adequate  study  of  conditions "o'^ate        co       '  "t  """°"' 
.capable  of  material  improvement  af  a  co.,   T         J'  "'""''^    ""^ 

ments  mav   in  ravipc    h«  ^^^  *    1  vvuac  gieat  improve- 

readilv   tlfe'  possibi  'itts  fn   thft'd' "''/"'""^  ~^''  ^"^  ''°- 
Without  elaborate  a.ld  cost"yt"  evl  "^^  '^   ^''''''"'^^^ 

The  subject  is  one  which  usually  requires  carefnl  .t   ^ 
so  much  for  determining  whether  or  nrir.  ^'  "°' 

vantageously  be  entered'on,  whiC.  .^     trZ^Tord"  t 

as  for  determining  precisely  how  and  whpre  U,e  ml  "' 

ment  can   be  effectpri  f.>r  \%      i  """ere  the  most  improve- 

•dangerthat  if^h!  '^''  "'°""-'''  ^°  ^^  '°  ^^oid  the 

«»igcr  mat,  it  the  improvements  pr^  ^nf«.-^^  1 

will  not  be  given  the  nVhTn       ?  '  "'^  «^Pe"diture 

only  Of  wha^  n^hM^atletra  crphtheVrTn":;:  ^  ''h" 
'■and.  will  include  much  that  was  not  essentLl  and  "" 

'"terest  on  the  capital  invested  '°  "°'  "■""'"" 


786 


CHAP.  XMV.-IMPROVEMENT  OF  OLD  LINES. 


CHAP.  XXIV.— IMPROVEMENT  OF  OLD  LINES.  'J%'J 


for  estimating  the  possibility  and  value  of  any  change  therein 
We  know  or  may  know  precisely  how  much  locomotives  do  and 
can  do  on  the  line,  how  much  they  are  now  assisted  by  momen- 
turn  in  passing  over  their  heavy  grades,  and  where  they  are 
most  taxed.  Above  all,  perhaps,  we  have  time  to  fully  consider 
and  investigate  all  the  conditions.  Usually,  moreover,  there  are 
certain  members  of  the  regular  staff  who  can  devote  a  moderate 
amount  of  time  to  investigations  and  minor  surveys  without 
serious  interference  with  their  regular  duties. 

1058.  On  the  other  hand,  we  have  the  disadvantage  that  any 
changes  of  line  or  grade,  or  of  positions  of  stations  or  water- 
tanks,  etc.,  etc.,  involve  the  throwing  away  of  a  certain  amount 
of  work  already  done,  instead  of  the  mere  addition  of  a  new  red 
line  to  the  maps  and  a  new  line  of  stakes  on  the  ground,     l^or 
this  reason,  a  change  which  might  have  been  in  every  way  ex- 
pedient   in  the   beginning  may  not  be  expedient  when  loaded 
with  the  cost  of'  two  lines  instead  of  one.     We  have,  moreover, 
the  disadvantage  that  the  value  of  property  and  number  of  bml^. 
ings  are  liable  to  have  greatly  increased,  often  to  a  prohibitory 
limit,  especially  near  stations  and  large  towns,  where  changes 
are  most  likely  to  prove  expedient.     Moreover,  in  cases  of  con- 
siderable  changes,  involving  the  abandonment   of   certain  sec- 
tions of  line  or  even  the  moving  of  minor  stations  or  sidings, 
legal  difficulties  may  arise,  with  expenses  of  unknown  magni- 
tude resulting,  perhaps,  from  the  mere  whim  of  a  jury,  and  re- 
nuiring  the  maintenance  and  operation  at  heavy  cost  of  work 
intended  to  be  abandoned.     It  has  been  successfully  disputed  in 
some  instances,  at  least  for  a  time,  whether  a  corporation  has 
the  right  in  law  to  abandon  sections  of  unprofitable  lines  to  the 
detriment  of  vested  interests  without  payment  of  heavy  damages 
as  compensation   for  contingent  as  well  as  actual  injury.     On 
the  other  hand,  instances  have  repeatedly  arisen  where  the  right 
of  such  abandonment  has  been  successfully  asserted  and  main- 
tained.    Much  depends,  no  doubt,  both  on  the  importance  of 
the  case  and  the  rigor  of  the  opposition,  but  in  general  it  seems 
reasonable  to  expect  that  moderate  changes  for  which  necessity 


or  good  reason  can  be  shown  will  not  be  accompanied  by  a  re- 
fusal of  legal  authority  to  make  them,  or  by  more  than  reason- 
able and  actual  damages.  It  constitutes  an  element  to  be  always 
remembered  and  weighed,  but  not  to  be  exaggerated  without 
weighing  it,  as  there  is  some  danger  that  it  may  be. 

1059,  The  disadvantage  of  having  to  build  a  line  twice  over  is 
one  which,  while  undoubted,  is  liable  to  affect  the  imagination 
far  more  than  its  real  importance  warrants.  The  constant  loss 
from  operating  a  bad  line,  on  the  other  hand,  being  so  gradual 
and  continuous  that  it  does  not  affect  the  imagination  at  all,  the 
two  causes  may  unite  to  indispose  responsible  officers  to  think 
of  entering  upon  a  policy  in  which  the  outlay  is  certain  and 
seems  larger  than  it  is,  while  the  gain  is  problematical,  and  even 
its  possibility  does  not  force  itself  upon  the  attention. 

To  construct,  say,  lo  per  cent  of  a  long  line  over  again,  for 
example,  inevitably  impresses  the  imagination  as  very  much  like 
adding  8  or  lo  per  cent  to  the  capital  invested;  and  as  the  ship 
is  nearly  sinking  under  the  load  it  carries,  what  may  happen  to 
it  with  that  load  added  ?  The  chances  are,  however  (Table  199 
and  14),  that  it  will  not  really  add  more  than  one  to  three  per 
cent.  On  the  other  hand,  what  can  seem  more  improbable, 
a  priori,  to  a  manager  who  is  only  hauling  25  or  30  cars  per  train, 
than  that  50  or  60  cars  can  be  drawn  over  the  same  road  with- 
out, say,  doubling  or  at  least  increasing  one  third  the  cost  of  the 
line  ?  Yet  this  has  been  repeatedly  accomplished,  and  can  be 
again  accomplished  on  many  thousand  miles  of  road,  at  far  less 
cost. 

1060.  The  defects  which  are  most  conspicuous  in  old  lines 
which  it  is  desired  to  improve  are,  in  general,  these: 

1.  The  passing  by  of  large  towns  or  other  sources  of  traffic 
which  should  have  been  approached  more  nearly.  This  defect, 
although  a  great  one  in  the  laying  out  of  old  lines,  is  ordinarily 
not  one  for  which  alone  it  is  expedient  to  change  the  main  line, 
but  it  is  often  an  element  in  considering  changes  which  are  de- 
sirable for  other  reasons. 

2.  Excessive  curvature;   a  defect  which  forces  itself  with 


HM 


788  CHAP.  XXIV.— IMPROVEMENT  OF  OLD  LINES. 


CHAP.  XXIV.— IMPROVEMENT  OF  OLD  LINES.  789 


quite  sufficient  force,  as  a  rule,  upon  the  attention  of  all  con- 
cerned, so  that  there  is  some  danger  that  expenditures  may  be 
incurred  in  efforts  to  remedy  this  evil  which  might  better  have 
been  given  some  other  direction.  Nothing  further  will  be  said 
on  this  subject  than  has  been  already  said  in  Chapter  VIII.  on 
curvature;  but  it  is  beyond  question  that  on  important  trunk 
lines  large  expenditures  may  often  be  usefully  devoted  to  this, 
as  to  almost  any  other  improvement. 

3.  Improvements  in  gradients,  which  are  generally  at  once 
the  cheapest  and  the  most  important  to  effect,  and  to  which  this 
chapter  will  hereafter  be  devoted. 

1061.  The  defects  in  gradients,  of  a  remediable  character, 
which  are  most  likely  to  exist  in  old  lines,  are  as  follows: 

1.  Stations  on  heavy  grades,  including  as  heavy  grades 
not  only  those  which  appear  heavy  on  the  profile,  but  those 
which  are  sufficient  to  prevent  starting  a  full  train,  although 
easily  enough  passed  over  by  trains  under  normal  headway. 
The  number  of  lines  is  great  on  which  several  limiting  stations 
of  this  kind  exist  on  a  single  division,  so  that,  as  the  trainmen 
put  it,  "  it  is  harder  to  start  the  trains  than  to  pull  them  up  the 
grade."  Very  frequently  these  bad  grades  at  stations  are  the 
only  obstacles  to  a  considerable  increase  of  train-load. 

2.  Grade-crossings  of  other  railroads,  which  have  often  been 
added  in  great  number  since  the  original  opening  of  the  line 
and  seriously  modified  the  handling  of  trains,  especially  in  the 

West. 

3  Needless  undulations  of  grade,  avoidable  by  slight  de- 
tours and  originally  introduced  only  because  the  importance  of 
low  grades  in  comparison  with  a  short  line  or  cheap  construe 
tion  was  underestimated. 

4  Failure  to  use  pushers,  or  assistant  engines:  in  some 
cases  from  mere  oversight,  but  more  generally  because  the  line 
Is  ill-suited  for  their  use  without  modifications  elsewhere.  It  is 
unfortunately  true  that  in  the  original  location  of  most  Amen- 
can  railwavs  this  possibility  has  been  little  considered;  part  y 
because  the  amount  of  future  traffic  was  not  foreseen;  partly 


because  the  grades  seemed  too  low  to  make  the  possibility  worth 
considering  (it  being  only  in  recent  years  that  the  use  of  pushers 
on  low  grades,  to  handle  very  heavy  trains,  has  become  common), 
and  partly,  in  some  instances,  from  mere  lack  of  thought. 

1062.  On  very  many  lines  it  has  happened  that  there  was 
some  one  short  stretch  on  a  division  where  a  50  or  60  ft.  per  mile 
grade  was  unavoidable.  Grades  approaching  this  limit  were  then 
used  on  other  parts  of  the  line  which  were  easily  avoidable  and 
can  easily  be  taken  out,  from  an  idea  (correct  enough  if  the  «se 
of  pushers  is  not  considered)  that  they  were  of  no  importance  if 
not  exceeding  the  maximum. 

Consequently,  when   the   line   was  opened,  trains   had  to  be 
quite  short.     Stations  were  laid  out  or  have  been  added  from 
time  to  time,  without  reference  to  the  use  of  any  other  than  the 
short  trains  then  handled,  and  new  roads  have  from  time  to  time 
put   in   grade-crossings,  at  which   all   trains  were  compelled  to 
stop,  with  similar  indifference  to  consequences,  provided  the  new 
Stop  did  not  require  a  still  shorter  train  than  was  then  handled. 
1063.  Thus  it  may  have  come  about,  in  the  course  of  years 
that  there  will  be  a  dozen  or  twenty  points  on  the  division  where 
the  demand  upon  the  power  of  the  locomotive  is  almost  as  great 
as,  and  frequently  greater  than,  the  resistance  on  the  maximum 
grade,  so  that  no  advantage,  or  very  little  advantage,  would  be 
gained  by  the  use  of  pushers  anywhere,  and  the  character  of  the 
hne  seems  fixed,  without  entire  reconstruction.     Yet  the  whole 
may  be  often  remedied  by  some  among  the  following  simple 
ways,  at  very  moderate  aggregate  cost: 

I.  The  point  or  points  offering  most  original  difficulties  and 
having,  probably,  the  heaviest  work  and  grades  (say  60  feet)  may 
be  in  some  cases  avoided  altogether  by  a  detour  of  a  few  miles, 
but  in  general  can  more  advantageously  be  operated  as  it  stands 
with  a  pusher,  thus  about  doubling  the  possible  train  over  it. 

1064.  2.  The  points  of  next  heaviest  grades— there  may  be  six 
or  eight  of  them,  having  grades  of  30,  40,  and  50  to  60  feet  per 
mile— will  in  some  instances  be  so  short  that  they  are  now,  or 
can   well    be,  operated  as  momentum  grades,  with   or  without 


i 


790  CHAP.  XXIV.^IMPROVEMEXT  OF  OLD  LIXES. 


CHAP.  XXIV.— IMPROVEMENT  OF  OLD  LINES.  79 1 


some  slight  modification.  The  feasibility  of  this  can  be  deter- 
mined simply  and  easily  in  tlie  manner  explained  in  par.  408.  In 
other  (and  frequent)  cases  short  sections  of  new  grading  will  be 
required,  to  wliich  the  track  complete  can  be  removed.  In  some 
cases  the  regrading  of  considerable  sections  will  be  necessary, 
enabling  the  line  perhaps  to  strike  some  new  town  by  a  detour, 
but  endangering  legal  complications  for  damages  unless  both 
lines  are  maintained.  Very  frequently,  however,  such  double 
construction  may  give  all  the  advantage  of  a  double  track,  for  a 
certain  distance,  since  the  objectionable  gradients  may  be  op- 
posed  to  trains  going  one  way  only. 

1065.  3.  The  disadvantageous  effects  of  grade-crossings  may 
now,  happily,  be  immediately  removed  in  all  cases  by  taking  ad- 
vantage of  the  laws  already  existing  in  some  States  (see  next  chap- 
ter), and  to  be  easily  obtained  by  effort  where  they  do  not  exist, 
permitting  such  crossings  to  be  operated  by  interlocking  signals 
without  requiring  trains  to  stop  at  them  regularly.  It  is  now 
universally  admitted  by  intelligent  and  well-informed  men,  that 
this  is  a  much  safer  and  cheaper  safeguard  than  the  stopping  of 
trains.  Exceptional  crossings  no  doubt  exist  where  (as  some 
trains  must  stop  when  another  happens  to  be  passing)  this  rem- 
edy would  not  be  a  perfect  one,  and  an  overhead  crossing  prefer- 
able, especially  to  effect  at  the  same  time  an  improvement  of 
grade,  but  in  general  dispensing  with  a  stop  by  interlocking 
would  be  all  that  was  practically  necessary.  The  expense  of  do- 
ing so  is  considered  more  fully  in  the  next  chapter. 

1066.  4.  The  unfavorable  gradients  at  stations— very  often  the 
chief  evil  to  be  cured,  although  none  but  the  trainmen  may  fully 
realize  the  fact — can  be  remedied  by  one  or  the  other  of  numer- 
ous wavs,  as  follows: 

(a)  By  moving  the  station  or  the  freight  tracks  only  a  little 
ahead  or  back,  so  as  to  reach  a  more  favorable  point;  if  neces- 
sary, at  important  stations,  by  completely  separating  the  freight 
and  passenger  yard  and  station,  and  incurring  some  extra  ex- 
pense for  extra  operators,  switchmen,  etc. 

{J})  By  modifying  the  gradients  of  the  station,  or  of  one  or 


two  tracks  thereat  in  the  manner  indicated  in  Fig.  254,  viz.,  rais- 
ing the  track  a,  at  the  lower  end  of  the  yard,  so  as  to  gi've  a  lower 
grade  for  starting  trains,  at  the  expense  of  a  somewhat  higher 
^rade  for  stopping  them,  the  latter  having  no  other  disadvan- 


Fig.  254. 


tageous  effect  than  to  check  the  speed  of  a  passing  train,  acting 
in  place  of  a  brake,  to  some  extent,  if  the  train  is  to  stop. 

{c)  By  stationing  a  switchman  to  open  certain  switches,  and 
thus  saving  the  necessity  of  a  train  stopping  at  an  unfavorable 
point  to  open  or  shut  them.  On  large  roads  and  at  large  sta- 
tions this  is  not  a  difficulty,  but  at  other  points  it  is  one  which 
must  be  fully  borne  in  mind. 

1067.  (d)  By  breaking  through,  if  necessary,  general  rules  as 
to  which  trains  shall  take  the  side  track,  and  even  (in  effect  if  not 
in  form)  which  trains  shall  have  the  right  of  way.     The  latter,  of 
course,  cannot  safely  be  done  in  form,  but  the  'desired  end  can 
be  accomplished  by  taking  care  in  despatching,  to  have  the  lightly 
loaded   trains,  or  those  which  the  grades  favor,  held  for  those 
which  cannot  well  stop  at  certain  stations  or  only  with  difficultv. 
A  general  rule  on  this  subject  is  commonly  established  and  put 
in  force  over  all  divisions  of  large  roads— as  for  instance  that  east- 
bound  trains  have   right  of  way  over  west-bound,  which  latter, 
consequently,  are  by  custom    always  obliged    to  take    the  side 
track  at  all  stations,  and  by  custom  of  the  despatchers  are  com- 
monly  held  so  as  to  favor  the  cast-bound  trains.    But  while  such 
a  rule   may  work  well   enough  on   most  divisions,  it  may   work 
very  unfavorably  in  others. 

1068.  For  example,  on  the  New  York,  Pennsylvania  &  Ohio 

Railroad,  the  general  rule  that  east-bound  trains  had  the  right 

of  way,  which  was  well  enough  for  the  remainder  of  the  road,  had 

{and  probably  still  has)  the  effect  on  the  Mahoning  Division  to 

•compel  the  heaviest-loaded  trains  to  stop  and  take  the  side  track. 


\^^M^ 


792 


CHAP.  XXIV.—IMPROVEMENT  OF  OLD  LINES. 


on  a  curve,  when   half  up  a  long  maximum  grade,  to  let  trains 
always  more  lightly  loaded  pass  down  hill  at  full  speed  past  them. 

Such  cases  are  not  infrequent,  and  come  to  be  looked  upon  as 
matters  of  course;  but  it  is  needless  to  say  that  they  can,  when 
occasion  arises  to  make  it  expedient,  be  modified  if  necessary  (i) 
by  reversing  on  one  division  the  usual  rule  as  to  which  trains  have 
right  of  way  ;  (2)  by  giving,  at  some  given  station  or  stations, 
trains  going  in  one  direction  the  right  to  hold  the  main  track  and 
require  an  opposing  train  to  take  side  track,  regardless  of  which 
has  right  of  way;  (3)  by  favoring  trains  in  dispatchers*  orders,  as 
before  suggested. 

Thus,  in  one  way  or  another,  it  may  generally  be  effected 
that  trains  passing  in  one  direction  past  some  one  station  on  a 
division,  at  least,  with  unfavorable  grades  which  cannot  other- 
wise be  remedied,  shall  not  be  compelled  to  stop  at  it. 

1069.  {e)  At  large  stations,  where  there  is  most  likely  to  be  diffi- 
culty or  great  expense  in  adopting  any  of  the  preceding  meth- 
ods, a  switch-engine  which  it  is  found  necessary  to  keep  at  the 
station,  but  which  is  not  kept  very  busy,  may  be  utilized  to  help 
trains  through  the  yard,  and  perhaps  also  over  some  uhfavor- 
able  grade-crossing,  which  is  particularly  likely  to  come  near 
to  such  a  station.  If  the  traffic  of  the  line  be  very  heavy  this 
may  not  be  possible;  but  in  that  case,  as  a  last  resort,  an  engine 
may  be  stationed  at  the  yard  for  the  sole  purpose  of  helping 
trains  through  it.  By  modifying  the  position  of  the  tele- 
graph office  it  may  in  general  be  arranged  that  the  use  of  such 
an  engine  shall  cause  no  extra  stoppage  of  the  train.  In  fact,  on 
manv  lines  of  heaw  traffic,  as  for  instance  the  Hudson  River 
Division  of  the  New  York  Central  Railroad,  pusher  engines  are 
used  to  help  trains  over  short  gra'des  without  stopping  trains  at 
all,  the  pushers  coming  up  behind  the  train  as  it  passes  a  switch, 
running  two  or  three  milles,  and  returning  on  the  same  track, 
protected  by  a  flag. 

1070.  The  best  method  of  determining  how  much  can  be  ef- 
fected in  these  various  ways  is  by  observations  of  the  variations 
of  velocity  in  the  handling  of  heavy  trains  on  the  present  line  in 


CHAP.  XXIV.— IMPROVEMENT  OF  OLD  LINES.  793; 


a  manner  shortly  to  be  described.  In  this  way  we  eliminate  the 
necessity  of  considering  and  allowing  for  a  long  list  of  doubtful 
elements — whicli  throw  a  haze  of  uncertainty  over  any  computa- 
tion in  which  they  must  be  separately  estimated  or  guessed  at 

by  simply  determining  by  direct  observation  the  resultant,  so  to 
speak,  or  net  effect  of  them  all.  For  lack  of  definite  knowledge 
on  a  number  of  variable  elements,  it  is  difficult,  if  not  impossible, 
either  to  compute  or  to  observe,  separately,  either  the  power  of 
the  engine  or  the  whole  resistance  of  the  train,  but  we  can  de- 
termine, very  accurately  and  simply,  the  relation  which  the  one 
bears  to  the  other— which  is  all  that  really  concerns  us— in  this 
way  : 

I.  When  the  engine  at  any  given  point  on  the  open  road 
LOSES  SPEED,  it  is  proof  that  working  with  the  given  steam-pres- 
sure and  point  of  cut-off  it  is  overloaded,  and  the  amount  of 
velocity  lost  can  be  made  a  measure  of  how  much  it  is  over- 
loaded (par.  400  et  al,). 

II.  Conversely,  if  the  engine  gain  speed  at  any  point  on  the 
open  road,  under  given  conditions  of  steam-pressure  and  cut-off, 
it  is  a  proof  that  it  is  underloaded,  and  the  observed  variations 
of  velocity  can  be  made  to  accurately  indicate  how  much. 

III.  If  an  engine  acquires  speed  in  starting  very  quicklv, 
under  given  conditions,  without  slipping  the  wheels  or  using 
sand,  etc.;  or,  on  the  contrary, 

IV.  If  the  engine  start  very  slowly,  or  not  at  all,  without 
slipping  the  wheels  or  using  sand,  or  both— the  observed  facts 
may  be  made  a  measure  for  accurately  determining  what  train  it 
could  start  under  similar  conditions  with  fair  working  efficiency. 

1071.  By  velocity  observations  of  the  nature  above  indicated 
under  varying  conditions  of  wind,  weather,  temperature,  longand 
short  trains,  loaded  and  empty  cars,  etc.,  etc.  (all  of  which  can 
be  observed  on  trains  by  simply  waiting  for  suitable  opportuni- 
ties without  affecting  or  interfering  with  normal  operating  prac- 
tices), we  have  a  positive  basis  for  determining  from  what  is 
done  under  those  conditions  whether  or  not  the  comparative 
ratio  of  power  to  resistance  on  various  parts  of  the  line  is  seri- 
ously imperfect. 


794 


CHAF.  XXIV.-^IMPROVEMENl'  OF  OLD  LINES. 


CHAF.  XXIV.— IMPROVEMENT  OF  OLD  LINES, 


795 


j4.s  respects  the  engine. . .  - 


In  other  words,  we  can,  by  the  simple  observations  suggested 
and  to  be  described,  construct  a  virtual  profile  of  the  road 
under  all  extremes  of  external  conditions.  We  can  then  com- 
pare these  virtual  profiles  and  determine  whether  or  not  a  given 
set  of  improvements  which  produce  a  desired  uniformity  of  re- 
sistance under  one  set  of  ponditions,  as  fair  summer  weather  and 
heavy-loaded  trains,  will  have  as  great  comparative  value  in 
stormy  winter  weather  with  long  trains  of  empty  cars. 

Positive  determinations  of  any  one  of  the  following  doubtful 
elements  we  save  the  need  of  altogether : 

The  ratio  and  amount  of  adhesion. 

The  cylinder-power. 

The  steam-power. 

The  head  resistance. 

The  rolling-friction  and  friction  of  machinery. 

The  gain  from  using  sand. 

The  rolling-friction. 

The  wind  resistance. 

The  effect  of  number  and  load  of  cars. 

The  effect  of  temperature,  state  of  rail. 

The  extent  to  which  momentum  may  be  re- 
lied upon  to  help  trains  over  short  heavy 
grades. 

1072.  To  accomplish  these  ends  the  system  of  observation 
should  in  detail  be  as  follows  : 

The  only  apparatus  or  previous  preparation  necessary  is  a  series  of 
distance-stakes  along  the  line,  a  stop-watch,  and  a  note-book,  with  an 
observer  on  the  engine  (at  times),  also  provided  with  a  note-book. 

The  stakes  are  set  at  various  governing  points  on  the  line  where 
speed  observations  are  desirable.  They  should  be  of  a  size  and  color  to 
be  easily  visible,  and  should  be  set  throughout  the  road  at  some  fixed 
and  uniform  distance  apart.  Boards  fastened  to  the  fence  may  be  more 
convenient  than  stakes.  It  is  unimportant  to  place  them  with  ref- 
erence to  mile-posts,  but  they  should  be  set  at  top  and  bottom  of  every 
doubtful  grade,  and  at  the  up-grade  starting-point  at  every  station  and 
stopping-place  which  either  is  or  may  become  in  any  way  a  difficult 
point,  requiring  consideration.  It  can  do  no  harm  to  place  them  at  all 
stations,  as  comparisons  may  be  instructive. 

A  train  moving  at  lo  miles  per  hour  passes  over  14.67  feet  per 
second.     As  our  time  observations  must  be  in  seconds,  it  will  be  more 


As  respects  the  cars  . 


As  respects  the  train  as 
a  whole 


convenient  to  set  these  stakes  at  some  multiple  of  14.67  feet  apart,  thus 
makmg  all  velocity  records  throughout  readily  convertible  into  miles 
per  hour  from  speed  notes  in  seconds.  A  suitable  distance  is  14.667  x  20 
or  293.33  feet.  If  set  at  that  distance  a  train  which  passes  over  the 
distance  between  any  two  stakes  in 

20  seconds  is  moving  at  10    miles  per  hour. 
15         "  "  -       13I       -    *^     .. 


f5 

10 
5 


<< 


15 

20 

if 
<< 

4( 
(< 

40 

i< 

« 

200 

A 

(< 

« 

In  other  words,  reciprocal  of  A  seconds  X  200  =  vel.  in  miles  per  hour 
between  the  two  stakes;  a  very  simple  computation  from  a  table  01  re- 
ciprocals which  the  following  Table  201  will  save  the  need  of. 

Table  201, 
Speed  in  Miles  Per  Hour  corresponding  to  the  Time  in  Seconds  in 

PASSING   OVER   A    DISTANCE   OF   293^    FeET. 


Seconds. 

Speed. 
66.7 

Seconds. 

Speed. 

3 

6i 

32.0 

3i 

61.6 

6i 

30.8 

3i 

57-1 

6f 

29.6 

3* 

53.3 

7 

28.6 

4 

50.0 

7i 

27.6 

4i 

47.1 

1\ 

26.7 

4^ 

44-4 

7f 

25.8 

4f 

42.1 

8 

25.0 

5 

40.0 

8i 

24.2 

Ik 

38.1 

8* 

23-5 

l\ 

36.4 

81 

22.9 

51 

34-8 

9 

22.2 

6 

33-3 

9i 

21.6 

Seconds. 


9i 

9f 
10 

loi 

II 

Hi 

12 

12\ 

13 

I3i 

14 

15 

16 


Speed. 


21. 1 
20.5 
20.0 
19.0 
18.2 
17.4 
16.7 
16.0 

15.4 
14.8 

14-3 
133 
12.5 


Seconds. 

17 

18 

19 
20 

22 

24 

26 

28 

30 

35 
40 

50 
60 


Speed. 


11.76 
II. II 

10.53 
10.00 

9.09 

8.33 
7.69 

7.14 
6.67 

5-71 
5.00 
4.00 

3-33 


The  disposal  of  the  stakes  at  stations,  where  speed  is  slow 
may  be  advantageously  modified  by  putting  in  half-stations  so 
that  they  are  only  146.67  feet  apart,  thus  giving  more  accuracy 
to  the  observations  ;  but  this  is  unessential,  and  does  not  modify 
the  principle. 


if 


I''" 


>■: 


796 


CHAP.  XXIV.—IMPROVEMENT  OF  OLD  LINES. 


1073i  Stop-watches  suitable  for  this  purpose  may  be  bought  of  any  dealer 
for  %i  to  $io  each.  They  read  to  quarter  or  fifths  of  seconds,  being  stopped 
and  the  hands  fixed  at  any  instant  by  the  movement  of  a  little  button.  Pres- 
_  sure  on  another  button,  B^  Fig.   255,   restores  the 

hand  to  zero,  ready  for  another  start.      They  are 
generally  durable  and  reliable. 

Two  stop-watches  may  advantageously  be  pro- 
cured and  mounted  together  on  a  board,  the  starting 
buttons  being  connected  to  a  single  lever,  as  shown 
in  Fig.  255,  in  such  manner  that  a  single  motion  of 
the  lever  will  start  one  watch  and  stop  the  other 
simultaneously.  This  will  throw  the  buttons  for 
turning  the  hand  to  o  on  the  outside,  so  that  they 
can  be  readily  used  without  danger  of  mistaking  one 
Fig.  955.  for  the  other.     It  is  not,  however,  essential  that  in 

taking  a  series  of  say  five  or  six  observations  we  should  return  the  hand  to  zero 
each  time.  We  may  simply  start  one  watch  and  stop  the  other  at  each  station 
and  note  the  actual  readings,  as  below  noted.  The  attachment  of  the  lever 
should  be  so  devised  that  there  is  a  single  point  in  a  central  position  of  the 
lever  where  neither  watch  will  be  started,  which  is  a  simple  matter  to  do.  A 
single  "split-second"  watch  will  answer  the  same  purpose,  but  is  more  expen- 
sive. 

Some  brass  clips,  C,  for  inserting  a  memorandum  slip  near  to  the  watches 
may  advantageously  be  placed  upon  the  board  to  which  they  are  attached,  and 
brackets  or  angle-plates  may  well  be  provided  for  readily  screwing  the  whole 
firmly  to  the  side  of  the  car.  It  is  convenient,  although  not  essential,  to  have 
an  observer  to  watch  and  call  off  the  instant  of  passing  each  stake,  so  that  the 
attention  need  not  be  distracted  from  accurately  taking  the  time  observations. 
A  little  stand  or  hook  to  carry  an  ordinary  watch  for  time  records  may  well  be 
added. 

1074.  The  records  of  a  series  of  six  or  eight  successive  observations 
at  any  desired  point  may  then  be  jotted  down  on  the  memorandum  pad, 
to  be  worked  up  later,  or  on  the  spot,  since  they  are  likely  to  be  needed 
at  infrequent  intervals  only.  It  answers  every  useful  purpose  of  a  dyna- 
mometer record,  for  the  fluctuations  of  speed  are  such  a  record. 

In  starting  out  from  a  station  the  intervals  of  time  will  be  consider- 
able, even  when  taking  half-stations  of  146.67  feet  each,  and  there  is  no 
difficulty  under  any  circumstances  in  taking  readings  with  all  essential 
accuracy. 

1075.  The  simple  preliminary  preparations  required  having  been 
made,  the  method  of  conducting  the  observations  of  the  actual  working 
of  trains  should  be  as  follows : 


CHAP.  XXIV.— IMPROVEMENT  OF  OLD  LINES.  79/ 


Before  beginning  the  more  careful  and  accurate  work  a  series  of  com- 
paratively rude  observations  may  well  be  made  in  which  exactitude  is 
not  desired  or  attempted,  solely  for  the  purpose  of  observing  the  varia- 
tions of  velocity  in  the  ordinary  routine  of  service,  and  to  learn  what  to 
expect  and  where  to  observe  most  carefully.  No  observer  on  the  enoine 
IS  needed  for  this  purpose,  and  it  is  as  well,  or  perhaps  better,  that'ihe 
trammen  should  know  nothing  of  the  particular  purpose  in  view. 

For  the  more  formal  and  careful  observations  an  observer*  on  the 
engme  is  necessary ;  and  it  is  desirable  that  the  train  should,  ih  several 
mstances  at  least,  be  run  on  an  accelerated  schedule,  and  that  the  engine- 
man  should  have  full  liberty,  and  indeed  express  instructions,  to  get  over 
the  ground  (and  especially  to  pull  out  from  stations)  as  rapidly  as  is  con- 
sistent with  due  caution  and  safety;  in  other  words,  to  see  how  quickly 
he  can  run  over  the  division,  remembering  always  that  the  cylinder 
tractive  power  of  locomotive  is  very  different  at  high  speed  and  low 
speed  (par.  557  et  seg.). 

1076.  The  duty  of  the  observer  on  the  engine  is  to  take  notes  from 
pomt  to  point  of  the  following  details;  not  for  the  purpose  of  making 
any  absolute  estimates  or  computations,  but  simply  to  have  a  full  record 
of  the  work  of  the  engine : 

(1)  The  steatn-pressure,  by  record  of  fluctuations  of  the  steam-gauge 
It  depends  largely  on  the  skill  of  the  fireman ;  how  much,  can  only  be 
determined  by  trial  of  different  men,  or  by  their  record,  if  on  a  road 
which  has  a  fuel  premium. 

(2)  The  point  of  cut-off ,  or  "  notch." 

(3)  The  slipping  of  wheels  and  the  use  of  sand.  The  record  as  to  the 
last  depends  very  largely  (par.  501)  upon  the  skill-and  even  in  some 
cases  on  the  good-will-of  the  engineman.  It  should  be  remembered 
that  he  can,  if  he  chooses,  slip  the  wheels  almost  anywhere,  and  he  will 
slip  them,  whether  he  wishes  to  or  not,  if  he  have  not  the  requisite  skill, 
or  is  not  disposed  to  be  careful.  Starting  is  ordinarily  effected  by  set- 
ting the  valves  in  full  gear  ahead  and  regulating  the  admission  of  steam 
by  the  throttle.  If  a  full  pressure  of  steam  be  admitted  too  suadenly, 
slipping  of  the  wheels  is  certain  to  ensue,  even  if  the  engine  be  haulin'c^ 
no  train  whatever.  ** 

1077.  Too  much  importance  must  not  be  attached  to  such  slipping-, 
therefore,  since  it  is  more  or  less  a  regular  incident  to  handling  heavy 
trains  by  locomotives,  which  cannot  be  wholly  avoided  without  cutting 
down  trains  to  an  uneconomical  point,  nor  perhaps  even  by  doing  so,  as  is 
witnessed  by  the  slipping  which  goes  on  constantly  in  yard  work,  result- 


■f  M 


798 


CHAP.  XXIV.— OLD  LINES— VIRTUAL   PROFILE. 


CHAP.  XXIV.-OLD  LINES-VIRTUAL   PROFILE. 


ing  not  from  the  excessive  load,  but  from  too  great  haste  to  get  the  load 
under  way. 

1078.  The  duty  of  the  observer  on  the  caboose  (or  at  any  other  con- 
venient point  on  the  train)  is  confined  to  taking  the  time  records.     He- 
should  know  the  points  at  which  they  are  to  be  taken  very  thoroughly. 
He  should  also,  before  starting  out  on  the  trip  or  after  completing  it, 
note  the  following  details  : 

Number  and  class  of  engine  and  name  of  engineman  and  fireman. 

Number  and  gross  weight  of  loaded  and  empty  cars,  and  whether  box 
or  fiat  cars,  and  how  many  ends  of  box  cars  are  left  exposed  in  the  train, 
by  being  preceded  by  flat  cars,  to  cause  extra  air  resistance. 

Temperature,  condition  of  rail,  and  direction  and  velocity  of  the  wind. 
The  latter  may  well  be  determined  by  an  anemometer  and  wind-vane  on 
the  caboose,  which  will  give  directly,  what  is  really  required,  the  resultant 
in  magnitude  and  direction  of  the  wind  caused  by  the  motion  of  the  train, 
and  that  otherwise  existing.  With  a  head  wind  the  resultant  will  lie  in  the 
direction  of  the  train  and  have  a  velocity  equal  to  the  two  combined  ; 
with  a  rear  wind,  it  will  have  a  velocity  equal  to  the  difference  of  the 
two,  which  may  be  zero;  with  a  side  wind  equal  in  velocity  to  the  speed 
of  the  train  the  resultant  will  lie  at  an  angle  of  45°  therewith,  and  have 
a  velocity  1.414  times  greater,  etc.  It  is  not  really  essential  that  very 
accurate  wind  observations  should  be  made,  since  we  are  not  after  abso- 
lute but  comparative  results,  and  it  is  easily  estimated  whether  a  storm 
or  wind  is  or  is  not  about  as  unfavorable  as  is  often  encountered. 

1079.  The  records  having  been  taken,  the  velocities  at  various  points 
are  taken  from  Table  201  and  the  vertical  "  head  "  in  feet  corresponding 
to  that  velocity  taken  from  Table  118,  in  the  manner  which  has  been  dis- 
cussed in  par.  397  et  seq.  on  virtual  profiles,  which  we  are  now  ready  to- 
construct,  preparatory  to  entering  upon  the  interpretation  of  the  obser- 
vations taken.     In  these  latter  steps  lie  the  delicate  parts  of  the  work. 

CONSTRUCTION    OF    THE    VIRTUAL    PROFILE. 

1080"  Taking  an  actual  profile  (which  need  not  necessarily 
cover  the  whole  line,  but  may  show  only  the  important  points; 
a  common  profile  to  working  scales  is  the  best),  lay  off  at  each 
point  where  time  records  have  been  taken  the  vertical  height  in 
feet  corresponding  to  the  velocity  which  the  train  had  at  that 
point.  By  an  assumption  which  is  practically  correct,  the  aver- 
age speed  which  a  train  has  between  any  two  stations  is  its  actual 


799 

!hriH\'^^  ^f"""-  "^^d^^y  between   them.     Tl^rtical  hei^ 
should   therefore  be  laid   off  at   corresponding   points  on^the 

In  this  way  we  obtain  our  virtual  profile,  parts  of  which  may 
be  sornething  like  the  dotted  line  on  the  following  Fig  LZ 
solid  line  being  the  actual  profile.  ^'  ^  ' 


Fig.  256. 


1081.  Tins  Virtual  profile,  as  we  have  seen,  is  that  which  alone 
needs  to  be   considered.     It   represents  a  line  over  which    if  it 
were  actually  constructed,  a  locomotive,  exerting  at  everv  point 
the  same  energy  and  overcoming  the  same  frictional  resis'tances 
would   move  at  every  point  without  either  gaining  or  losin<^ 
speed.     O,.  tins  profile  what  appears  to  be  and  what  is  coincide! 
M  the  vntual  profile  shows  a  low  enough  rate  of  grade  we  need 
not  be  disturbed  if  the  actual  profile  below  it  shols  a  consider 
ably  h.gher  grade.     On   the  other  hand,   if  the  virtual  profile 
shows  a  short  heavy  grade  in  pnlling  out  from  a  station,  which 
cannot  be   reduced  by  taking  more  time  in   starting  trains   its 
disadvantage  is  no  whit  less  because  it  is  short  or  because 'the 
actual  grade  below  it  is  almost  a  level. 

The  virtual  profile  will  differ  according  to  the  direction  the 

but  from  all  these  notes  together  a  safe  average  is  supposed  to 
have  been  determined  at  each  point. 

1082.  Studying  how  to  reduce  this  virtual  profile,  we  recoe- 
nize  three  ways:  ° 

in  ^^X  H  "'^  T'''T'^'  ^°  ^^""^  ^"'  "^^"^"^  by  increasing  it 
llimin«,  '  g'-!«Jes  and  decreasing  it  on  the  summits  and  by 
eliminating  or  taking  longer  time  for  stops.     By  carrying  this 

Stfn  r""  T^'*  ""  ""''  '■^'"•^^  '"^^  ^''•'-'  P-fil^  °f  -  un- 
dulating hne  having  very  heavy  grades  to  a  level,  as  we  have 


8oo 


CHAP.  XXIV.— OLD  LINES— VIRTUAL  PROFILE. 


seen  (par.  399);  but,  practically,  only  minor  variations  of  this 
kind  are  admissible. 

Secondly  (and  next  simplest),  by  using  pushers. 

Thirdly^  by  reconstruction  or  amendment  of  the  actual 
profile. 

1083.  Let  us  suppose,  as  examples  are  most  readily  followed, 
that  these  observations  have  been  taken  and  the  virtual  profiles 
made  over  a  given  division  with  the  results  at  various  points 
outlined  on  the  following  Figs.  257  to  264. 

Some  long  hard  pull  on  a  1.2  per  cent  grade  {d^-Z'^  ^^et  per 
mile)  shows  that  the  given  engines  can  handle  25  cars,  more  or 
less,  on  this  grade  with  great  ease,  except  in  very  unfavorable 
weather.  Under  fairly  favorable  conditions  the  velocity  gained 
without  overtaxing  the  boiler  capacity  is  such  as  to  indicate  a 
virtual  maximum  grade  of  1.4  per  cent,  or  even  more. 

The  same  is  true  at  a  number  of  minor  points  on  the  same 
•division. 

In  pulhng  out  at  stations,  by  comparison  of  many  observa- 
tions, it  is  found  under  average  conditions  that  the  virtual  grade 
was  1.3  to  1.5  without  using  sand  (being  somewhat  lower  be- 
<:ause  of  the  greater  journal-friction,  and  lower  because  the  full 
adhesion  was  more  nearly  used  and  there  was  less  air  and  other 
velocity  resistance),  while  when  sand  was  used  the  virtual  grade 
was  raised  to  r.6  or  1.8.  On  the  other  hand,  with  very  unfa- 
vorable weather  and  a  bad  rail,  the  virtual  profile  in  starting  is 
1.2  to  1.4,  even  with  use  of  sand.  ' 

1084.  Under  these  conditions  we  have,  in  the  first  place,  an 
indication  that  the  trains  now  handled  on  the  road  as  it  stands 
are  somewhat  smaller  than  they  might  be — an  indication  which 
is  alone  worth  the  trouble  of  an  investigation  of  this  kind,  and 
can  in  no  other  way  be  so  accurately  determined.  Passing  that 
question,  however,  as  not  now  under  consideration,  we  have  a 
very  positive  indication  that  we  shall  be  safe  in  assuming  that 
by  using  a  pusher  of  equal  power  over  the  worst  grade,  we  shall 
in  effect  reduce  it  to  the  equivalent  for  a  single  engine  of  a 
pusher  grade  of  1.2  per  cent,  which  is  (Table  182,  page  593)  0.45 


CHAP.  XXIV.-OLD  LmES-VIRTUAL  PROFILE.  8or 


try  for  over  the  remainder  of  the  division.     If  vve  find  it  ea.sv  nf 
accomp  ishment,  we  may  consider  reducing  it  stiU   lot      and 

by  use  of  san^d  may' l^ZZ^:;:^::  t  r^'ditLrs'."^ 


Fig. 


»57- 


fl^*!i-- 


Over  the  remainder  of  the  division  we  are  liable  at  various 
points,  to  have  cases  like  the  following- 

1085.  A  station  grade  at  ^,  Fig.  .57,  on  an  actual  grade  of 
0.6,  ,s  operated  very  easily  now.  the  train  quickly  getting  under 
way  even  without  the  use    --.^  .y  gcLLiug  unaer 

of  sand.     By  taking  more  *"**'-»-. 

time    for    starting    heavy 
trains  (say  attaining   full 

working  speed  at  ^)   the  p,,.,,,.  -^  4 

virtual  grade  might  be  reduced,  perhaps,  to  75,  but  it  is  nTces 
sary  to  reduce  it  to  0.5  at  least,  and  if  possibi" to  o  4   tl  e  actual' 
grade  needing  to  be  considerablv  less.  ' 

The  neatest  and  most  effectual  method  is  to  remove  the  sta 
t  on  at  once  from  A  to  £,  this  alone  having  the  effect  to  favlr 
ably  modify  the  virtual  profile  far  more  than  was  de 'ir  d  'fwn. 
that  shown  in  Fig.  .58.  If  this  be  impossible,  thlnex?  be"! 
m  thod  ,s  to  take  out  the  bad  gradient  in  the  virtual  profile  bv 
aising  the  grade  at  A  on  the  actual  profile  to  A',  giLlhiZ 
orm  shown  in  Fig.  .5,.  Changes  of  this  kind 'a^apV to  be 
expensive  because  of  their  locality;  but,  on  the  other  hand,  they 


'III 


8o2 


CHAP,  XXIV.— OLD  LINES— VIRTUAL   PROFILE. 


are  inexpensive  in  that  they  are  seldom  very  long.  The  effect  is 
to  substitute  (in  the  lower  half  of  the  diagram)  a  broken  actual 
but  good  virtual  profile,  in  place  of  a  good  actual  but  bad  virtual 
profile,  as  in  the  upper  half'of  Fig.  259. 

1086.  A  modification  of  the  same  case  may  be  as  follows:  A 

station  originally  well  situ- 
ated, as  Sy  Fig.  260,  but 
which  has  been  complicated 
by  subsequent  additions  of 
grade-crossings  for  other 
lines  C  and  C,  at  which  all 
trains  have  to  stop  and 
^'°'  "59-  start  again  on  a  grade. 

The  first  and  best  remedy  for  this  evil  is  the  use  of  inter- 
locking signals,  saving  the  necessity  of  a  stop  except  to  let 
another  train  pass;  but  as  that  is  a  contingency  which  may  hap- 
pen not  infrequently,  it  can  never  be  a  perfect,  nor  in  some 
cases  sufficient,  remedy.     The  evil  may  also,  in  cases,  be  reme- 


CIIAP.  XXIV.-OLD  LINES-VIRTUAL   PROFILE. 


-fti. 


Fig.  260. 

died  by  raising  the  grade  of  the  track  approaching  the  crossing 
as  outlined  at  C and  C\  provided  the  virtual  grade  of  the  approach 
be  not  increased  thereby  to  an  inadmissible  rate.  The  only 
remaining  course  is  either  to  use  a  yard  engine  as  a  helper  over 
the  crossings  or  to  boldly  lower  the  grade  by  passing  under 
each  road,  and  grading  a  new  road-bed  or  lowering  the  existing 
one,  for  which  room  may  be  so  scant  as  to  require  retaining- 
walls.  This  will  make  the  improvement  a  costly  one,  and  yet 
the  cost  will  probably  be  small  in  proportion  to  the  gain, 
unless  it  is  only  one  among  many  costly  improvements  required 

for  the  desired  end. 

1087.  At  large  towns  it  is  a  very  common  thing  to  find  the 
station  located  at  some  point,  like  5  or  5',  Fig.  261,  which  was 


Fig.  261. 


S03 

originally  fixed  more  with  reference  to  the  c^^ience  of  the 
town  than  to  the  grades.  This  is  of  course  the  proper  thing  to 
do,  and  a  decrease  of  station  ^ 

facilities,  or  a  change  causing 
inconvenience  to  the  patrons  of 
the  line,  will  in  general  be  inex- 
pedient. Such  large  stations, 
moreover,  are  generally  well  provided  with  side  tracks,  so  that 
the  result  is  that  they  are  largely  used  by  train-dispatchers  as 
passing  points. 

The  proper  remedy  in  such  cases  is  to  establish  sidings  For 
F,  to  serve  as  passing  points  for  through  trains  only  with  a 
:separate  telegraph-office,  leaving  the  local  facilities  undisturbed 
Ihis  requires  the  services  of  two  operators  to  do  the  work  of  one' 
and  perhaps  one  or  two  other  otherwise  needless  employes  but' 
the  wages  of  one  train  crew  for  a  single  trip,  it  should  be  re- 
membered,  will  pay  the  wages  of  a  good  operator  for  a  week. 

1088.  The   case   sketched    in    Fig.    261,    moreover,    is  one  of 
those  where  the  whole  difficulty  in  handling  heavier  trains  may 
be  made  to  vanish  by  a  modification  of  the  system  of  dispatch- 
ing,  to  the  effect  that  only  trains  going  down  grade,  or  say  east 
shall  be  held  at  this  station  and  compelled  to  take  side  track 
'(except,  of  course,  in  emergencies),  especiallv  if  there  be  another 
regular  station  near  to  it,  as  For  K',  which  may  be  used  as  a 
passing  point,  by  holding  one  or  the  other  train,  in  case  it  is  im- 
possible  for  the  eastward  train  to  reach  ^  or  S'  first.     It  is  not 
essential,  although  it  is  convenient,  that  a  dispatcher  should  feel 
at  liberty  to  hold  any  train,  bound  either  way,  at  any  station   in 
the  regular  routine  of  business,  provided  that  to  do  so  interfeVes 
with  a  material  addition  to  the  train-load.     It  is  the  rule  and 
not  the  exception,  however,  that  he  can  and  does  do  so. 

1089.  The  decision  as  to  what  course  to  adopt  for  modifica- 
tions of  gradients  on  the  open   road  is  a   much   simpler   matter 
than  at  stations.     The  vital  point  to  be  determined  in  the  begin 
ning,  before  studying  the  details  of  the  various  difficult  points  at 
•ail,  IS  what  rate  of  speed  is  practicable  and  allowable  at  the  foot 


mu 


rt' 


% 


8o4 


CHAP.  XXIV.— OLD  LINES— VIRTUAL   PROFILE. 


CHAP.  XXIV.-OLD  LINES-VIRTUAL   PROFILE. 


805 


of  the  grade,  which  largely  depends  on  tlie  alignment.  The 
modern  tendency  is  very  decidedly  to  permit  of  higher  speed  in 
handling  freight  trains,  and  it  is  essential  to  do  so  at  points  to 
handle  the  maximum  train  on  all  undulating  gradients.  The 
probable  introduction  in  the  near  future  of  freight-train  brakes 
and  more  mechanical  coupling  devices  than  are  now  in  use  will, 
when  accomplished,  greatly  increase  the  admissible  maximum 
of  speed  for  equal  safety;  but  even  as  freight  equipment  stands 
at  present  it  is  probable  that  30  or  35  or  even  40  miles  per  hour, 
for  short  distances  at  special  points  (the  writer  must  not  be 
understood  to  recommend  the  latter  speed),  are  quite  as  safe  as 
50  to  65  miles  per  hour  for  passenger  trains.  It  has  been  tolerably 
well  determined  (par.  664  et  al?)  that  higher  speeds  than  15  miles 
per  hour  are  more  economical  for  freight  trains;  and  the  not  un- 
common feeling  that  any  speed  of  over  15  or  20  miles  per  hour 
verges  on  the  dangerous  is  in  part  a  relic  of  the  old  days  of  iron 
rails,  poor  ballast  and  road-bed,  and  less  solidly  constructed  roll- 
ing-stock. 

1090.  Therefore,  when  required  for  reducing  virtual  gradients 
by  taking  a  **  run  at  them,"  as  part  of  a  general  system  of  im- 
provements, a  speed  of  30  miles  per  hour  (which  takes  31.95  ver- 
tical feet  out  of  the  depth  of  a  hollow;  Table  118)  should  be 
freely  permitted  and  counted  on,  with  fair  alignment;  and  with 
a  tangent  in  the  hollow  of  the  gradients  this  limit  may  in  gen- 
eral be  safely  increased  to  35  miles  (43-49  vertical  feet),  if  that 
speed  seems  essential.  These  speeds  and  even  higher  ones  are 
now  frequently  used  in  handling  freight  trains  on  many  lines. 
Whatever  the  limit  adopted,  however,  it  should  be  determined 
in  advance,  by  reference  to  the  records  obtained  as  already  de- 
scribed, and  especially  with  careful  consideration  as  to  whether 
the  assumed  speed  can  with  certainty  be  counted  on  as  attainable  at 
the  given  point.  Unless  there  be  a  descending  gradient  in  the 
approach  so  as  to  give  the  required  speed  quickly,  the  high  speeds 
mentioned  cannot  be  counted  on  safely. 

1091.  This  preliminary  being  determined  and  the  present  and 
desired  gradients   being  the   same  as   already   assumed,  viz.,  1.2^ 


Fig.  a62. 


actual  and  0.45  desired.  Figs.  262  to  265  will  serve  as  types  of  all 

the  cases  which  can  arise  on  the  open  road.     In  Fig.  262  let  AB 

be  a  long  i.o  per  cent  grade  with 

curved   alignment  at  B  so  that 

more  than  30  miles  per  hour  is 

not   deemed    safe  at  that  point, 

but  that  or  even  higher  velocity 

is  easily   attainable.      With  the  .. 

short  trains  heretofore  in  use  the  grade  has"not'"been  a  difficult 
one,  so  that  the  virtual  profile  obtained  in  observations  on  trains 
as  now  run  has  been  nearly  parallel  with  the  grade,  the  speed 
bemg  lower  at  B  and  higher  at  A  than  was  necessary  It  is  de- 
sired  to  determine  to  what  extent  (i.e.,  for  what  length)  such  a 
grade  can  be  operated  as  a  virtual  0.5  gradient. 

1092.  A  certain  speed  at  A,  not  less  than  10  miles  per  hour 
{3.55  vertical  feet),  must  be  assumed,  as  a  margin  for  error 
whether  there  be  a  stationatA  or  not  (par.  1095).  Then  31  95  ~  ,  c  J 
=  28  4  vertical  feet,  as  the  maximum  through  which  momentum 
can  be  relied  on  to  lift  the  train.  Moreover,  the  actual  grade  i  o 
--  0.5  (assumed  virtual  grade)  =0.5  feet  per  station  as  the  defi- 
ciency  in  power  of  the  locomotive  which  must  be  made  up  bv 
—     -  28.4  ^    ^ 

—  50.8  stations,  or  over  9  mile. 


05 


momentum.     We  have  then 


Fig.  263 


Zf     ^^  °^  "'*''  ^'  "'"  '""»"'  °f  'his  grade  which  it 

>s  possible  to  operate  in  this  manner.     If  the  grade  be  longer  or 
^horter  than  this,  the  overplus,  but  the  overplus  only,  must  be 

^ruJT-   I  "^":  ~"^'™«'°".  either  by  raising  the  grade  at  B 
or  (what  .s  better)  lowering  it  at  ^.    If  the  grade  were  ten  stations 


^'\*  ■ 


i.: 


806 


C//AP.  XXIV.— OLD  LINES— VIRTUAL   PROFILE. 


longer,  those  ten  stations,  but  those  only,  must  be  reduced  to- 
0.5  actual  grade  in  one  or  the  other  of  the  methods  outlined  in 
Fig.  263.  If  the  change  be  made  at  the  bottom  of  the  hill,  as  at 
B,  we  shall  have  the  disadvantage  that  on  the  whole  of  the  new 
0.5  gradient  a  speed  of  30  miles  per  hour  must  be  maintained  to- 
have  the  desired  effect.  As  this  may  be  or  may  seem  objection- 
able, the  modification  may  need  to  be  more  extensive  to  effect 
the  desired  end,  and  should  be,  wherever  possible. 

1093.  The  same  is  true,  in  less  degree,  of  the  change  at  the 
top.  The  train,  under  the  assumptions,  will  not  be  able  to  move 
faster  than  10  miles  per  hour  until  it  has  passed  entirely  over  it. 
Therefore  the  maximum  figures  for  the  gain  by  momentum 
should  be  used  only  for  determining  whether  or  not  any  vwdification 
of  the  grade  will  be  required.  If  it  is  even  then  found  necessary,  3 
more  liberal  margin  should  at  once  be  adopted,  if  attainable  at 
moderate  increase  of  cost,  as  it  generally  will  be. 

In  fact,  when  some  construction  in  any  case  has  been  once 
found  necessary  it  may  often  be  best  and  almost  as  cheap  to  take 
the  whole  hill  out  at  once  by  a  detour;  perhaps  making  the  new 
and  old  lines  together  serve  as  in  effect  a  double  track. 

1094.  It  is  to  be  remembered  in  considering  what  allowance 
it  is  safe  to  make  for  assistance  by  momentum,  that  in  many 
cases  an  error  in  the  estimate  of  the  possible  gain  from  that 
source  will  have  no  disastrous  consequences,  since  if  it  be  found 
that  the  assumed  speed  was  too  great  to  be  relied  on  it  is  pos- 
sible at  any  time  to  raise  the  grade  three  to  five  feet  in  the  hol- 
low, as  outlined  in  Fig.  264,  and  thus  materially  reduce  the  speed 

required.  To  do  this  is  in 
most  cases  a  comparatively 
simple  matter,  since  the  fills 
need  not  be  very  long  to 
p,j3^g  raise  the  hollow  between  two 

gradients  by  a  considerable  amount.  If  the  two  gradients  are  i 
per  cent,  the  total  length  of  the  fill  is  only  200  feet  per  foot  of 
lift  ;  with  0.5  gradients,  400  feet  per  foot  of  lift;  and  with  1.5 
gradients,  133  feet  per  foot  of  lift,  etc.     To  make  fills  by  train  in 


CHAP.  XXIV.— OLD  LINES— VIRTUAL  PROFILE.  807 


Fig.  265. 


such  locations,  even  if  of  considerable  magnitude,  is  rarely  ex- 
pensive, and  it  can  be  done  at  any  time  when  found  convenient 
and  essential.  Therefore,  when  it  is  seen  that  a  not  excessive 
fill  will,  if  made,  fulfil  all  necessities,  it  is  proper  to  rely  quite 
largely  on  momentum  for  the  time  being,  if  by  so  doing  the  fill 
can  be  dispensed  with  for  a  time  at  least,  and  perhaps  forever. 

1095.  On  the  other  hand,  there  is  a  danger  connected  with 
the  study  of  such  virtual  profiles,  which  has  been  alluded  to 
above,  but  which  should  be  still  more  explicitly  pointed  out. 
When  the  question  whether  or  not  we  can  keep  within  a  certain 
virtual  gradient  is  at  stake,  as  in  Fig.  265,  it  is  in  no  case  safe, 
even  when   there  is  a  station  at  .->>_ 

the  top  of  the  hill  at  A,  to  assume 
that  we  can  arrive  there  with  no 
velocity,  and   can   consequently 
lay  the  virtual  gradient   directly 
on  the  actual.     It  seems  plausi- 
ble that  we  can  do  this,  as  we  are  certain  that  we  shall  need  no 
velocity  at  A-,   but  what  we  are  not  sure  of  is  of  never  falling 
below    the  desired  velocity  at    B,    and   if   we  do,   our  virtual 
gradient  is  at  once  increased.     If  we  assume  a  certain  moderate 
velocity  at  A,  say  10  miles  per  hour  (3.55  vertical  feet),  and  any 
maximum  velocity  deemed  reasonable  at  B,  as  in  cases  where  no 
stop  is  contemplated,  we  are  safe,  because  our  velocitvat  ^may 
then  fall  quite  a  little  below  that  assumed  without  endangering 
our  arriving  at  A  with  some  velocity,  so  as  to  float  the  train  over 
It;  but  if  we  assume  we  are  to  arrive  at  A  with  no  velocity,  sim- 
ply because  the  train  must  stop  there,  we  are  liable  not  to  reach 
there  at  all.     No  advantage  can  be  assumed,  therefore,  from  the 
fact  of  a  stop  at  the  top  of  the  gradient  more  than  would  exist  if 
there  were  to  be  no  stop  there  at  all.     In  either  case  we  must  be 
sure  of  reaching  the  top,  and  in  neither  case  is  it  important  to  be 
sure  of  more  than  that. 

1096.  The  temptation  may  be  great  to  fall  into  this  plausible 
error,  when  an  estimate,  perhaps,  must  be  kept  very  close  to  have 
the  work  go  through  at  all,  and  when  there  may  be  an  expensive 


8o8 


CHAP.  XXIV.— OLD  LINES— VIRTUAL  PROFILE. 


bridge  at  B,  making  it  difficult  to  lift  up  the  grade  at  that  point; 
but  if  a  reasonable  velocity  at  B  and  some  velocity  at  A  will  not 
suffice,  there  is  nothing  for  it  but  either  to  raise  the  bridge, 
lower  the  station,  increase  the  distance  between  them,  or  give  up 
the  desired  virtual  maximum  as  unattainable. 

1097.  By  attacking  the  work  of  improving  old  lines  in  the 
method  here  outlined,  halving  the  more  formidable  and  inevi- 
table grades  at  once  by  using  a  pusher  on  them,  without  spend- 
ing a  dollar  on  them,  and  spending  all  our  money  on  what  were 
before  the  very  easy  grades,  and  hence  are  usually  in  light  work, 
the  average  train-load  may  be  doubled  at  small  cost  on  thousands 
of  miles  in  this  country  ;  whereas  by  merely  attacking  the  heav- 
iest grades  which  show  on  the  profile  with  force  and  arms,  so  to 
speak,  a  great  deal  of  money  must  be  spent,  and  there  will  be 
comparatively  little  to  show  for  it. 


CHAP.  XXV.—GRADE-CROSSINGS  AND  INI^ERLOCKING.    809 


CHAPTER   XXV. 


GRADE-CROSSINGS   AND    INTERLOCKING. 

1098.  The    multiplication    of   grade-crossings   has  become  a 
•great  and  serious  question,  especially  in  the  West.     The  topo- 
graphical conditions  in  the  East  greatly  restrict  the  danger  from 
such  crossings,  as  well  as  their  frequency;  but  throughout  vast 
regions  of  the  West  there  is  absolutely  nothing   to   prevent  a 
railway  being  built  from  anywhere  to  anywhere  in  very  nearly 
an  air-line  by  accepting  "moderate"  grades  of  40  to  80  ft.  per 
mile.     As  a  consequence,  many  important  lines  have  little  or  no 
assurance  that  crossings  may  not  be  demanded  of  them  sooner 
or  later  on  any  single  mile  of  their  track,  and  it  becomes  of  great 
importance  to  determine  how  strenuously  they  should    oppose 
^uch    crossings,   what   expense   they  may   and    should   incur  to 
avoid  them,  and  what  can  be  done  to  reduce  their  disadvantages 
to  a  minimum  when  unavoidable. 

The  problem  has  been  greatly  simplified  in  recent  years  by 
the  fact  that  the  disadvantages  of  grade-crossings  may  be  largely 
•diminished,  and  sometimes  almost  destroyed,  by  the  use  of  inter- 
locking apparatus,  as  we  have  seen  in  par.  1086  and  elsewhere; 
but  while  there  were  in  1885  some  60  railways  in  the  United 
States  using  interlocking  more  or  less,  the  total  amount  in  use 
was  considerably  less  than  on  the  London  &  Northwestern 
alone. 

1099.  There  are  18  different  sizes  of  standard  signal-cabins  on  the  London 
-&  Northwestern  Railway,  which  are  : 

A.  5    levers,    6    X    6  ft.  D.  20  levers,  16  ft.  i\  in.  X  12  ft. 

B.  10       **  9    X    9  ft.  (and  so  on  to—) 

C.  15       "        i3i  X  12  ft.  T.   180  levers,  96  ft.  6  in.  X  12  ft. 

The  usual  rule  being  that  the  cabins  are  all  12  ft.  wide  and  are  6  in.  long  per 
iever,  plus  about  6^  ft.     There  are  1344  of  these  cabins  on  1753  miles  of  road. 


8lO     CHAP,  XXV,— GRADE-CROSSINGS  AND  INTERLOCKING. 


containing  26,500  levers.  The  annual  average  cost  for  maintenance  is  $187,000,. 
which,  divided  by  the  number  of  levers  in  use  on  the  line,  comes  to  $7.07  per 
lever.  This  amount  includes  not  only  the  renewal  and  repairs  of  the  lockingf^ 
apparatus,  but  that  of  the  signal-cabins,  signals,  and  all  subsidiary  apparatus, 
and  also  the  cost  of  providing  any  new  and  additional  apparatus,  when  under 
$50.  The  amount  of  work  to  be  maintained  has  increased  80  per  cent  since 
the  year  1874,  while  the  cost  of  maintenance  has  only  increased  5^  per  cent. 

In  the  whole  United  States  there  are,  of  all  systems  (1885),  somewhat  less 
than  250  cabins  and  3000  levers,  or  but  about  one  fifth  as  many  cabins  and 
about  one  ninth  as  many  levers  as  are  in  use  on  the  London  &  Northwestern 
alone. 

1100.  In  England  there  are  practically  no  grade-crossings- 
of  railways,  and  this  apparatus  is  used  chiefly  for  yards  and 
junctions.  In  America  there  are  a  great  many  grade-crossings^ 
even  on  important  lines;  but  the  clumsy  and  costly  precaution, 
of  a  full  stop  of  every  train  at  every  crossing  is  still  the  rule,  al- 
though it  can  hardly  be  that  such  an  absurd  relic  of  barbarism- 
will  linger  much  longer,  now  that  there  is. a  considerable  and 
increasing  number  of  grade-crossings  operated  without  a  stop* 
by  the  aid  of  interlocking  apparatus,  and  always  with  perfect 
safety  and  success. 

1101.  In  part,  the  slow  progress  in  this  matter  is  easily  ex- 
plained.  The  great  loss  and  delay  from  grade-crossing  stops- 
goes  on  quietly  and  silently,  sapping  the  life-blood  of  the  com- 
pany, as  do  the  consequences  of  bad  location  (page  2),  without 
interfering  much  with  the  routine  of  operation,  and  at  points- 
removed  from  the  managing  officers'  immediate  observation, 
whereas  the  difficulties  at  yards  obtrude  themselves  on  .atten- 
tion, and  many  of  tlie  most  crowded  yards  have  passed  the  limit 
of  their  capacity  without  some  such  mechanical  aid. 

1102.  Nevertheless,  from  an  economical  point  of  view,  abol- 
ishing the  stop  at  grade-crossings  is  by  far  the  most  important,, 
especially  when,  as  is  so  frequently  the  case,  they  reduce  the  num- 
ber of  cars  hauled  below  what  it  otherwise  would  be.  To  reach* 
this  conclusion  we  need  not  adopt  any  of  the  wild  estimates 
which  give  the  cost  of  a  stop  at  anywhere  from  a  dollar  up. 
Without  going  elaborately  into  the  details  of  the  estimate,  to- 
discuss  which  properly  by  items  would  take  considerable  space,. 


CHAP,  XXV.— GRADE-CROSSINGS  AND  INTERLOCKING,     8ir 

^rom  30  to  60  cents  may  fairly  be  taken  as  the  cost  of  a  stop 
apart  from  all  effect  on  length  of  trains.  An  estimate  of  40  cts' 
per  stop  for  average  trains  on  lines  doing  considerable  through 
busmesscan  hardly  be  considered  excessive,  and  at  this  rate  the 
cost  per  year  of  each  train  per  day  stopping  at  the  crossings  is 
365  X  40  =  $146  per  year.  If  therefore  there  is  an  average  of 
ten  trains  per  day  each  way  for  each  of  the  roads  which  cross 
(and  the  average  at  grade-crossings  would  probably  be  more 
rather  than  less  than  this),  we  have  $146  X  10  X  2  X  2  =  $5840- 
as  the  annual  loss  to  both  roads  from  the  fact  of  the  existence  of 
this  crossing. 

1103.  The  cost  of  saving  this  loss  by  constructing  a  new  line 
or  by  interlocking,  will  vary  more  or  less  with  the  locality  and 
in  less  degree  with  the  system  of  interlocking  adopted  •  but  the 
variation  in  the  latter  respect  is  not  important,  and  the  outside 
limit  for  a  complete  system  of  interlocking  switches  and  signals 
for   either   single   or   double    track    (it    makes    little  difference 
which),  by  one  system  of  approved  excellence  may  be  stated  to^ 
be  from  $2500  to  $4000,  averaging  $3000.     This  includes  ei^ht 
signals  (four -home"  or  near  signals,  and  four  distant  signals 
two  for  each  track),  four  derailing  switches,  one  for  each  track' 
which  throw  the  train  off  onto  a  graded  road-bed  (having  no 
rails  and  ties  for  only  a  short  way),  if  the  signal  be  carelessly  run 
by,  and  (for  a  separate  sum  of  $400),  electric  locking  apparatus 
which  renders  it  impossible  to  change  the  signals  after  a  train, 
has  once  passed  the  first  distant  signal  until  it  is  over  the  cross- 
ing.     The  cost  of  the  building  and  of  erection  is    included    in 
the  above. 

One  man  only  is  required  to  attend  to  the  signals  as  is  re- 
quired without  interlocking,  and  his  wages  need  be  little  if  any 
higher,  so  that  this  item  may  be  considered  unaffected. 

1104.  Even  with  the  lightest  ordinary  traffic,  therefore  the 
lowest  reasonable  estimated  cost  of  stop,  and  the  highest  prob- 
able rate  of  interest,  the  sum  saved  annually  is  far  more  than 
enough  to  cozier  the  additional  expense  of  thoroughly  protecting  a  grade- 
crossing  so  that  no  stop  need  be   made,   without  considering   the 


Si« 


^12     CHAP.  XXV  —GRADE-CROSSINGS  AND  INTERLOCKING. 

greater  safety  and  convenience.  At  more  important  crossings 
it  would  be  hard  to  find  a  clearer  case  of  an  expedient  improve- 
ment, even  if  the  stops  do  not  cut  down  the  length  of  train. 

1105.  If  the  length  of  train  is  cut  down,  so  as  to  take,  say, 
21  instead  of  20  trains  per  day  to  handle  the  traffic,  the  very 
lowest  cost  for  which  the  extra  train  can  be  run  is  (Table  176) 
35  to  40  cents  per  train- mile  (for  an  average  cost  of  70  to  80 
cents),  or  say  $38  for  a  trip  of  100  miles,  amounting  to  $13,870  per 
annum,  or  $693.50  for  each  of  the  20  trains,  or  $1.90  per  stop  (if 
only  one  stop  causes  the  decrease  of  train-load)  in  addition  to 
THE  DIRECT  COST  of  the  Stop.  In  such  cases,  of  which  there  are 
many,  it  is  culpable  folly  to  delay  availing  one's  self  of  so  cheap 
and  easy  a  remedy  for  such  losses  as  interlocking  affords,  if  the 
<:onditions  are  not  favorable  for  the  still  better  and  in  the  end 
often  cheaper  remedy,  an  over-  or  under-crossing. 

1106.  A  fact  which  explains  rather  than  excuses  the  prevail- 
ing negligence  in  this  matter  is  this, — that  the  protection  of 
grade-crossings  requires  the  joint  action  of  two  roads,  usually 
under  different  and  often  under  antagonistic  management,  and 
it  requires  no  little  negotiation,  and  a  conciliatory  spirit  on  both 
sides,  to  arrange  the  details  of  the  distribution  of  tiie  expense. 

It  can  hardly  be  doubted  that  this  difficulty  is  a  serious  one, 
and  it  is  largely  the  fault  of  the  laws  which  authorize  the  use  of 
interlocking  as  a  substitute  for  stops.  By  some  singular  over- 
sight, all  these  laws  as  yet  passed  (1886)  authorize  roads  to 
"agree"  on  putting  in  interlocking,  but  do  not  provide  a  way  by 
which  one  road,  anxious  to  act  under  the  law,  can  compel  an- 
other road  to  accept  a  reasonable  settlement  by  arbitration  or 
otherwise,  unless  it  chooses  to. 

1107.  The  provisions  of  the  State  laws  as  to  dispensing  with  crossing  stops 
may  be  briefly  summarized  as  follows  : 

The  Massachusetts  law  passed  in  1882.  after  somewhat  urgent  recommen 
dations  by  its  Commission,  which  were  at  the  time  regarded  by  many  as  some- 
what heretical  (because  the  public  knowledge  of  interlocking  was  much  less  then 
than  it  is  now,  even  among  railroad  men),  provides  that  "The  approval  of  the 
Board  shall  be  required  for  a  system  of  signals  to  be  established  and  maim 
stained  in  concert"  by  railroads  which  cross  each  other,  but  that  a  full  stop  shall 


CHAP.  XXV.— GRADE-CROSSINGS  AND   INTERLOCKING.     813 

not  be  dispensed  with  "  unless  a  system  of  interlocking  or  of  automatic  signals 
approved  m  writing  by  the  Board,  is  adopted  by  both  corporations." 

Ohio,  at  almost  the  same  time,  provided  by  law  that  "any  works  or  fix- 
tures" approved  by  the  Commissioner  of  Railroads  and  Telegraphs  as  render- 
ing it  safe  to  dispense  with  stops,  plans  having  been  filed  with  him  shall 
dispense  with  the  necessity  of  a  stop;  and  if  the  Commissioner  shall  fail  to 
approve  the  plan  within  twenty  days,  -such  companies'  may  apply  to  the  Court 
of  Common  Pleas,  where  appropriate  action  will  be  held.  This  enactment 
seems  to  require  not  only  that  both  companies  shall  consent  passively  but 
that  they  shall  unite  in  active  legal  proceedings  to  avert  a  decision  which  might 
be  not  unwelcome  to  one  of  them. 

Michigan  (1883)  passed  first  a  very  absurd  enactment  that  "authority  is- 
hereby  given  to  said  Commissioner,  and  it  shall  be  his  duty,  if  he  shall  deem  it 
practicable,  to  prescribe  the  use  of  the  interlocking  switch  and  signal  svstem 
provided  that  at  crossings  where  all  trains  come  to  a  full  stop  no  other  system, 
than  that  requiring  such  stop  shall  be  prescribed." 

The  absurdity  of  thus  cutting  oflf  one  of  the  chief  advantages  of  interlocking 
signals  struck  the  Legislature  almost  immediately,  however,  and  another  act  of 
the  same  session  provided  that  "whenever  there  shall  be  adopted  and  used  at 
any  such  crossing  an  interlocking  switch  and  signal  svstem.  or  other  device  " 
wh.ch  the  Commissioner  thinks  makes  it  safe  to  dispense  with  a  stop,  he  may 
authorize  it  in  writing,  with  any  regulations  as  to  speed  or  other  matters  which, 
ne  deems  necessary,  and  with  power  to  revoke  his  action 

In  the  strict  letter  of  these  laws,  the  Commissioner  may  prescribe  automatic 
signals  without  dispensing  with  a  stop,  but  can  only  authorize  the  stop  after  the 
apparatus  is  adopted  and  in  use.  Neither  is  he-what  is  a  more  serious  matter 
-given  any  specific  power  to  say  what  part  of  the  expense  each  of  the  twc 
companies  concerned  shall  bear.  These  provisions  come  the  nearest,  however, 
of  those  o  any  State  to  providing  means  by  which  one  railwav  which  is  anxious 
to  escape  from  the  burden  of  stopping  at  a  crossing  can  compel  the  other  bene- 
ficiary to  bear  its  fair  share  of  the  cost. 

The  Indiana  law  (1883)  is  merely  permissive,  authorizing  the  Auditor  of 
State  to  approve  interlocking  or  automatic  signals  at  crossings,  from  plans 
submitted  by  -two  or  more  railroads."  which  have  erected  or  are  about  to  erect 
them  and  thereafter  to  authorize  the  omission  of  stops.  It  is  specifically  pro- 
vided that  such  signals  shall  not  be  "  used  or  put  in"  at  any  crossing  "  to  the 
detriment  of  any  other  railroad  company,"  unless  with  the  consent  of  that  com- 
pany ,n  writing^  Under  this  provision,  the  manager  who  wishes  to  dispense 
^v.th  twenty  different  crossings  must  first  undertake  the  interesting  task  of 
persuading  twenty  different  companies  that  it  will  not  be  "  to  their  detriment" 
to  do  so. 

The  New  York  law  (1884)  provides  that  the  requirement  of  a  full  stop  may 
be  dispensed  with  whenever  the  Board  of  Commissioners  "decide  it  to  be- 


I  ■ 


S14     C//AF.  XXV.— GRADE-CROSSINGS  AND  INTERLOCKING. 

impracticable"  or  where  "interlocking  switch  and  signal  apparatus  is  adopted 
and  put  in  use  by  the  railroads  there  crossing  each  other  at  a  level,"  of  a  form 
approved  by  the  Board. 

Illinois  passed  through  one  house  in  1S86  an  act  essentially  similar  to  that 
of  New  York,  which  was  expected  to  become  a  law  at  the  following  session. 

1108i  It  is  easy  to  see  how,  under  any  of  these  laws,  a  manager  attempting 
in  good  faith  to  benefit  his  company  and  benefit  the  roads  crossing  and  the 
public  as  well,  by  perfectly  fair  and  equitable  arrangements  for  dispensing  with 
slops  at  crossings,  might  find  it  an  irritating  and  almost  hopeless  task,  and 
might  feel  compelled  to  give  it  all  up  in  disgust  before  he  had  fairly  begun. 

The  difficulty  of  agreement  is  precisely  the  same  as  would  exist  in  cities  as 
respects  party-walls,  without  the  law  which  authorizes  any  man  to  build  half  his 
wall  on  his  neighbor's  land  and  compel  his  neighbor  to  pay  for  it  when  he  uses 
it.  The  equities,  and  the  great  advantage  to  both  sides,  are  here  exceedingly 
<lear,  yet  how  often  would  it  be  impossible  to  arrange  the  matter  if  it  could 
only  be  done  by  mutual  consent  and  agreement  in  each  case? 

The  case  is  worse  with  crossings  because  they  are  very  frequently  so 
situated  that  the  joint  consent  of  three  or  four  lines  is  necessary  for  any  action, 
and  in  still  more  instances  a  great  part  of  the  advantage  to  be  realized  from 
dispensing  with  any  one  crossing  can  only  be  obtained  by  dispensing  with  a 
series  of  perhaps  a  dozen. 

1109t  To  require  that  grade-crossings  should  never  be  per- 
mitted would  unquestionably  be  going  too  far,  especially  now 
that  interlocking  apparatus  has  been  invented  and  perfected;  but 
the  unrestricted  freedom  with  which,  in  most  of  the  States,  grade- 
crossings  can  be  forced  over  any  line  at  almost  any  point,  regard- 
less of  the  injury  inflicted,  is  an  unfortunate  and  shameful  state 
of  things,  which  pressingly  requires  correction,  and  which  per- 
haps might  readily  be  corrected  if  the  older  and  more  important 
railways  would  make  a  united  effort  to  secure  reasonable  and 
proper  restrictions.  Unfortunately  they  overreach  themselves  by 
asking  far  too  much. 

1110.  The  theory  of  the  present  laws  is  a  very  simple  one ; 
something  like  this  : 

1.  "  Railways  are  a  supreme  public  necessity,  and  no  private 
interest  or  ownership  shall  be  allowed  to  stand  in  the  way  of 
their  cheap  and  easy  construction. 

2.  *'  When  two  railways  want  the  same  spot  of  ground  they 
shall  occupy  it  in  common." 


CHAP.  XXV.—GRADE-CROSSINGS  AND  INTERLOCKING.     815 

Unfortunately,  like  most  short  and  easy  cuts  to  justice,  it  is 
unequal  and  unfair  in  practice. 

The  theory  of  the  great  existing  railways  is  equally  simple, 
^nd  would,  if  it  were  allowed  to  prevail  in  practice,  be  equally 
unfair : 

1.  "Our  railway  is  a  much  greater  public  benefit  than  these 
other  new  projects,  and  we  have  bought  and  paid  for  our  prop- 
erty. 

2.  "If  they  want  to  pass  over  our  property  they  must  keep 
out  of  our  way." 

1111.  This  preposterous  attitude— from  corporations  whose 
very  existence  was  made  possible  only  by  the  exercise  of  the 
supreme  power  of  the  State,  and  whose  very  nature  is  to  per- 
form one  of  the  duties  of  the  State  to  the  public— is  all  but 
universally  assumed  by  established  corporations  in  discussions 
of  crossing  cases ;  except  in  those  cases  when  they  wish  to  build 
branches  or  sidings  over  a  rival's  road.  They  are  very  quick  to 
point  out  that  some  new  line  can  build  an  over- crossing  for  less 
money  than  they  lose  by  a  grade-crossing,  but  they  rarely  offer 
to  pay  a  reasonable  proportion  of  the  extra  cost  of  the  course 
they  desire.  Even  when  they  do  so,  there  being  no  recognized 
tribunal  to  decide  the  matter,  they  will  higgle  and  chaffer  over 
the  amount  to  be  paid  till  the  whole  negotiation  goes  for  naught. 

1112.  The  solution  of  the  whole  matter  seems  comparatively 
simple.  The  law  very  properly  takes  the  position  that  mere 
priority  of  construction  shall  be  allowed  little  or  no  weight.  AH 
railways  alike  are  supposed  to  be  of  pressing  necessity  to  a  cer- 
tain number  of  people— many  or  few,  as  the  case  may  be;  and 
the  necessities  of  even  a  very  few  are  given  greater  weight' than 
a  loss  and  inconvenience  which  is  comparatively  trifling  to  each 
individual  affected,  and  can  only  become  very  large  when  dis- 
tributed among  a  large  number  of  people.  This  is  right  and 
proper  as  far  as  it  goes,  but  the  law  should  also  take  this  further 
precaution  :  without  paying  any  attention  to  the  vested  interests 
<:oncerned,  as  such,  it  should  endeavor  to  enforce  that  course 
which  is  for  the  best  interest  of  the  community  as  a  whole,  and  which 


8l6     CHAP.  XXV.—GRADE.CROSSINGS  AND  INTERLOCKING. 


involves  the  least  aggregate  waste  of  human  labor  and  property; 
and  it  should  endeavor  to  distribute  the  cost  of  so  doing  as. 
nearly  as  may  be  in  proportion  to  benefits  derived,  and  in  such 
manner  that' each  party  shall  be  benefited,  by  taking  what  is 
abstractly  the  proper  course.  All  this  might  be  obtained  by 
something  like  the  following  simple  provisions  : 

1113.  I.  Every  railway  hereafter  attempting  to  cross  another 
at  grade  shall  be  obliged  to  erect  and  pay  for  a  system  of  inter- 
locking  signals,  to  be  thereafter  maintained  at  the  joint  expense 
of  the  two  roads,  unless  it  shall  appear  that  less  than  twenty 
trains  per  day  pass  the  crossing. 

2.  Any  railway  may  at  any  time  erect  interlocking  apparatus 
at  any  grade-cros'sing,  and  half  the  cost  of  erection  and  subse- 
quent maintenance  shall  be  chargeable  to  the  other  party  con- 
cerned, with  certain  provisions  for  exceptional  cases  ;  and  also 

provided — 

3.  Either  party  wishing  to  avoid  a  grade  crossing  should  be 
at  liberty  to  locate  an  over-  or  under-crossing  on  unobjectionable 
gradients,  and  to  demand  the  appointment  of  arbitrators  in  the 
usual  manner.  It  should  be  the  duty  of  these  arbitrators, /rj/,  to 
determine  that  the  grades  and  alignment  of  the  new  line  are  of  a 
suitable  and  appropriate  cliaracter,  or  to  make  them  such; 
secondly,  to  determine  the  excess  in  cost,  if  any,  of  the  over-cross- 
ing over  the  grade-crossing;  and,  thirdly,  to  assess  this  difference 
in  cost  upon  the  two  lines  in  proportion  to  the  benefit  to  each  of 
avoiding  a  grade-crossing. 

1114.  These  three  provisions  seem  calculated  to  accomplish 
what  every  good  law  ought  to  accomplish.  They  would  make 
it  for  the  interest  of  both  parties  to  take  that  course  which  would 
be  best  for  their  joint  interest,  if  they  were  one  corporation.. 
Thus,  supposing  a  new  road  which  will  run  say  five  trains  a  day 
wishes  to  cross  a  trunk  line  running  50  trains  a  day.  The  actual 
loss  to  the  community  of  a  grade-crossing  at  such  a  place  is  the 
cost  of  stopping  55  trains  a  day,  and  no  one  has  a  right  to  en- 
force such  a  loss  upon  others  to  save  an  investment  of  a  few 
thousand  dollars.     On  the  other  hand,  if  the  new  project  wanted 


CHAP.  XXV.— GRADE-CROSSINGS  AND  INTERLOCKING,     817 

to  cross  another  minor  line  like  itself,  running,  say,  five  ti^ain^ 
day,  neither  road  would  be  likely  to  move  for  an  over-crossing 
nor  perhaps  even  for  interlocking  signals;  nor  is  it  for  the  interest 
of  the  community,  considered  as  a  whole,  that  they  should  do  so 
It  IS  not  true  at  all  that  every  element  of  danger  must  be  wholly 
eliminated  before  any  saving  of  expense,  however  great,  is  per- 
m.ssible,  but  that  methods  which  are  at  once  more  dangerous 
and  more  costly  should  have  continued  in  such  wide  and  all  but 
universal  use  so  long  will  seem  in  later  years  a  strange  comment 
on  our  civilization. 
52 


'W 


I 


8i8 


CHAP.  XXVL-TERMINALS. 


CHAPTER  XXVI. 

,    TERMINALS. 

1115.  Terminal  facilities,  or  the  lack  of  them,  have  so  many 
times  been  a  leading  factor  in  the  success  or  failure  of  railways, 
and  are  in  all  cases  so  important  a  factor,  that  it  seems  desirable 
to  show  more  fully  than  has  been  yet  done  how  great  a  part  they 
are  of  the  investment  in  and  the  expenses  of  prosperous  lines, 
and  hence  how  dangerous  it  is  for  a  new  line  to  neglect  ample 
provisions  for  them.  This  perhaps  can  be  best  accomplished  in 
a  small  space  by  presenting  some  details  as  to  the  terminal  facil- 
ities at  a  few  great  traffic  points. 

1116.  Table  202  gives  an  unofficial  approximate  estimate,  com- 
piled by  Gratz  Mordecai,  C.E.,  of  the  actual  capital  represented 
in  the  terminal  work  of  moving  and  handling  freight  by  the 
trunk-line  railroads  at  the  port  of  New  York.  It  includes  the 
work  of  handling  coal  on  the  Delaware,  Lackawanna  &  Western 
Railroad,  but  on  no  other,  and  only  includes  a  small  part  of  the 
expenses  of  handling  and  lighterage  of  grain,  oil,  and  live-stock, 
and  none  of  the  expenses  of  clerical  work  and  management  on 
any  of  the  roads.     It  may  be  summarized  thus  : 

Estimated  Cost  of  New  York  Terminal  Facilities. 

Capital      Cost         P  C. 

sum,         per  of 

millions,      year.       totaL 

200  miles  track f  ^'°'^  'n       ""'^        ""'^ 

378  acres  yards       ., |  52.ooo  200 

2.2  millions  sq.  ft.  piers ^  i^o  2.2 

2.0  millions  sq.  ft.  floor  area @  o.bo  i.b 

0.89  millions  sq.  ft.  N.  Y.  city  stations @  6.00  54 

6q  yard  engines  (cost) ®  0,700 

4!  tellers  (cost, |  =5-^  ■■ 

230  lighters  (cost) V©  Q.ooo       ^-^ 

Total  investment  charges ;•  35©       2.1         385 

A  700  emDlov6s     (^  $2  per  day  47  o       2  82       5»  <> 

Jso^onTcoafperiay @l^.  J^      ^^      ^ 

Total 9i.o      546     loao 


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CI/AP.  XXVI.-TERMINALS. 


The  only  direct  return  received  from  tlie  merchants  by  these 
railways  for  tliis  work,  tlie  plant  of  which  represents  an  aggre- 
gate capital  of  at  least  $35,ooo>o°0'  and  the  power  and  force  em- 
ployed  an   annual  expenditure  of  at  least  $3.5oo>ooo,  are  the 
charges  collected  for  long-distance  lighterage.     There  is,  how- 
ever, a  considerable  fixed  terminal  charge  of  five  cents  per  cwt., 
more  or  less,  which  is  credited  to  the  terminal  road  before  the 
division  of  rates  is  made  according  to  distance  (par.  210),  so  that 
the  roads  terminating  at  New  York  are,  perhaps,  less  burdened 
than  the  average  by  the  terminal  expenses.    Assuming  6  percent 
interest,  this  estimate  shows  a  total  annual  expense  of  $5,500,000, 
and  taking  into  account  clerk  hire,  management,  repairs,  taxes, 
light,  stationerv,  insurance,  and  all  other  expenses,  the  total  is 
probLbly  not  far  from  $10,000,000,  or  an  average  burden  on  each 
road  of  $2,000,000  every  year. 

1117.  If  we  include  the  terminal  expenses  paid  by  the  indi- 
vidual shippers,  as  well  as  by  the  railways,  the  above  totals,  large 
as  they  are,  sink  into  insignificance.  It  was  estimated  in  1875 
by  a  committee  of  the  American  Society  of  Civil  Engineers  that 
on  some  4,632,000  tons  of  the  freight  delivered  at  New  York  the 
total  terminal  expenses  were  $3.07  per  ton,  or  about  three  fifths 
of  the  then  rate  (25  cts.  per  100  lbs.)  from  Chicago  to  New  York. 
The  total  receipts  at  New  York  in  that  year  were  about  15,000,000 
tons  of  all  kinds  of  freight,  and  on  half  of  this  the  cartage  charge 
alone  was  estimated  at  $1.60  per  ton. 

Inasmuch  as  so  much  more  for  cartage  means  so  much  less- 
available  for  freight   rates,  and  vice  versa,  on  a  large  proportion 
of  the  freight,  and  more  or  less  so  on  all  of  it  (par.  47),  we  have 
in  these  figures  some  indication  of  how  serious  a  deduction  the 
total   terminal  expenses  must  make  from  the  amount  available 
for  railroad   transportation  proper,  and  how  important  it  is  to 
have  terminal  facilities  of  the  best.     New  York,  however,  is  a 
true  terminal,  in  the  strict  sense  of  the  word.     Some  of  the  ter- 
minal points,  which  are  really  only  yards  of  interchange,  are  of 
even   greater  magnitude,  if   not   cost.     Lest  the  great  error  be 
fallen  into  of  assuming  that  the  terminal  facilities  at  New  York 
are  as  much  greater  than  those  at  other  cities,  as  New  York  is 


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CHAP.  XXVI.— TERMINALS. 


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822  CHAP.  XXVI.— TERMINALS. 

greater  in  population,  some  notes  may  be  added  as  to  what  is 
really  only  the  largest  of  many  examples  of  interior  yards — those 
at  Buffalo,  N.  Y.  So  far  from  there  being  anything  exceptional 
in  the  New  York  terminals,  they  are  probably  smaller  in  extent 
and  cost  per  head  of  population  than  at  most  important  termi- 
nals, and  vastly  smaller  than  at  a  number  of  them. 

1118,  The  statistics  presented  in  Table  203  of  the  yards  in  Buf- 
falo leave  no  reasonable  doubt  that,  of  its  kind,  it  is  the   greatest 
in  the  world.     How  much  of  this  abnormal   magnitude   is  the 
healthy  and  natural  result  of  peculiar  traffic  conditions,  and  how 
much  of  it  is  mere  fungous  growth  from  diseases  of  management 
whose  existence  is  universally  felt,  it  would  be  useless  to  inquire 
here,  because  as  things  are  it  is  all  necessary,  and  there  is  no  im- 
mediate evidence  of  any  probable  change.     The  headings  to  Ta- 
ble 203,  in  which  fourteen  different  kinds  of  side  tracks  are  spe- 
cified, will  at  once  explain  in  part  why  so  much  of  some  of  them 
is  necessary.     In  the  aggregate  there  is  a  total  of  some  300  miles 
of  side  track  within  an  area  of  some  eight  square  miles  (about  i^ 
by  si  miles,  5.63  square  miles  being  actually  owned  by  the  rail- 
ways within  the  city  limits),  which  it  is  expected  to  increase  im 
the  near  future  to  some  450  to  500  miles,  mostly  by  accessions  to* 
the  trackage  of  the  newer  lines  entering  Buffalo,  and  required  by 
them — as  will  be  seen  by  the  detailed  table — to  afford  to  them  no- 
greater  facilities  than  the  older  lines  already  enjoy.     The  lease 
of  the  West  Shore  to  the  New  York  Central  saved,  it  is  estimated 
(somewhat   liberally,   it  would   appear),  the  construction  of  as 
much  as  50  miles  of  track  which  would  otherwise  have  been  ne- 
cessary, but,  barring  that,  there  is — 

, M  iles. , 

Single  track. 

Tracks  of  all  kinds  in  city  limits  of  Buffalo  or  immediately  ad- 
jacent thereto 436.  i 

And  to  be  laid  by  the  new  roads  (chiefly)  now  imperfectly  sup- 
plied    176.0       612.I 

Of  this  there  is  main  track,  including  three  double-track  lines 
swinging  around  the  city  to  a  connection  with  the  Interna- 
tional Bridge 155- 1 

And  projected  (minor  extensions) 5-7       100^ 

Leaving  as  side  track 45iS 


CHAP.  XXVI.— TERMINALS.  823 

Of  the  main  track  a  considerable  portion  is  only  nominally  main 
track,  but  really  more  in  the  nature  of  track  for  yard  use 
only,  which  may  be  estimated  as  at  least 50.0         50.0 

T         •  V  •  ,         .  (Main.)  (Side.) 

Leavmg  as  the  true  proportions  of  mam  track  and  side  track  ac- 

tual  and  projected.         uo.S  501.3 

Of  which  there  was  laid,  October,  1884 100.3  326.8 

An  d  projected,  a  considerable  fraction  of  which  has  since  been 

constructed j  5  174  e 

1119.  If  we  compare  this  with  the  figures  for  the  yards  of  New 
York  City,  as  given  in  Table  202,  we  shall  have  a  better  idea 
of  the  magnitude  of  the  Buffalo  yards.  The  total  miles  of  track, 
main  line  and  sidings,  at  the  two  points  compare  as  follows  : 

New  York    Buffalo 
New  York  Central 28  ^sV 

P't •••      49  116 

Lackawanna 50  b*? 

West  Shore  (and  Ont.  &  West.) *...*!'..*.*      34  23 

Pennsylvania og 

Other  roads 'm\ 

Total 200  436 

It  will  be  seen  that,  with  all  the  immense  traffic  of  New  York, 
there  is  less  than  half  as  much  track  at  New  York  as  at  Buffalo. 
In  the  yards  of  Boston  there  are  150  miles  of  side  track,  on  568 
acres,  with  26  acres  of  buildings;  the  total  side  track  on  all  the 
nine  roads  centring  there  being  765  miles  for  a  total  of  814  miles 
of  main  line. 

1120.  The  New  York  tracks  are  also  different  from  those  at 
Buffalo  in  not  being  all  bunched  together,  so  as  to  be  in  fact,  if 
not  in  form,  one  vast  yard,  whose  different  parts  are  constantly 
interchanging  business  with  each  other.  The  New  York  yards 
are  miles  apart  from  each  other,  and  have  comparatively  the 
most  insignificant  interchange  relations.  Most  of  them,  in  fact, 
could  be  most  fairly  compared  with  the  thirteenth  class  of  Buffalo 
side  tracks,  those  for  "local  city  freight"  alone,  of  which  there 
are  in  Buffalo  2o|  miles,  with  as  much  more  projected  ;  for,  al- 
though there  is  a  very  large— in  fact  immense— coal,  steamer, 
and  stock-yard  traffic  at  New  York,  as  well  as  the  usual  shop 


824  CHAP.  XXVI.— TERMINALS. 

and  coaling  tracks,  yet  the  business  of  New  York  is  carried  on 
under  such  different  conditions  from  that  at  Buffalo  that  the 
same  traffic  requires,  as  is  apparent  from  the  figures,  several 
times  less  track  room.  For  example,  there  are  39  miles  of  shop 
and  coaling  track  at  Buffalo,  and  35  miles  more  projected,  of 
which  the  New  York  Central  and  the  Erie  have  each  some  13 
miles,  which  (without  being  able  to  present  the  exact  figures)  is 
undoubtedly  several  times  greater  than  the  same  roads  have  for 
the  same  purposes  at  New  York,  the  reason  being  that  sick  and 
wounded  cars  from  all  over  the  continent  tend  to  accumulate  at 
Buffalo,  while  they  are  kept  away  from  New  York  so  far  as  pos- 
sible. The  same  contrast  is  visible  in  the  16  miles  of  transfer 
tracks  at  Buffalo,  which  it  is  proposed  to  double  ;  and  the  enor- 
mous aggregate  of  87  miles  for  the  direct  use  of  trains  from  the 
East  and  West  and  Canada,  and  for  distributing  West-bound 
freight  (columns  3,  4,  5,  6,  7,  Table  203),  to  which  it  is  proposed 
to  add  over  40  miles  more,  mostly  by  the  newer  roads,  is  in 
itself  something  for  which  there  is  no  very  exact  parallel  in  New 
York,  either  in  quantity  or  quality,  although,  of  course,  the 
mileage  devoted  to  similar  uses  is  very  great. 

1121.  The  same  contrast  exists  to  an  even  larger  extent  in  the 
areas  of  land  occupied  in  the  two  cities,  which  compare  as  fol- 
lows : 

In  New  York,  land 378  acres. 

piers .     5     •' 

383  acres. 
In  Buffalo,  land 3,600  acres. 

Land  in  Buffalo  is,  of  course,  a  very  different  and  much 
cheaper  thing  than  land  in  New  York,  and  this  area,  moreover, 
includes  several  hundred  acres  of  what  is  more  properly  main- 
line right  of  way,  not  properly  chargeable  to  yards.  But  after 
making  all  allowances  in  this  respect,  the  immense  proportion- 
ate magnitude  of  the  Buffalo  yard,  due  to  the  nature  rather  than 
to  the  absolute  volume  of  the  business  transacted,  which  makes 
Buffalo  a  point  where  innumerable  side  tracks  naturally  accumu- 
late, is  clearly  indicated. 


CHAP.  XXVI.-.TERMINALS. 


825 


1122.  While  Buffalo  seems  to  be  far  ahead  of  any  other  one 
point  in  Its  yard  facilities  proper,  yet  that  it  is  only  the  leading 
example  of  a  general  tendency  may  be  indicated  by  the  figures 
given  in  Table  204  of  the  total  side-track  mileage  of  the  foads 
entering  there,  which  well  illustrate  the  immense  aggregates  o 
s.ce  track  which  even  ordinary  yard  demands   produ^.^T  ere 
seems  to  be  what  might  almost  be  called  a  rude  law,  that  trunk 
ines    proper    as   distinguished    from    roads  of   the  next  grade 
beow,  will  have  at  least  as  much   sidetrack  as  the   length  of 
then    main  line.     Thus,   the  Boston    &    Albany,  in    additfon   to 
•being  somewhat  more  than  double-tracked,  has  almost  exactly 
Xhis  amount  of  sidings,  viz.,  .03.2  miles  against  201.6  miles  of 
main  line.     Exceptions,  no  doubt,  exist;  but  Table  204  indicates 
that  the  assumed  ''  law"  has  at  least  some  foundation  in  fact. 

Table  204. 
Mileage  of  Sidings  in  the  Aggregate  and  at  Buffalo  and  New  York 
^^  '^"E  Leading  Lines  entering  Buffalo. 


Road. 


"New  York  Central. 
Lake  Shore 


Miles 
Main 
Line. 


•  Miles  op  Sidings. 


Total 

'^'^ 

Lackawanna 

B..  N.  Y.  &  P 

Rochester  &  Pittsb'jr. 

West  Shore 

N.  Y.,  C.  &St.  L.... 


442 
540 


Buffalo. 


982 
460 

413 
430 
213 
426 
512 


94.1 
9-3 


103.4 
77.2 
30.8* 
19.0* 

4  9* 
16.3* 

3.5* 


N.  Y. 


28.0 


Else- 
where. 


Total. 


418.9 
539-7 


490 
50.0 


34-0 


958.6 
430.8 
442.2 
129.0 
48.1 
91.7 

85.5 


541.0 
549 -o 


1,090.0 
557.0 
523.0 
148.0 
53.0 
142.0 
89.0 


Per  Cent 

of  all 
Sidings 

in 
Buflfalo. 

17.4 
16.9 


9.5 
13.9 


♦  These  roads  have  completed  less  than  one  half  of  their  pro^BC^^^^^^^^^, 

The  immense  aggregate  of  capital  expenditure  represented 
^y  these  aggregates  of  side  track,  and  the  still  larger  capital 
-um  represented  by  the  annual  expenditure  to  "operate''  tte 
^de  tracks,  are  plainly  factors  in  the  future  of  new  and  old  lines 
Which  can  never  be  safely  forgotten. 


1 

I 


If 


I 


826 


C/fAP.  XXVL— TERMINALS, 


1123.  It  is  estimated  that  fifteen  miles  alone  of  the  local 
tracks  at  Buffalo  have  cost,  or  would  cost  to  replace,  $350,000 
per  mile,  or  $5,250,000,  tliis  particular  fraction  of  the  local  track- 
age being,  as  is  often  necessary,  on  exceptionally  expensive  land, 
where  it  is  readily  salable  at  $300  to  $500  per  foot  front.  The 
railways  own  strips  varying  from  60  to  100  ft.  deep,  and  on  them 
are  laid  three  to  five  tracks,  giving  the  following  estimate  for  four 
miles  of  track : 

5280  ft.  of  land  at  $250  per  front  foot $1,320,000 

Planking,  60x5280  ft.  X3  in. =  1050  M.  ft.,  or  with  sub-sills 

1200  M.  ft.  at  18  cts 21,600 

Grading,  averaging  3  ft.  deep  at  25  cts.  per  cu.  yd   .  .  i i.75o 

4  miles  of  track  at  $6000 24,000 

Total $1,377,350 

Per  mile  of  track 344»34<^ 

Add   for  approaches   of  paved   streets,  paving  many  of  the 

tracks  themselves,  and  incidentals 5,66a 

Total  per  mile $350,000 

We  need  not  attempt  the  difficult  task  of  estimating  the  total 
exactly,  but  for  the  other  items  :  At  $10,000  per  mile  the  300 
miles  of  side  track,  more  or  less,  in  the  Buffalo  yards  represent 
$3,000,000.  At  $5000  per  acre  for  the  3600  acres  of  land  owned 
and  used  for  railway  purposes,  the  capital  investment  would  be 
$18,000,000.  The  shop  facilities  alone,  with  the  tracks  for  their 
use,  represent  $3,000,000.  Vast  as  these  sums  appear  and  are,  the 
interest  on  them  represents  but  a  small  part  of  the  addition  to 
the  cost  of  haulage  which  the  terminal  facilities  cause,  and  still 
less  is  the  bare  trackage  required  any  fair  criterion.  This  will 
be  clearly  indicated  by  referring  back  to  Table  202,  where  it 
will  be  seen  that  at  New  York  the  bare  cost  of  the  track,  esti- 
mated at  a  very  liberal  figure,  and  exclusive  of  land,  amounts  to 
but  2.2  per  cent  of  the  total  cost  of  yard  work,  and  that  this 
total  is  as  great  a  tax  upon  the  five  lines  concerned  as  if  they 
had  $91,000,000  invested,  say  in  three  thousand  miles  of  idle,  un- 
operated,  and  tolerably  costly  railroad,  at  $30,333  per  mile,  on 
which  they  had  to  pay  interest,  but  which  contributed  nothing 
to  revenue. 


CHAP.  XXVI.— TERMINALS. 


%2J 


1124.  Nothing  equal  to  this  in  degree  exists  in  Buffalo,  but 
the  analogous  tax  at  that  point  is  very  great  indeed,  and  is  in  ad- 
dition to  the  New  York  tax,  as  is  likewise  the  yard  tax  at  Chicago, 
and  all  other  intermediate  points.  Therefore,  vast  as  is  the  tax 
of  maintaining  within  the  city  limits  of  Buffalo  enough  track 
for  local  purposes  only  to  build  a  new  line  to  New  York,  that 
direct  expenditure  is  but  a  small  part  of  the  total  burden  repre- 
sented by  those  facilities,  even  if  a  many  times  larger  part  than 
at  New  York,  as  no  doubt  it  is. 

At  no  other  point  in  this  country,  not  even  at  Chicago,  do  so> 
many  conditions  combine  to  bring  about  such  abnormal  growth, 
and  the  same  is  still  more  true  of  even  the  largest  cities  of  the 
old  world.     Buffalo,  therefore,  although  outdone  by  many  other 
cities  as  a  traffic  point,  will  doubtless  continue  to  be  the  greatest 
yard,  properly  so  called,  in  the  world,  even  after  that  consider- 
able fraction  of  its  trackage,  which  is  with  reason  felt  to  be  due 
to  profligate  and  discreditable  imperfections  of  management,  has 
been  done  away  with.     But  its  interest  for  our  immediate  pur- 
pose  lies  in  the  fact  that,  large  as  it  is,  it  is  only  the  largest  out- 
growth of  universal  tendencies;  and  that  road  which  attempts  to 
compete  with  another  without  having  approximate  equality  in 
such  terminal  facilities,  competes  on  about  as  favorable  terms 
as  it  would   in  crossing  a  river  by  some  new  bridge  in  which 
every  span  but  the  last  had  been  built,  and  was  of  very  superior 
quality. 

Much  greater  sums  have  been  spent  in  Europe  than  here  in  building  stations 
in  the  trade  centres  of  cities  close  to  the  warehouses  and  wholesale  stores.  In 
Liverpool  (600,000  inhabitants),  the  London  «&  Northwestern  Railway  up  to 
1881  had  expended  $9,300,000  in  providing  freight  stations  alone.  In  London 
it  had  expended  $11,200,000.  Interest  at  the  rate  of  4  per  cent  on  the  cost  of 
these  stations,  less  rents  received  for  warehouses,  etc.,  amounted  at  Liverpool 
to  14.6  cents,  and  at  London  to  32  cents  per  ton  of  freight  handled.  Thus  the 
mere  payment  of  interest  on  the  terminal  facilities,  excluding  any  charge  for 
handling  the  freight,  would,  on  a  haul  from  Liverpool  to  London,  amount  to- 
46.6  cents  per  ton,  or  nearly  \  cent  per  ton-mile.  These  figures  do  not  include 
the  cost  of  collecting,  distributing,  and  sorting  sidings,  of  which  there  are  38^ 
miles  at  Edgehill  (Liverpool),  and  proportionate  lengths  at  other  places.     The 


f' 


828  CJ/AP.  XXVI.— TERMINALS. 

London  &  Northwestern  is  in  no  way  exceptional  in  this  respect  among  the 
great  English  railways. 

The  total  actual  average  cost  of  loading  and  unloading  freight  per  gross  ton, 
exclusive  of  interest,  was  given  as  under  for  the  year  1880,  at  the  following 
places  : 

London 70-i  cents. 

Manchester 4i-0 

Birmingham 34-0 

Liverpool 39  4 

This  total  cost  includes  everything  incidental  to  carrying  on  the  business  of 
the  station,  but  no  charge  for  risk,  breakage  and  pilferage,  or  for  cartage. 


PART  V. 


THE  CONDUCT  OF   LOCATION. 


r 


X 


"  O,  what  a  precious  book  the  one  would  be 
That  taught  observers  what  they're  net  to  see!" 

— O.  W,  Holmes:  A  Rhymed  Lesson, 
••  Some  things  can  be  done  as  well  as  others."— Sam  Patch. 


*ii 


*.^  i 


PART  V. 

THE  CONDUCT  OF  LOCATION. 


r 


CHAPTER   XXVII. 

THE    ART    OF    RECONNAISSANCE. 

1125.  An  art,  as  distinguished  from  a  science,  is  something  which, 
:although  it  m  part  can  be  taught,  yet  cannot  be  written  down  in  definite 
fixed  rules  which  have  only  to  be  followed  with  exactness.  A  science, 
correctly  so  called,  however  difficult  or  intricate  it  may  be,  is  always  m' 
its  nature  susceptible  of  rigorous  and  exact  analysis.  An  art  is  not. 
Thus  we  may  speak  with  strict  propriety  of  the  science  of  bridge-build- 
ing, but  only  of  the  art  of  reconnoitring. 

Nevertheless,  just  as  there  is  no  scientific  branch  of  the  practical  work 
of  life  so  purely  a  science  that  it  is  possible  to  dispense  with  a  certain  apti- 
tude and  tact  which  is  outside  of  and  beyond  written  rules,  so,  on  the 
other  hand,  even  in  what  is  so  purely  an  art  as  discerning  the  physical 
possibilities  of  a  given  region  by  the  aid  of  the  eye  alone,  certain  general 
rules  and  cautions  will  greatly  diminish  the  danger — which  often  rises  to 
certainty— that  without  such  aid  an  inexperienced  engineer  will  fail  to 
discern  the  possibilities  which  lie  right  before  him,  and  reach  wholly 
mistaken  conclusions  as  to  v»rhat  he  can  and  cannot  do  with  the  region 
brfore  his  eyes. 

1125.  For  there  is  nothing  against  which  a  locating  engineer  will  find 
it  necessary  to  be  more  constantly  on  his  guard  than  the  drawing  of  hasty 
and  unfounded  conclusions,  especially  of  an  unfavorable  character,  from 
apparent  evidence  wrongly  interpreted.  If  his  conclusions  on  reconnais- 
sance are  unduly  favorable,  there  is  no  great  harm  done— nothing  more 
at  the  worst  will  ensue  than  an  unnecessary  amount  of  surveying;  but 
a  hasty  conclusion  that  some  line  is  not  feasible,  or  that  further  improve- 


832         CHAP.  XXVII.— THE  ART  OF  RECONNAISSANCE. 


ments  in  it  cannot  be  made,  or  even  sometimes— often  very  absurdly — 
that  no  other  line  of  any  kind  exists  than  that  one  which  has  chanced  to 
be  discovered— these  are  errors  which  may  have  disastrous  consequences. 
On  this  account,  if  for  no  other,  the  locating  engineer  should  culti- 
vate and  habitually  preserve  what  may  be  called  an  optimistic  habit  of 
mind.  He  should  not  allow  himself  to  enter  upon  his  work  with  the 
feeling  that  any  country  is  seriously  difficult,  but  rather  that  the  problem 
before  him  is  simply  to  find  the  line,  which  undoubtedly  exists,  and  that 
he  can  only  fail  to  do  so  from  some  blindness  or  oversight  of  his  own,, 
which  it  will  be  his  business  to  guard  against. 

1127.  The  chances  are  greatly  in  favor  of  his  ultimately  finding  this 
assumption  to  be  correct.  Occasionally  he  may  be  deceived,  but  the 
young  and  inexperienced  engineer  cannot  proceed  on  a  safer  hypothesis 
than  this :  That  however  forbidding  the  region,  a  line  exists  which  is 
conspicuously  better  than  any  other,  and  which  will  in  all  cases  be  found 
to  be — in  comparison  with  what  was  expected — a  line  cheap  to  build  and 
economical  to  operate;  and  that,  on  the  other  hand,  the  line  which  he, 
as  an  inexperienced  man  and  acting  without  special  training  for  the 
work,  will  be  likely  to  first  select  as  the  best,  is  perhaps  twice  as  costly 
in  first  cost  and  considerably  less  favorable  in  gradients  and  operating 
value  than  that  which  he  can  secure  by  greater  care,  attention,  and 
study.  Although  this  may  seem  a  sweeping  generalization,  it  is  so  near 
a  general  average  of  probabilities  in  both  easy  and  difficult  country,  that 
in  a  rude  way  it  may  be  assumed  as  truth. 

1128.  For  the  reason  that  there  is  so  much  danger  of  radical  error  t'u 
the  selection  of  the  lines  to  be  sun>eyed  (or,  rather,  of  the  lines  not  to  be 
examined),  it  results  that  the  worst  errors  of  location  generally 
ORIGINATE  IN  THE  RECONNAISSANCE.  This  truth  once  grasped,  the 
greatest  of  all  dangers,  over-confidence  in  one's  own  infallibility,  is  re- 
moved. 

1129.  The  most  fundamentally  important  technical  qualification  for 
entering  upon  the  reconnaissance  is  an  understanding  of  the  economic 
questions  considered  in  the  first  parts  of  this  volume,  especially  as  to 
what  a  railway  should  be  from  a  business  point  of  view,  and  what  the 
relative  importance  is  of  engineering  (or  geometric)  and  commercial  ex- 
cellence ;  for  if  the  engineer  cannot  correctly  distinguish  between  the 
financially  important  and  unimportant,  as  well  as  between  the  practically 
feasible  and  the  practically  impossible,  he  will  be  almost  as  liable  to  go 
astray  as  if  he  were  physically  blind,  by  omitting  to  examine  as  worthless 
the  very  possibilities  which  he  should  look  into  most  carefully.     It  fol- 


CHAP.  XX VII. -THE  ART  OF  RECONNAISSANCE.        833 


lows  also  that  he  should  be  well  posted  as  to  the  relative  cost  and  diffi- 
culties  of  construction. 

1130.  These  qualifications  being  presupposed,  before  beginning  the 
reconnaissance,  as  well  as  during  it  and  after  it,  the  nature,  extent"  and 
probable  sources  of  the  traffic,  and  especially  of  wav  traffic,  should  be 
carefully  looked  mto.  as  a  consideration  which  will  "be  often— it  might 
almost  be  said  usually-so  important  as  to  fix  the  general  route  in  de- 
spite of  quite  important  engineering  disadvantages.  The  small  effect 
on  profit  and  loss  of  even  considerable  differences  of  distance,  and  the 
small  effect  on  distance  of  even  considerable  and  "ugly"  swerves  from  a 
straight  Ime.  may  well  be  especially  studied  up,  not  to  make  one  reck- 
less of  sacrificing  distance,  but  to  enable  one  to  sacrifice  it  and  save  it 
mtelligently. 

1131.  On  the  other  hand,  the  engineer  should  with  especial  care  dis- 
abuse his  mind  of  the  very  natural  feeling  that  what  mav  be  called  his 
own   particular  and  especial  department-getting  a  cheap  line  to  sub- 
grade-is  of  much  relative  importance  to  the  future  of  the  company    He 
should  remember  that  it  requires  a  continuous  cut  or  fill  of  about  7  feet 
or  say  an  average  maximum  cut  or  fill  of  10  to  12  feet,  with  its  ordinarv^ 
accompaniments  of  mason r>^  to  equal  the  cost  of  superstructure  readv 
for  operation ;    that  the  total  investment  for  rolling-stock,  machinery 
buildin-s.  and   miscellaneous   purposes   will,  on  a  line  of  active  traffic 
ve^ry  nearly  equal  that  for  road-bed  and  track  complete,  and  that,  finally' 
and  more  important  than  all.  the  interest  on  the  total  de-facto  invest- 
ment for  all  purposes  rarely  absorbs  more  than  from  one  sixth  to  one 
fourth  of  the  gross  revenue.     Broadly  speaking,  therefore,  we  may  say 
m  general  terms  that—  ^      ^ 

To  increase  gross  revenue  \  we  may  double  the  whole  investment 

•nr  "  cost  of  road-bed  and  track. 

^  "  "      grading  and  masonry. 

These  percentages,  of  course,  are  subject  to  important  fluctuations  but 

the  fact  still  remains  in  all  cases  that,  for  obvious  reasons,  the  tendency 

Of  an  engineer  is  to  concentrate  his  attention  unduly  on  the  work  below 

suD  grade. 

self?'"  ^^  n"'°''^  '"'■^"  qualification,  the  engineer  sl>ouId  prepare  him- 
nrl  ir""  'f 'u""'""'"  •"  ^°™  ■•«^^°"«''Iy  accurate  estimates  of  the 
probable  cost  of  the  work  per  mile  on  various  lines  and  grades  The 
feculty  of  making  tolerably  close  approximations  of  this  kind,  assisted 
t>y  the  eye  alone,  is  not  so  very  difficult  to  acquire,  but  can  only  be  gained 


«* 


834         CHAP.  XXVII.— THE  ART  OF  RECONNAISSANCE. 


CHAP.  XX VII.- THE  ART  OF  RECONNAISSANCE.        835 


isiii 


'!=* 


I 


by  careful  observation.  The  best^manner  of  obtaining  it  is  by  noting 
the  general  appearance  of  as  many  lines  as  possible,  either  before  or 
after  their  completion,  and  then  comparing  a  guess  based  on  this  appear- 
ance with  the  actual  cost  or  quantities.  Experienced  contractors  can 
guess  in  this  way  within  a  very  small  percentage  of  how  many  yards  per 
mile  a  given  piece  of  work  will  run.  The  engineer  should  by  previous 
practice  and  study  have  at  least  so  far  perfected  himself  in  this  art  as  to 
have  some  idea  as  to  his  "personal  equation"  or  probable  range  of  error. 

1133.  The  danger  with  most  young  and  inexperienced  engineers  in 
making  estimates  of  the  cost  of  work  is  decidedly  that  they  will  make 
too  small  estimates,  influenced  by  a  natural  hope  and  anxiety  to  show 
good  results.  But,  on  the  other  hand,  there  are  some  who,  especially  in 
preliminary  estimates,  go  to  the  other  extreme.  Just  as  it  is  the  mark 
of  an  untrained  engineer  to  make  estimates  too  low,  so  it  is  the  mark  of 
a  half-trained  man  to  persistently  make  estimates  too  high,  especially  on 
work  involving  difficult  or  doubtful  points,  which  it  may  be  in  question 
whether  to  attempt  at  all ;  a  practice  which  some  of  them  adhere  to 
through  life,  from  an  idea  that  they  are  being  thereby  more  prudent  and 
"  practical."  Each  error  is  equally  discreditable.  An  estimate  should 
lean  in  the  direction  of  excess,  but  a  moderate  error  in  either  direction  is 
a  pardonable  fault  (par.  21). 

1134.  To  these  qualifications  is  to  be  added— not  by  any  means  as 
least  important,  but  as  last  in  order  of  importance,  if  the  intended  dis- 
tinction can  be  grasped— what  is  generally  known  as  an  "eye  for  coun- 
try," the  nature  and  importance  of  which  has  already  been  considered  in 
par.  18.  Such  rules  and  cautions  for  acquiring  an  "eye  for  country"  as 
can  be  committed  to  paper  (which  are  not  a  few)  will  be  given  in  the  fol- 
lowing chapter.  The  fundamental  rule  is  to  have  an  abiding  conviction 
that  a  much  better  line  than  at  first  sight  appears  can  be  found  by  open- 
ing one's  eyes. 

1135.  Undertaking  a  reconnaissance  with  a  reasonable  measure  of 
these  qualifications,  it  will  require,  often,  nothing  more  than  careful  ob- 
servation and  one  or  two  trips  over  the  line  to  definitely  determine, 
once  for  all,  which  is  the  proper  general  route  to  adopt,  and  so  save  all 
necessity  for  running  any  duplicate  lines  whatever  except  for  short  alter- 
nate sections  of  2,  10,  20,  or  30  miles,  which  are  almost  always  necessary 
at  points,  and  which  may  be  called  matters  of  detail.  It  would  be  dan- 
gerous, perhaps,  to  state  that  it  is  a  general  rule  that  only  one  line  will 
need  actual  survey,  but  the  writer's  experience  is  that  this  is  far  more  often 
true  than  not,  and  that  it  is  true,  perhaps,  of  a  larger  proportion  of  heavy 


ines  than  of  Jight  Imes.  When  all  the  traffic  and  business  considera, 
tions,  as  well  as  engineering  difTerences.  have  been  dulv  considered  the 
writer  has  never  known  an  instance  where  there  seemed  the  slightest 
need  to  survey  more  than  two  general  routes,  althouoh  such  instances 
may  well  occur.  In  any  case  the  reconnaissance  should  be  conducted 
always  with  as  much  care  as  if  it  was  expected  to  make  by  its  means  a 
final  selection  of  route. 

In  conducting  the  reconnaissance,  while  individual  habits  of  mind  no 
doubt  differ  greatly,  and  with  them  the  direction  in  which  error  is  most 
to  be  feared,  the  following  rules  and  cautions  are  believed  to  be  of  uni- 
versal application,  the  first  one  especially  being  fundamental : 

1136.  I.  The  reconnaissance  must  not  be  of  a  line,  but  of  an 
AREA,  including  at  all  times  in  the  mind  as  wide  a  belt  on  each  side  of 
an  an- line  between  the  two  fixed  termini  as  there  is  the  remotest  pos- 
sibihty  of  the  Imes  reaching  to;  "remotest  possibility"  being  considered 
for  the  time  being  as  only  bounded  by  some  marked  and  decisive  topo- 
graphical feature  or  traffic  centre. 

Thus,  in  reconnoitring  a  proposed  line,  AB,  Fig.  266,  supposed  to  be  about 
100  miles  long,  we  may  reasonably  take  the  valley  line  V  to  the  right  or  the 
town  C  to  the  left,  as  the  lateral  limits,  but  nothing  less  than  this,  and  the 
whole  area  between  them  should  be  studied  as  an  area,  and  a  topographical 
map  ••  m  the  mind's  eye"  made  of  it  all ;  exact  comparative  knowledge  of  all 
the  various  passes  and  other  governing  points  being  obtained  on  leconnais- 
sance,  or  by  subsequent  survey  or  spur-lines. 

This  simple  rule  is  one  rarely  thought  of  or  acted  on  until  repeated  blunders 
have  enforced  it.     Error  is  particularly  liable  to  follow  from  neglecting  it   as 
will  be  shown  later  by  a  few  examples  from  practice.     We  may  surz'cy  lines 
but  we  must  never  reconnoitre  them.     If  we  do.  it  is  not  a  reconnaissance.       ' 

1137.  2.  All  prepossessions  in  favor  of  any  particular  line  must  be  aban- 
doned, especially  in  favor  of  that  line  which  seems  most  obvious  The 
importance  of  this  is  too,  obvious  to  need  dwelling  on,  yet  it  is  one 
thing  to  admit  it  in  theory  and  quite  another  to  do  it  in  practice.  Not 
to  do  so  is  a  dangerous  and  frequent  error. 

1138.  3.  A  tendency  to  see  with  undue  clearness  the  merits  of  LINES 
LYING  CLOSE  TO  HIGHWAYS  or  the  more  settled  and  open  districts  must 
be  carefully  guarded  against.  This  is  another  dangerous  and  frequent 
-error,  which  is  always  imminent,  partly  because  it  seems  too  obvious  a 
danger  to  be  a  real  one.  The  writer  now  recalls  no  less  than  thirty  in- 
stances,  some  of  them  of  the  first  importance,  in  which  the  deceptive 
conveniences  of  highways  alone  were  responsible  for  serious  error   as 


836 


CHAP.  XXVII.— THE  ART  OF  RECONNAISSANCE. 


,1;  . 


\'3 


«:.] 


in  the  instances  of  Chapter  XXIX.  and  Appendix  C.     Allied  to  the 
above  are : 

4.  Lines  hard  to  get  over  on  foot,  or  overgrown  with  timber  or 
tangled  undergrowth,  seem  infinitely  worse  by  comparison  than  they 
really  are ;  and, 

5.  Raggedness  of  detail,  sharp  rocky  points,  steep  bluffs,  and  the  like, 
exert  an  entirely  undue  influence  upon  the  mind  as  compared  with  long 
rolling  slopes  spread  out  over  a  longer  distance. 

These  two  dangers  are  so  imminent  where  ihe  conditions  specified  exist  at 
all,  as  in  comparing  many  valley  lines  wiih  ridge  lines,  that  they  will  be  sepa- 
rately discussed  (par.  1162).  The  disadvantages  of  a  route  for  a  railway  must 
not  be  measured  by  its  disadvantages  as  a  foot-path,  even  after  all  brush  and 
iimber  have  been  removed,  yet  it  is  hard  not  to  do  so  to  some  extent. 

1139.  6.  A  complete  mental  map  of  the  watercourses  should  be  made 
as  the  reconnaissance  proceeds — sufiiciently  exact,  at  least,  to  enable  the 
engineer  to  state  positively  where  the  water  of  every  stream  crossed 
ioins  another,  and  what  streams  run  in  together,  until  they  have  passed 
off  the  limits  of  the  area  under  examination. 

It  is  not  always  convenient  to  do  this  for  each  stream  as  it  is  passed,  with- 
out undue  delay  ;  but  wherever  a  stream  is  passed  without  dping  it,  there,  it 
should  be  noted,  is  a  gap  in  the  necessary  knowledge  of  the  country,  which  may  be 
dangerous. 

A  skeleton  framework  for  this  information  can  generally  be  obtained  from 
maps.  It  is  in  respect  to  the  minor  streams  that  the  caution  is  particularly 
necessary,  and  it  is  even  more  important  to  adhere  to  it  in  the  smoother  than 
in  very  rough  country.     Neglect  of  it  often  carries  one  off  on  a  false  track. 

1140.  7.  False  summits,  or  those  which  appear  to  interpose  between 
two  water-sheds,  when  in  reality  they  are  only  between  different  parts  of 
the  same  water-shed,  are  very  liable  to  deceive  under  certain  circum- 
stances. The  latter,  fortunately,  do  not  often  occur;  but  when  they  do 
occur  the  deception  is  often  very  perfect,  introducing  an  apparently  im- 
possible obstacle  to  the  progress  of  the  line  which  is  only  apparent.  One 
of  many  reasons  for  the  preceding  rule  is  to  avoid  this  danger. 

See  also  overlaps  (par.  1161),  which  are  a  kind  of  imaginary  false  summits. 

1141.  8.  As  a  very  necessary  safeguard  acjainst  error,  the  engineer 
should  MAKE  IT  A  RULE  to  invariably  discredit  all  unfavorable  reports, 
from  whatever  source  derived,  which  do  not  accord  with  what  he  expects. 

This  merely  means  that  if  he  has.  or  thinks  he  has,  any  reasonable  shadow 
of  ground  for  hope  that  certain  things  are  possible  at  controlling  points,  he 
should  go  there  and  look  for  himself  before  he  finally  abondons  hope.     Not  un- 


CHAP.  XXVII.-THE  ART  OF  RECONNAISSANCE.         837 


necessanly  co„,p,eted  all  at  once.     On  the  contrary,      shodin';e"se 
oe  made  in  part  while  a  party  is  running  some  first  experimental  line 

but  as  broad  a  belt  should  ZLuLT  "'"""«^  ""=  '"P^' 

possible  to  keep  ,n   mind      Th.fr     '  ?  ""=«'"'"'°"  «  '^^'^  as  it  is 

mind  of  the  en«i„eeTthat  l^l  t'"^  k""""*  ''""^^  "^  P''^^'"  '"  '"e 
-.h.  !,„  •  ^"S'neer  that  he  ought  to  be  somewhere  over  the  pricrp  ^f 
the  horizon,  or  on  the  other  side  of  the  valley  or  ridge  instead  of  fnf 
Jowmg  his  nose  where  he  is.  instead  of  fol- 

field!ru"tItn'ontTm°:ir'""''  "  "°'  ordmanly  camed  on  in  the 


Ill 


f 


838         CHAP.  XXVII.— THE  ART  OF  RECONNAISSANCE. 


tnat  an  aneroid  barometer  will  be  of  assistance  to  fix  the  approximate 
elevation  of  points,  if  too  great  confidence  be  not  placed  in  it, — may  be 
supposed  to  be  understood. 

A  hand-level  is  a  more  important  tool,  which  should  always  be  at 
hand.  In  looking  through  it  do  not  close  one  eye,  but  while  one  eye 
looks  through  the  tube  of  the  hand-level  let  the  other  look  at  the  na- 
tural landscape.  The  bubble  will  then  be  seen  superimposed  on  the 
latter.     Hand-levels  are  very  often  out  of  adjustment,  and  still  more  often 

have  very  dull  bubbles^ 
which  read  quite  difTerent- 
ly  if  the  tube  has  been 
raised  or  lowered  to  posi- 
tion. A  guess  should  al- 
ways be  made  first,  before 
using  the  hand-level,  but 
no  man  ever  acquires  a 
very  trustworthy  faculty  of 
guessing  at  a  horizontal 
line.  In  ordinary  locali- 
ties a  practical  eye  will 
estimate  elevations  and  a 
horizontal  line  with  a  good 
deal  of  precision,  but  there 
are  peculiar  topographical 
conditions  which  make 
the  evidence  of  the  eye 
worse  than  worthless  (par^ 
1160),  and  no  one  can  tell 
where  they  are  in  advance. 
An  odometer  may  be 
fastened  to  the  wheel  of 
the  carriage,  if  a  vehicle 
be  used  ;  but  distances  can 
usually  be  guessed  or  as- 
certained, by  time  esti- 
mates or  otherwise,  nearly 
enough  for  preliminary  purposes.  A  pocket  compass  is  a  necessity,  and 
a  succession  of  travelling  companions  with  a  local  knowledge  of  the 
country  are  very  desirable.  More  outfit  than  this  and  the  best  attainable 
maps  will  not  be  particularly  useful. 


C^^P'  XX VII.— THE  ART  OF  RECONNAISSANCE.         839 


1H5.  As  a  preliminary  to  starting  out  to  explore,  say  from  B  to  A, 
Fig.  266,  one  should  strike  an  arc  mentally  across  the  country  with  B  as 
a  centre,  and  with  a  radius  of  2  to  20  miles,  according  as  some  definite 
topographical  feature  may  indicate.  In  country  at  all  rough  this  arc 
should  be  at  least  200°  long.  In  smoother  country  it  maybe  less.  A  pass 
through  a  range  of  hills  at  e  on  the  direct  line  to  A  may  determine  where 
to  strike  this  arc. 

Before  allowing  himself  to  pass  by  this  arc  at  any  point  the  engi- 
neer  should  mentally  ask  himself  this  question,  and  either  answer  it  posi- 
tively  and  definitely  on  the  spot,  or  note  that  he  must  find  an  answer: 
How  many  different  routes  are  there,  and  what  are  their  comparative 
merits,  for  passing  from  B  to  beyond  THIS  arc  at  any  point  in  its  whole 
extent?  If  there  be  some  point  like  ^  or/ which  is,  in  the  first  place,  out  of 
the  proper  direction  ;  secondly,  difficult  of  access  ;  and,  thirdly,  highly  un- 
promising in  appearance,— it  must  not  be  passed  until  it  is  known  that  it 
is  not  feasible,  or  else  noted  as  a  point  to  be  continually  remembered  as 
of  unknown  and  presumably  great  capabilities. 

Usually  there  will  be  three  or  four  routes  for  crossing  this  first  arc, 
which  will  appear  distinctly  better  than  any  others,  and  perhaps  be  the 
only  possible  ones.     Noting  every  one  of  those  which  have  not  been  ex- 
amined, and  assuming  that  everything  is  possible  which  is  not  clearly 
seen  to  be  impossible,  the  imaginary  aVc  may  be  crossed  to  the  next  belt. 
1146.  Here,  at  some  fixed  topographical  feature  where  obstacles  occur, 
or  at  some  town,  a  second  mental  arc  may  be  struck,  likewise  with  B  as 
a  centre,  but   it  is  no  longer  necessary  to  make  it  200°  long,  but  merely 
long  enough  to  cover  a  route  to  A  from  every  possible  pass  of  the  first 
arc,  and  the  method  should  be  the  same.     The  question  should  be  :  In 
THIS  ANNULAR  BELT  what  is  the  best  way  to  pass  from  some  attainable 
point  in  the  first  arc  to  beyond  the  second,  and  which  will  give  the  best 
complete  route  from  B} 

By  thistime  we  shall  be  so  far  away  from  B  that  we  cannot  really  cover 
mentally,  eren  in  the  rudest  way,  all  the  area  we  should  investigate,  and 
we  must  drop  the  furthest  half  of  it  entirely  from  mind  for  the  time 
being.  Remembering  that  it  is  dropped,  however,  the  method  is  the  same, 
so  far  as  it  goes.  By  assumption,  all  the  most  hopeful  chances  are  in  the 
region  beyond  the  horizon,  but  it  is  necessary  to  leave  them  for  the  time 
being. 

1147.  As  the  reconnaissance  approaches  A  it  will  be  more  natural  that 
our  work  should  be  carried  on  with  that  as  a  centre,  and  as  soon  as  pos- 
sible the  examination  of  the  whole  possible  area  at  once,  in  a  cursory 


,^' 


840         CHAP.  XXV IT. —  THE  ART  OF  RECONNAISSANCE. 


way  at  least,  should  be  resumed.  On  reaching  A,  before  the  territory 
passed  over  is  again  examined,  all  the  remaining  possible  area  should  be 
gone  over  in  the  same  way,  and  it  should  not  be  regarded  as  completed 
until  the  limits  of  the  water-shed  of  every  stream  in  the  whole  area  are 
well  understood,  and  the  lowest  passes  through  the  ridges.  It  is  not  by 
any  means  the  roughest  regions  which  require  the  most  care  in  this  re- 
spect. Thus,  in  Fig.  266,  if  the  country  were  very  rough  the  chances 
would  be  very  strong  indeed  that  the  valley-line  BVA  would  be  the  best, 
and  a  very  cursory  examination  of  sonie  cross-line  VD  might  suffice  to 
prove  it.  In  moderately  easy  country  the  line  BCDA  would  be  far  more 
likely  to  be  the  best,  and  there  might  of  course  be  considerable  variations 
in  it;  or  the  valley  at  be  might  be  so  low  and  the  town  Cso  small  that 
the  preference  clearly  lay  with  the  most  direct  line.  It  does  not  by  any 
means  follow  that  the  whole  area  should  be  examined  with  equal  care. 
If  one  part  is  positively  known  to  be  worse  than  another,  it  matters  little 
to  determine  liow  much  worse  ;  only,  it  must  be  known,  and  not  guessed 
at. 

By  following  strictly  on  the  line  of  these  suggestions  serious  over- 
sights are  not  probable  ;  otherwise  they  are  exceedingly  probable.  Such 
assistance  as  it  seems  possible  to  give  for  training  the  eye  to  take  in  the 
meaning  of  what  it  sees  before  it,  is  given  in  the  following  chapter.  One 
general  caution  may  be  added  :  "  Rough  country  "  is  a  purely  relative 
term.  To  the  tyro,  the  rolling  hillocks  of  Ohio,  Michigan  and  New  Jer- 
sey are  rough.  The  same  man,  with  a  little  experience  in  really  rough 
country,  will  take  the  worst  the  Rocky  Mountains  or  the  Andes  can  offer 
with  equanimity  ;  and  equanimity  is  in  every  calling  essential  for  success. 
No  country  in  which  most  of  the  surface  has  a  layer  of  soil  over  it  de- 
serves the  name  of  rough.  It  needs  but  little  study  and  care  to  get 
several  lines  of  reasonable  cost  through  it.  The  art  of  location  consists 
merely  in  making  a  judicious  choice, — not  in  getting  a  line,  which  is 
always  easy  in  such  regions. 

1148.  An  accomplishment  which  is  not  very  difficult  to  acquire,  and  which 
is  constantly  useful  on  reconnaissance,  is  to  estimate  the  rate  of  fall  of  streams 
from  their  general  appearance.  No  general  rules  can  be  laid  down,  because  so 
much  depends  upon  the  volume  of  the  stream.  A  fall  of  4  to  8  feet  per  mile 
will  give  a  good-sized  stream  or  river  a  very  rapid  current,  with  many  stretches 
where  it  will  seem  to  the  careless  eye  as  if  there  were  nearly  that  fall  at  a  single 
point,  succeeded  by  pools  above  and  below.  On  the  other  hand,  a  fall  of  30  or 
35  feet  per  mile  does  not  necessarily  give  to  a  small-sized  river  the  character  of 
a  torrent,  and  large  brooks  or  small  creeks  must  fall  100  feet  per  mile  or  more 
before  they  have  any  violent  current. 


_  ^"■*''-  ^Xl'Il.-THE  ART  OF  KECOfJNAISSANCB.        84I 

II49.  A  special  report  on  .he  Water-Power  of  the  United  States  in  the 
T=n>h  Unued  States  Census  gives  a  tabular  statement  of  the  slopes  of  he 
pnncpal  strean,s  flowing  into  the  Atlantic  and  the  Eastern  Guf,th7ch  might 

pretty  much  the  same  per  tu.le  from  the  Merrimack  to  the  Chattahoochee-  the 
average  slope  of  twenty  one  main  streams  being  5.4  feet  per  mile   with  the  Sus 

feefpT^lle!  ""'"'■  "  "'  '"  "'"^'  """'  '''  ""''^°"  ""-"  '"'  "sCs'  af .0 
The  slope  of  some  of  the  southern  tributaries  of  the  Ohio  River  is  verv  lieht 
rang,„g  from  0.41  foot  per  mile  for  the  Green  River  to  2.84  feet  for  the  AUe 
gheny  as  a  maximum.     The  falls  in  these  streams  generally  take  the  form  o 
long  shoals.     As  an  example,  however,  of  the  rapidity  which  some  of  tise 

Jon  LITZ  T  o'"'  '■"''''  ^°"""  '"  '"'  «=""=  ^'°P=  of  'heir  subsequent 
course.  Mr.  Dw.ght  Porter  mentions  that  the  Cheat  River,  in  West  Virginia  falls 
2400  feet  m  the  last  eighty  miles  of  its  way  to  the  Monongahela,  while  the  latter 
nver  descends  but  75  feet  in  the  ninety  miles  between  the  mouth  of  the  Chel 
and  Pittsburg.  The  northern  tributaries  of  the  Ohio  have  usually  steeper  slopes 
but  the  average  ,s  far  below  the  rivers  on  the  upper  Atlantic  coast.  The  Ohfo 
R.ver  uself,  from  Pittsburg  to  its  mouth,  a  distance  of  ,67  miles,  falls  430°.^^ 

T^o  mrs"''  °**  '  '"  """  ^'  ^""'^"'"^  '""^  '^  ^  '-"  of  = ''«'  in 
The  Upper  Mississippi,  from  its  extreme  sources  to  St.  Paul,  500  miles  by 
.he  r,ver.  falls  1000  feet.  The  Missouri  River  falls  2464  feet  in  he  2644  milel 
o  ,ts  course  below  Fort  Benton,  being  navigable  to  that  point.  The  ritltarie 
■of  the  M,ss,ss,ppi  from  Eastern  Iowa  have  a  general  slope  of  about  3  feet  per 
mile,  rangmg  from  1.84  to  3.83  feet  per  mile.  '^ 

f..,?*  ^'^^"^^^  River,  from  its  source  to  Pueblo,  Colorado,  averages  34.1, 
fee  per  mde.  In  the  upper  ,20  miles  the  river  falls  40  feet  per  mile  the" 
flattens  out  .0  8  feet  per  mile  for  500  or  600  miles,  and  at  .50  miles  above  its 
mouth  Its  slope  is  only  0.46  foot  per  mile. 

The  Niagara  River,  in  its  short  course  of  37  miles,  descends  333  feet  to  Lake 
Ontario  w.th  a  vertical  plunge  of  160  feet  at  the  Falls,  discharg  ng  avo  ume  of 
wate      ear,,  half  as  great  as  the  Mississippi  River,  or  t66.6<^  cubic  f  eT  pe 

ZZ.  Z,  ,    "  '°  '  ■"""  ^""^^  '"^  ^^"='  '"^  "^■"  ''««"ds  20  feet,  or 

ir^nk  of  ZfT,       :•  '"  '"'  '"■"'"  "  '"""'"y  "^''S^''"^:  f^-""  'his  point  ,0  the 
*nnk  of  the  Falls  ,t  descends  about  53  feet,  or  18  feet  per  mile. 


842 


CHAP.  XXVIII— OCULAR  ILLUSIONS. 


CHAP.  XXVIII.— OCULAR  ILLUSIONS. 


i 


14^ 


< 


CHAPTER  XXVIII. 


OCULAR    ILLUSIONS. 


1150.  The  natural  eyesight  is  readily  deceived  even  where  the  ap- 
parent differences  are  so  great  as  to  seem  clear  and  positive.  Among- 
the  more  serious  ways  in  which  this  danger  may  make  trouble  are  : 

I.  The  eye  foreshortens  the  distance  in  an  air-line  and  materially  ex- 
aggerates the  comparative  length  of  a  lateral  offset,  so  as  to  greatly  exag- 
gerate the  loss  of  distance  (and  hence  of  curvature)  from  any  deflection. 
A  deflection  which  will  not  in  reality  add  more  than  lo  to  15  per  cent  to 
the  length  of  a  line  will  seem  to  the  eye  to  double  it.  This  marked  ten- 
dency to  great  exaggeration  results  from  the  effect  of  two  concurrent 
causes:  (i)  the  foreshortening  alluded  to,  and  (2)  the  tendency  of  the  mind 
to  exaggerate  the  distance  lost  by  lateral  deflections  even  when  looking 
down  upon  a  map— as  Fig.  13.  page  237.  where  the  loss  of  distance  in  C 
might  be  easily  estimated  at  four  or  five  times  what  it  is. 

These  two  causes  combined,  both  of  them  having  much  effect  in  the 
same  direction,  make  the  judgment  of  inexperienced  men  on  this  subject 
almost  absurdly  deceptive. 

1 1 51 .  2 .  The  eye  exaggerates  the  sharpness  of  projecting  points  and  spurs, 
and  the  degree  of  curvature  necessary  to  pass  around  them :  an  exceed- 
ingly common  difficulty,  leading  to  serious  consequences.  It  results  from. 
a  combination  of  natural  causes,  viz.:  (i)  The  eye,  in  looking  at  all  nat- 
ural slopes,  from  any  point  of  view  whatever,  greatly  exaggerates  their 
steepness.  A  60°  slope  seems  almost  vertical ;  a  45°,  fully  75°;  a  i^  to  i 
slope  fthe  rate  of  the  very  steepest  mountain  sides),  at  least  i  to  i  ;  etc., 
etc.  This  tendency  is  especially  strong  in  looking  at  slopes  from  above. 
(2)  Such  points  are  generally  looked  at  from  above  ;  but  whether  looked 
at  from  above  or  below,  the  eye  instinctively  searches  for  something  fixed 
and  definite  to  start  from,  which  is  usually  found  in  the  crest  or  ridge  line, 
especially  if  the  latter  runs  nearly  to  a  knife-edge.  Likewise  the  eye  al- 
most invariably  tends  to  exaggerate  angles,  from  whatever  point  the  view 
is  taken  on  which  the  judgment  is  formed.  If  formed  from  the  side 
(Fig.  267),  it  exaggerates  the  distance  C  in  comparison  with  AB\  making: 


845. 


it  seem  half  as  long,  for  example,  when  it  is  only  one  fourth  as  long,  thus 
making  the  point  seem  to  require  a  curve  of  180°  where  perhaps  no' 
only  will  suffice.  If  formed  from  in  front  of  very  sharp  points.  Fig.  268, 
the  tendency  is  to  look  upon  the  two  range-sights,  B,  C,  as  at  a  much 
sharper  angle  U  to  each  other  than  they  really  2iV&,because  the  eye  ranges 
along  both  slopes  at  once— an  unusual 
circumstance,  the  more  common  case 
being  that  of  Fig.  269,  in  which  the 
tendency  is  in  the  opposite  direction. 
In   Fig.  268  one  tends  to  approximate 


r 

I 

I 

o 


Fig.  267. 

the  angle  V  to  180':  or,  in  other  words,  to  think  of  B  and  C  as  nearly  par- 
allel to  each  other,  as  if  we  were  looking  from  £  at  an  infinite  distance. 

1153.  From  these  causes  combined,  the  eye  at  £  first  fixes  on  the 
crest-line  and  then  exaggerates,  say.  a  li  to  i  slope  into  a  i  to  i  slope  •  in 
other  words,  makes  the  chord-line  A.  Fig.  268.  one  third  shorter  than  it 
IS.  This  alone  gives  a  15°  curve  where  10°  will  suffice.  But  having  fir^t 
got  our  chord-line  too  short,  we  then  proceed  to  mentally  exaggerate  the 
angle  to  which  it  is  a  chord,  and  thus  still  further  shorten  the  supposed 
radius,  so  that  we  may  easily  picture  a  20°  curve  where  10°  would  prove 
on  .-survey  all-sufllicient. 

Whether  this  explanation  of  the  philosophy  of  the  tendency  to  error 
be  correct  or  not,  the  fact  of  its  existence  in  about  the  degree  stated  is 
beyond  question,  especially  with  those  who  are  for  the  first  time  con- 
fronted with  "rough  country."  They  are  almost  sure  to  exaggerate 
greatly  the  difficulties  of  such  localities. 

1154.  3.  An  opposite  tendency-to  decrease  the  probable  an^rles  re- 
qu.red-exists  in  looking  at  smooth  gentle  slopes,  especially  'from  a 
distant  point  of  view,  for  reasons  hinted  at  in  part  in  Fig.  269.  Smooth- 
ness and  gentleness  of  slope  mean  that  we  must  either  go  out  a  loner  wav 
to  gam  a  little  difference  of  elevation,  or  must  put  up  with  very  \on^  if 
not  very  deep,  cuts  or  fills.     In  order  to  bring  down  the  work  to  reason- 


N 


«44 


CHAP.  XXVIII.— OCULAR  ILLUSIONS. 


CHAP,  XXVIII.— OCULAP  ILLUSIONS. 


845 


y 


^ble  lightness,  therefore,  we  must  often  adopt  a  quite  crooked  alignment 
on  the  smooth  and  (for  foot  travel)  very  tractable  slopes,  and  even  then 
have  pretty  heavy  work. 

This  error  is  especially  liable  to  occur  on  the  long  gentle  rolling  slopes 

which  are  met  over  vast  areas  of  the  far- 
western  United  States,  Mexico,  South 
America,  and  (the  writer  believes)  much 
of  Asia,  Africa,  and  Australia,  in  all 
of  which  regions  Nature  seems  to  have 
planned  all  her  works  on  a  vast  scale  and 
taken  plenty  of  room  to  spread  out  in. 
In  the  Eastern  United  States  and  in 
Europe  west  of  Russia  it  is  less  immi- 
nent. 

When  we  happen  to  be  comparing  two 
lines,  one  of  which  lies,  say,  in  a  valley,  where  the  tendency  is  to  exaggerate 
the  sharpness  of  curves  and  angles,  while  another  lies  on  a  smoother  and 
higher  region,  where  the  tendency  is  in  the  other  direction,  these  two 
opposite  tendencies  may  combine  to  cause  most  calamitously  mistaken 
conclusions,  one  line  being  made  up  in  large  part  of  points  like  Fig. 
268  and  the  other  like  Fig.  269. 

1155.  The  unassisted  eye  is  also  liable  to  be  deceived  in  many  ways 
as  to  gradients  and  elevations,  as  noticeably  in  the  following: 

4.  A  slope  looked  at  from  a  distance  always  appears  steeper  and 
higher  than  it  really  is,  especially  if  we  are  standing  on  ground  descend- 
ing towards  it,  when  the  eye  tends  to  look  on  the  slope  where  we  stand 
as  more  nearly  level  than  it  is,  and  to  exaggerate,  often  to  an  absurd  ex- 
tent, the  steepness  of  the  rising  ground  in  front.  This  is  a  familiar  ex- 
perience, which  most  men  have  learned  to  allow  for,  more  or  less.  The 
best  training  for  the  eye.to  check  the  danger,  is  to  study  the  phenomenon 
on  highways  or  constructed  railways,  where  the  effect  of  a  given  vertical 
angle  is  far  more  marked  than  on  a  natural  unbroken  surface,  for  the 
reason,  probably,  that  where  the  mind  looks  for  uniformity,  as  on  a  rail- 
way or  road,  it  is  forcibly  impressed  by  a  deviation  from  it,  but  where,  on 
the  other  hand,  irregularities  are  looked  for  and,  as  it  were,  "discounted" 
in  advance,  the  very  same  surface  angle  produces  less  impression. 

1156.  Another  and  perhaps  truer  explanation  of  this  and  many  other 
ocular  illusions  is  that  it  is  simply  lack  of  practice  and  training  of  the 
eye  under  those  particular  conditions.  The  child  had  absolutely  no  per- 
ception of  distance  or  perspective,  and  hence  of  size,  but  puts  out  his 


hand  to  touch  everything  he  sees  within  his  field  of  view,  even  on  the 
distant  horizon.     To  measure  distances  and  sizes  as  accurately  as  we  do 
by  the  aid  (,)  of  the  short  base-line  of  2i  inches  between  the  two  eyes 
and  (2)  of  our  gradually  acquired  knowledge  of  the  probable  sizes  of  ob^ 

wh  rh''  '"  ,^  ''  ""'"'".^  P'""'"''  ""^  extraordinary  difficulty  and  delicacy, 
wh.ch  IS  only  acquired  by  the  incessant,  unconscious  practice  of  years 
Under  the  conditions  in  which  we  have  been  most  trained  we  do  tolerl 
ably  well ;  but  whenever  we  strike  the  unfamiliar  and  unusual,  then  the 
eye  reverts  to  its  original  untrained  tendency  to  bring  evervthincr  in  the 
distance  up  into  its  own  vicinity,  with  an  inevitable  LtortC  effect  on 
what  the  mind  makes  out  of  the  picture  seen.     Thus  it  is  thft  the  sun 

se"  tirr'^'H"  ''  '''.  '''  '  ^"^'  ''''  '^'^'^  -^-"  ^^-y  -^  -i"/or 
forced  to  do  so  by  seeing  them  beyond  the  immediate  horizon      Thus 
rather  than  by  the  common  explanation  that  there  are  no  intermediate 
objects  to  fix  on,  distances  across  water  are  always  under-estirted  by 

fZJrZTT'  "h  %  ^^^  ^'^  ^^"^^  ^^^^°"'  ^^'^'^'^y'  ^h^  ^ye  brings 

forward  the  farther  end  of  a  long  line  of  rails  beyond  a  hollovv  untill 
a  ded  son^ewhat  by  the  further  assumption  that  we  are  standing  on  a 
level-they  seem  almost  to  stand  up  and  down.  For  the  same  reason 
the  steepness  of  the  slopes  of  mountains  are  exaggerated  ;  and  possibi; 
for  the  same  reason,  in  part  at  least,  the  immense  scale  on  which  the 
topographical  features  of  the  great  West,  Mexico.  South  America,  and 


P^lG. 


270. 


Similar  regions  are  laid  out.  deceives  as  to  distances  the  Eastern  man  or 
Jiuropean,  accustomed  to  a  pettier  topography. 

1157.  A  comparison  of  the  different  effect  upon  the  eye  of  railway 
gradients  and  natural  slopes  of  the  same  rate,  wherever  two  descending 


■846 


CHAP,  XXVIII.— OCULAR  ILLUSIONS. 


gradients  can  be  found  nearly  following  the  natural  surface,  is  an  in- 
structive training  of  the  eye.  By  standing  first  on  the  track  and  then  a 
few  hundred  feet  to  one  side,  the  difference  in  the  degree  of  the  decep- 
tion is  marked  ;  but  trial  from  various  points  of  view  will  show  that  it 
always  exists,  even  on  tlie  natural  surface. 


Fig.  271. 

1158.  5.  Allied  to  the  above,  but  operating  more  obscurely  and  on  a 
larger  scale,  is  the  deception  which  comes  from  the  propinquity  of 
LARGE  MASSES  OF  HILLS  OR  MOUNTAINS  when  looked  at  from  a  dis- 
tance, or  even  from  a  mere  general  slope  in  one  direction  of  the  whole 
foreground  within  view,  especially  if  it  be  much  broken  up  in  detail  by 
minor  hillocks  and  ridges,  so  that  the  general  trend  of  the  surface  is  not 
readily  detected.  The  best-trained  eye  is  quite  incapable,  under  these 
circumstances,  of  estimating  horizontal  ity  so  as  to  detect  the  lowest  points 
with  the  same  success  as  under  ordinary  circumstances.     Fig.  212,  page 


Fig.  272.— A  Distant  View  of  an  Overlap. 

^80,  reproduces  admirably  an  ocular  illusion  of  this  kind.  The  grades 
against  the  stream  seem  enormously  steep,  and  those  with  it  nearly  level. 
The  reverse  is  the  case  at  the  viaduct  in  the  background,  and  elsewhere 
the  rate  is  the  same.  In  Fig.  270  the  pass  A,  which  seems  to  the  eye  of 
a  distant  observer  to  be  slightly  lower  than  B,  may  be  counted  on  with 
great  certainty  to  be  considerably  higher.  To  be  in  fact  on  a  level  with 
it,  it  must  appear  to  the  eye  very  much  lower.     Fig.  270  was  sketched 


CHAP.  XXVIII.-OCULAR  ILLUSIONS. 


847 

from  an  instance  where  half  a  dozen  skilled  men  under- estimated"^ 
height  of  A,  and  over-estimated  B,  by  nearly  200  feet,  from  a  point 
of  view  less  than  3  miles  off.  over  an  apparently  level  plain,  on  a  line  of 
sight  nearly  parallel  with  the  slopes  of  the  mountain,  and  with  A  and  B 
hardly  more  than  half  a  mile  apart;  the  pass  having  been  looked  at, 
likewise,  from  both  sides. 

1159.  Another,  the  most  extraordinary  ocular  deception  which  the 
writer  has  ever  encountered,  and  for  which  he  could  not  then  or  later 
imagine  an  explanation,  is  badly  sketched  from  memory  in  Fig  271  In  a 
gently  rolling  but  much  ••  accidented  •'  country,  through  a  little  pass  with 
(seemingly)  long  gentle  slopes  on  each  side,  the  little  hut  appeared  only 

/t°j!f «  r  l^  "^T""  °^  "^"^  "°"^''  '^^^  '"="'  400  ft.  off.  when  in  fact 
It  was  80  ft.,  there  being  in  this  case  no  preponderance  of  large  masses 
on  either  side  of  the  field  of  view  to  unbalance  the  eyesight.    tL  de';^ 

corn-  InT""',  ""'  """7°"  '°  "^"'^  '"^"  °'  ^  '='^8^  ''"''  experienced 
and  ,:,  h"  ^^'  ""''  ^'■°"'  ""  "^^""'^  '■""'"  «f  association  with  a  sharp 
and  tremendous  descent  a  short  distance  back  (1500  feet  in  a  six  mil^ 
view),  which  might  have  been  seen  in  part  by  ejes  in  the  back  o  on  ' 
head  while  looking  at  the  hut.  but  which  neither  existed  in  fact  nor  an! 
peared  to  exist  in  the  view  taken  in  by  the  natural  eyesight,  as  rudely 
and  very  inadequately  sketched  in  Fig.  27..  The  hut  look!  far  too  high 
m  the  cut,  and  the  very  bottom  of  the  valley  was  in  sight 

1160.  Similar  ocular  illusions,  and  perhaps  more  remarkable  ones 
^ay  be  seen  wherever  there  are  irrigating  or  other  nearly  level  ditches 
>wmdmg  around  the  slopes  of  n,ountains  above  rapidly  descending  vat 


Fig.  273.— The  same  Overlap— Near  View. 

leys.     They  invariably  appear  to  run  up  hill,  and  often  in  a  very  marked 

and  extraordmary  way.  as  with  many  of  the  irrigating  ditches  of  Colorado. 

These  examples  are  but  pronounced  types  of  frequent  topographical 

rregulanties,  which  make  the  eyesight  utterly  worthless  for  measuring 

mportant  elevations  and  slopes  in  certain  localities;  and  where  those 

localities  are,  unfortunately,  cannot  be   determined   in   advance.    The 

aneroid  barometer,  altazimuth,  or  hand-level,  consequently,  should  be 


« 


I ' 


S4S 


CHAP.  XXVIII.— OCULAR  ILLUSIONS. 


I 


constantly  used  on  reconnaissance,  and,  in  general,  all  such  points,  if 
important,  should  be  actually  visited,  for  another  reason: 

1161.  6.  Overlaps  of  hills  or  elevated  ground  at  a  distance  are  a 
frequent  source  of  deception  and  error.  Views  which  from  a  distance 
appear  like  Fig.  272  are  found  on  nearer  acquaintance  to  be  more  like 
Fig.  273,  with  an  easy,  open  valley,  and  perhaps  a  running  stream  pass- 
ing through  what  seemed  to  be,  "  beyond  question,"  a  solid  ridge.     Illu- 


CIIAP.  XXVIII— OCULAR  ILLUSIONS. 


849 


Fig.  274. — Better  Country  than  it  Looks. 

sions  of  this  kind  are  often  very  perfect,  even  in  the  near  vicinity  of  the 
observer.  An  example  on  a  small  scale  (small,  because  the  mind  realizes 
that  it  must  be  a  deception)  may  be  seen  in  ascending  the  Hudson  River 
when  approaching  Peekskill,  especially  in  the  early  summer  evenings, 
when  the  lights  and  shades  are  such  as  to  produce  a  very  vivid  feeling 
that  it  is  a  closed  basin  without  further  outlet  to  the  north.  It  is  said 
to  be  on  record  that  it  deceived  Hendrick  Hudson  himself,  and  almost 
induced  him  to  turn  back. 


The  great  safeguard  against  errors  of  this  kind  is:  Form  a  complete 
picture  of  the  water-shed  over  the  area  to  be  reconnoitred,  so  that  it  is 
known  where  water  falling  on  it  anywhere  will  flow  to 

r.^T'  ''l^^^  ^^^  "^'^"  ''^"'^^'  ''"^"  '"  estimating  quantities,  for 
reasons  wh.ch  m  part  result  from  what  has  preceded.  Most  serious  con- 
sequences flow  from  this,  leading  to  the  abandonment  without  survey  of 
Imes-especially  valley-lines-which  should  have  been  regarded  as  the 


Fig.  275.— Worse  Country  than  it  Looks, 


most  promising  of  all.     The  root  of  the  difficulty,  in  addition  to  the 
various  causes  of  deception  which  have  been  noted,  lies  in  the  inability 
of  the  mind  to  distinguish  (i)  between  what  seems  rough  and  what  is 
and  (2   between  what  is  rough  for  foot  or  horse  travel  and  what  is  rou»h 
tor  railway  construction.  " 

hv  1^^  ^"^"'^°f  the  first  cause  for  deception  will  be  better  appreciated 
thev^niLt"     "u  ':'  ^"y -"-derable  experience  in  consfr'u ctio     U 
they  will  but  recall  what  a  tremendous  reduction  in  the  apparent  diffi- 


f 


CHAP.  XXVJII.-OCULAR  ILLUSIONS. 


{ 


850 

li^f  work  follows  from  the  mere  act  of  thoroughly  clearing  the 
eround  even  if  there  were  nothing  on  it  before  but  light  undergrowth 
Td  brush.  To  a  thoroughly  trained  eye  this  should  make  no  apprec- 
able  difference,  yet  the  unconscious  feeling  of  every  one  .s  "well  begun. 

half  done."  .  ,         , 

1,63.  When  to  ordinary  timber  we  add  tangled  v-es  and   unde  - 

„!!ih  makin"  progress  on  foot  exceedingly  slow  and   difficult,  this 

^Jt  is  "crea;ed      We  are  apt  to  measure  distances  by  time  under  such 

Jances  so  that  if  we  went  over  an  aggregate  of  .0  miles  at  one  nule 

"''hou    and  of  i  r^  les  at  five  or  six  miles  per  hour,  in  exploring  .00 

!"  es  w;  shallfinTsh  with  a  feeling  that  fully  a  third  of  the  line  has  been 

Te      ;ough     On  the  other  hand,  when  we  strike  a  highway  and  go  along 

mIv  over  the  ground,  we  at  least  never  exaggerate  the  difficulties 

T.  ,  we  wVk  over  the  hill  to  take  a  glance  at.  and  the  long  stretches 

;tt  coltry  are  what  we  have  been  most  conscious  of  and  remember 

"In ^^''74  we  have  a  sketch  of  a  jagged  rocky  point  in  a  river  valley; 
in  FilTs  a  sketch  of  a  line  on  a  gently  rolling  side-h.lK     Nine  mn  in 

:e7b^«"::;;'::rb:  rc^p^st.  i/additio^i  to  having  the  best  grade^^ 

««i    Tl,l,  results  from  the  fact  that  in  following  a  valley-line  it  is 

.    -T   Hffiru     to  make  due  allowance  lor  the  fact  that  Nature 
exceeding^.  difficuU  to  „ake^  du  ^^  ^^  ^^^^  ^  ^^^^  ^,^^ 

H^S  ^.ADE  OUR  F.LLS^     It  m  y  ^^^^^  ^       ,_^^^    ^^^^^^  ^^^,, 

r       donele%mucrlrk  on  it  we  have  excavated  enough  material 
have  done  ve  y  muc  .^  ^  ^^^^^^^,  ^„^  ^^„^, 

to  carry  t^!^ j'"^ J^"' ".°^„  .^e  point,  as  on  ordinary  ground,  to  avoid 
a,enotoWigedtoliug  mto  p^^^,  ,^  ^^^  ^^,,^^  ^^^^^ 

running  our  line  aDove  ai        vy         g  t.  ^^ 

THere  "«  - j-  ow^^^^utl    ^^^^^^^^^  Ltom-land,  already 

come,  probably,  to  a  "a  ^  ^^^  ^,  ^„  y,,,^^,  do  (when 

rip.rapped  "f  ^^Sf/'''°";^"°J  ^hat'pictured.  just  above  the  ordinary 

r^i^rhl^wlteTso        t^h^^^^ 

level  of  h'g>'-»at^^' =°  '       else  when  they  are  overflowed,  are  not  sub- 

"■^^d^ra^lXt'e  c„      n't     The  more  violent  and  rapid  the  ordi- 
"  ^.nt  the  less  likelihood  there  is  that  the  bottoms  are  often  de- 

Tcriy  ove^ow:^      If  overflowed,  the  current  cannot  be  rapid,  or  the 

nteX!  wrefwXe  passed  the  rocky  bluff  in  Fig.  .74  we  have 


CHAP.  XXVITL— OCULAR  ILLUSIONS. 


851 


comfortable  running,  and  can  get  a  good  alignment  until  we  come  to  the 
next  similar  point.  At  every  one  of  them,  although  we  are  thrown  out  to 
and  into  the  water,  Nature  has  provided  the  material  to  resist  the  water  on 
the  spot.  The  profile  of  such  a  line  is  very  apt  to  be  quite  light ;  rather 
deceptively  so  in  fact,  since  there  will  be  a  great  deal  of  workin  protect- 
ing banks  and  working  very  steep  slopes,  which  will  not  show  on  the 
profile  at  all. 

1165.  On  the  other  hand,  in  Fig.  275,  gentle  as  is  its  general  effect,  we 
must  cut  into  our  hills  far  more  than  the  eye  will  appreciate  in  order  to 
avoid  enormous  fills.  If  the  slopes  be  at  all  steep  (they  might  well  be 
steeper  in  the  view  to  bring  out  the  effect  desired),  the  eye  when  reconnoit- 
ring will  underrate  the  depth  of  these  fills,  especially  from  a  distance,  by 
taking  a  mental  section  of  them  on  a  plane  Jiormal  to  the  slope  instead  of 
on  a  vertical  plane.  The  loss  from  the  side-hill  slope  of  the  ground, 
likewise,  will  be  very  likely  to  be  under-estimated:  not  that  the  eye  will 
not  exaggerate  the  slope  of  the  ground  relatively  to  the  horizontal,  for  it 
will,  but,  by  a  seeming  paradox,  the  angle  of  the  ground  with  the  side- 
slopes  of  a  cut  or  fill  will  be  rather  underrated,  because  the  mind  men- 
tally exaggerates  the  latter  also,  and  still  more. 

It  is  almost  an  invariable  rule  that  fills  turn  out  deeper  than  they  are 
expected,  and  on  a  side-hill  line  most  of  the  water-ways  are  in  fills  of 
considerable  depth.  The  water  channels  are  also  more  ramified,  and 
hence  more  numerous,  on  high  slopes  than  lower  down  in  the  valleys, 
where  the  total  discharge  is  more,  but  the  water  has  collected  in  larger 
streams. 

Much  expense  can  be  saved  on  side-hill  lines,  and  danger  of  washouts  as 
well,  by  catching  the  water  in  a  ditch  at  or  a  little  below  grade  and  carrying  it 
under  the  road-bed  in  a  small  structure,  with  the  foundations  of  the  discharging 
end  of  the  structure  properly  secured,  instead  of  putting  the  structure  in  the 
very  bottom  of  the  gulch. 

1166.  Cul-de-sacs  are  another  incessant  source  of  deception  and  error,  al- 
though rather  due  to  negligence  or  inexperience  than  to  ocular  illusion  proper. 
It  constantly  happens  that  men  walk  into  them  as  a  mouse  into  a  mouse-trap, 
and  for  the  same  reason— blindly  following  one's  nose;  or  rather,  from  recon- 
noitring a  LINE,  foot  by  foot  and  mile  by  mile,  instead  of  an  area  as  a  whole.  A 
man  sees  a  beautiful  open  area  ahead  of  him  as  far  as  the  eye  can  reach,  prob- 
ably with  a  highway  through  it.  He  is  satisfied,  and  looks  no  farther,  until  he 
comes  to  the  end  of  it.  Then  it  is  too  late.  He  has  accepted  his  line  so  far 
as  a  finality,  and  knows  no  other.  He  assumes  that  he  can  do  nothing  better 
behind,  and  "  therefore"  must  get  out  of  his  trap  ahead  as  best  he  can.  Unless 
he  is  confronted  with  very  great  difficulties,  he  is  likely  to  do  so.     To  read  in 


It  V 


V 


C//AP.  XXVIIL— OCULAR  ILLUSIONS. 


852 

cold  print,  this  seems  an  improbable  bit  of  stupidity.     It  is  one  of  the  common- 
est of  faults. 

1167.  A  single  instance  on  an  important  survey,  affecting  40  miles  of  line, 
will  illustrate  how  it  happens.  In  a  very  broad  flat  valley  which  extended  for  six 
or  eight  miles  farther  a  dry  run  was  encountered.  It  was  assumed  to  drain  to 
the  west,  and  passed  as  of  no  moment.  It  really  drained  to  the  east,  through 
a  small  rocky  overlap  about  two  miles  off,  which  opened  out  half  a  mile  be- 
yond  into  a  broad  open  valley  leading  directly  to  the  desired  terminus.  The 
ruUe-sac  gave  a  fine  line  as  long  as  it  lasted,  and  then  over  2o  miles  of  rather 
heavy  work,  with  bad  grades  and  bad  curves,  yet  it  was  run  by  an  engineer  of 
large  experience,  and  came  very  near  being  built. 

1168.  Of  all  these  types  of  ocular  deceptions  there  are  many  varia- 
tions To  thoroughly  guard  against  them  comes  with  experience  alone, 
and  rarely  with  that.  Until  they  have  been  learned  by  experience,  and 
the  engineer's  "personal  equation'  determined,  very  wide  limits  of 
error  alone  can  be  safely  assumed.  Nevertheless,  provided  the  danger 
of  error  be  realized,  it  is  not  a  particularly  serious  one,  because  errors 
of  the  eye  will  be  checked  by  surveys.  The  greater  danger  is  that 
the  untrained  eve  will  tell  such  wholly  delusive  tales  as  to  make  the 
worse  appear  the  better  course,  and  cause  that  line  or  part  of  a  line  to 
be  rejected  without  survey  which  was  really  the  best.  To  guard  against 
this  danger,  and  not  to  advise  substituting  the  eye  for  the  precision  of 
surveys  except  within  known  limits  of  safety,  this  chapter  has  been 
written. 

1169.  A  single  example  of  the  way  in  which  ocular  illusions  and  some 
of  the  causes  mentioned  in  the  previous  chapter  may  combine  to  lead  to 
wron-  conclusions  by  errors  of  reconnaissance,  pure  and  simple,  may  be 
of  vaFue  to  save  the  student  from  underrating  the  magnitude  and  .m- 
minence  of  the  dangers  against  which  he  has  been  cautioned.  It  surn- 
marizes  the  facs  of  a  very  important  piece  of  Ime  on  which  a  number 
of  causes  combined  to  bring  about  calamitously  wrong  conclusions. 
Those  particular  causes  for  wrong  conclusions  against  which  cautions 
have  been  given  are  printed  in  italics.  The  map  is  modified  somewhat, 
but  the  other  conditions  are  in  no  way  exaggerated.  Appendix  C  con- 
tain another  example,  and  the  writer  bad  made  a  list  of  nearly  a  dozen 
others  which  he  ha,d  intended  to  annotate  similarly,  but  -^-^J^^'^'^ 

The  line  was  about  loo  miles  long  from  A  to  G.  Figs.  276-7.  through 
a  region  of  much  difficulty  after  reaching  the  crucial  point  B  ot  B. 
there  an  exit  was  to  be  found  from  an  easy  open  basin  surrounding 


CffAP.  XXVIH.— OCULAR  ILLUSIONS. 


853 


A.  An  established  and  much-travelled  highway  followed  the  general 
route  selected.  ABCFG.  The  pass  B  was  a  little  easier  than  B',  and 
seemed  for.  special  reasons  much  easier  than  it  was.  The  difficulties  of 
construction  were  distributed  over  almost  the  entire  line  ACG,  so  that, 


•^{i;"">:=-y^. 


•//, 


I.  "^ 


c« 


'f' 


iv^ 


•y«&5. 


'-'l^A 


-^fv 


'# 


.vl//^ 


^■ 


'^U/., 


'I%l! 


7^- 


c>% 


Wr 


l/A> 


% 


%V^i 


7/(» 


W. 


^i^i'i^' 


%. 


% 


-^^ './/<./. 


"^"^./^i'^' 


<sM 


^<r?^i'\' 


^  2r  —  ■ 


Fig.  276. 


Fig.  277, 

although  a  costly  line  in  the  aggregate,  the  work  Tras  at  no  point  of  a 
•specially  forbidding  character. 

Another  route,  AB'DEG,  for  these  and  other  more  pardonable  rea- 
sons, was  not  even  examined  until  too  late.     Tiie  pass  B'  was  slightly 


:|» 


854 


CHAP.  XXVIII.-OCULAR  ILLUSIONS. 


CHAP.  XXVIII— OCULAR  ILLUSIONS. 


855 


I* 


higher  and  more  difficult  of  approach.    Upon  reaching  it  the  outlook  for 
the  next  few  miles,  to  the  pass  A-which  was  indeed  visible  from  B,  but 
could  not  be  recognized  as  a  pass  from  that  distance  owing  to  an  overlap. 
so  that  the  mo\intain  range  appeared  unbroken.— was  over  a  deep  and 
ugly  basin,  and  so  was  exceedingly  forbidding,  admitting  of  easy  grades 
but  plainlv  requiring  heavier  work  and  worse  alignment  to  get  them  than 
any  stretch  of  equal  length  on  the  other  line.    On  the  other  hand,  the  en- 
tire difficulties  of  construction  were  concentrated  on  this  short  stretch  of  6 
to  8  miles.     Once  through  the  pass  D  {which  could  be  reached  from  B' 
only  with  much  difficulty  and  a  long  detour),  an  open  and  unobstructed 
valley  admitted  of  a  light  and  straight  surface-line  for  some  6o  miles  to 
the  point  £,— a  traffic  of  special  value  to  the  line  being  distributed  from 
E\.oH.      At  ^  a  valley  was  struck  leading  by  a  comparatively  easy  de- 
scent directly  to  the  terminus  G,  whereas  the  other  line  at//' was  so  high 
above  the  valley  that  a  costlv  side-hill  descent  on  a  heavier  grade  was  the 
only  resource.     The  comparative  profiles  of  the  two  lines  are  shown, 
without  exaggerating  the  contrast,  in  Fig.  277. 

The  dotted  line  was  in  this  case  superior  in  every  detail,  unless  pos- 
siblv  in  cost,  for  the  stfetch  B'D,  although  not  over  8  miles  long,  was 
more  costly  than  any  40  miles  on  the  other  line.  But  the  grades  were 
materially  better,  the  line  shorter  and  with  less  curvature,  and  the  local 
traffic  it  offered  was  many  times  more  valuable  than  all  on  the  other  Ime 

put  together.  .       »     •  u 

1170.  The  error  on  reconnaissance  lay  in  passing  the  point  B  with- 
out completely  investigating  all  the  possibilities  of  the  line  B'D  before 
leavincr  it,  and  so  determining  for  a  certainty  that  the  possible  line  turn- 
ing off  through  the  gap  to  the  left  not  only  began  bad.  but  continued 
bad  Once  having  passed  through  B,  and  accepted  that  pass  as  a 
finalitv  the  case  was  hopeless.  The  two  lines  then  speedily  diverged 
from  each  other  completely,  till  they  were  40  miles  apart  and  ^Soo  feet 
different  in  elevation.  Cthen  became  another  fixed  point,  from  which 
there  was  no  possible  escape.  F  and  H'  in  their  turn  followed ;  and 
when  at  last  the  long  and  open  valley  E  came  within  sight,  the  false 
premise  that  B  must  be  the  pass,  now  70  miles  behind,  made  it  a  legiti- 
mate  and  logical  conclusion  that  it  offered  no  possibilities  for  considera- 

tion. 

1171  Had  the  reconnaissance  happened  to  begin  from  G,  the  error 
would.* in  this  particular  instance,  have  been  avoided,  for  the  natural 
line  GEHD  would  alrfiost  certainly  have  been  followed  in  the  hrst  m- 
stance.  no  natural  line  whatever  existing  in  the  direction^;//  /-.so  that  a 


large  portion  of  the  whole  cost  of  the  line  was  concentrated  on  the  initial 
stretch  GH', 

This  very  circumstance,  however,  with  the  conditions  of  relative  ad- 
vantage reversed  (especially  with  the  pass  B  a  little  less  tempting  and 
no  highway  along  GFCA),  would  have  been  almost  certain  to  result  in  an 
vrror  precisely  similar  in  principle,  with  a  reverse  result.  Starling  at  G, 
the  fine  open  line  GEH  vioxiXd  have  been  followed  with  increasing  cer- 
tainty that  it  was  the  only  line  to  take,  the  possibility  G^iV' having  been 
turned  from  as  out  of  the  question  or  perhaps  impossible  (almost  cer- 
tainly the  latter  with  an  inexperienced  man,  for  it  took  much  skill  to 
obtain  it).  Arriving  at  D,  the  reconnoiterer  would  find  himself  in  a  cul- 
de-sac,  caught  in  the  mazes  of  his  own  negligence  and  hasty  preposses- 
sions. A  beautiful  line  was  behind  him,  but  8  miles  of  tunnels  and  via- 
ducts were  before  him,  from  which  there  was  absolutely  no  escape  with- 
out going  back  again  to  G,  mentally  as  well  as  physically,  and  picking 
out  the  line  GHFC,  every  foot  of  which,  while  nowhere  excessively  diffi- 
cult, was  a  forced  line,  resulting  from  having  got  into  the  hole  C  and 
having  to  get  out  of  it  somehow  in  the  direction  G.  Under  these  cir- 
cumstances, there  being  but  the  two  lines,  so  widely  separated,  it  would 
have  been  well-nigh  a  certainty  that,  had  the  reconnaissance  began  at 
G  instead  of  yi,  the  tempting  plains  GD  would  have  proved  an  even  more 
irresistible  bait  than  the  pass  B  to  bias  the  mind  against  fair  and  com- 
plete examination  of  even  the  possibilities  of  the  other  line. 

1172.  The  writer  is  able  to  give  no  more  apt  illustration  than  this  oi" 
the  importance  of  following  the  seemingly  over-minute  instructions  of 
this  and  the  preceding  chapter,  whether  because  of  the  importance  of  the 
instance,  or  because  of  the  salient  and  marked  topographical  features, 
which  do  not  confuse  the  mind  with  a  multitude  of  detail.  There  was 
just  one  point  on  the  line  of  reconnaissance,  and  that  point  one  affording 
a  most  forbidding  and  helpless  outlook,  where  there  was  reasonable 
chance  to  discover  the  error.  Guessing  that  an  overlapped  mountain 
eight  miles  off  had  no  pass  through  it,  and  that,  even  if  it  had.  the  ragged 
eight  miles  which  could  be  seen  meant  a  ragged  eighty  miles  beyond  it 
which  could  not  be  seen,  and  which  was  smooth  as  a  prairie,  cansed  the 
error.  Examples  might  easily  be  multiplied  of  similar  errors,  and  some 
of  them,  as  in  the  instance  mentioned  in  Appendix  C,  of  much  greater 
magnitude.  Valley  lines  are  particularly  apt  to  be  rejected  in  this  way, 
without  thorough  examination,  because  of  supposed  obstacles  which  are 
largely  imaginary. 


\ 


856 


CHAP.   XXIX.— WHEN   TO  MAKE   SURVEYS, 


CHAP.   XXIX.— WHEN  TO  MAKE  SURVEYS.  857 


i. 


CHAPTER  XXIX. 


WHEN    TO    MAKE    SURVEYS. 


1173.  The  reconnaissance  having  been  thoroughly  and  carefully  made, 
the  most  important  part  of  the  location  is,  in  general,  concluded.  For, 
assuming  all  business  as  well  as  topographical  questions  to  have  been  as 
carefully  weighed  as  is  possible  in  advance  of  surveys,  a  difference  be- 
tween any  two  lines  which  cannot  be  detected  by  such  an  examination 
can  hardly  be  a  vital  one,  seriously  affecting  the  future  of  the  property. 

Nevertheless,  although  really  ruinous  errors  can  rarely  come  from  an 
inadequate  amount  of  surveying  or  from  imperfect  balancing  of  their 
nice  results,  good  or  bad  judgment  in  the  conduct  of  surveys  may  well 
make  a  large  difference  in  the  earning  capacity  of  the  line,  and  a  still 
larger  difference  in  first  cost, — that  so  often  vital  consideration  for  the 
original  projectors. 

1174.  Drawing  an  analogy  from  the  construction  of  a  building,  the 
reconnaissance  is  like  the  selection  of  the  site  for  a  building,  the  deter- 
mination of  its  size  and  general  plan,  and  the  rough  but  (in  skilled  hands) 
close  guessing  at  the  cost  of  comparative  plans.  The  survey  is  like  the 
preparation  of  the  detail  plans  and  exact  estimation  of  cost.  The  con- 
struction of  a  railway  is  like  the  construction  of  a  building  after  all  these 
details  have  been  determined. 

1175.  The  seeming  paradox  is  yet  true,  that  both  too  much  and  too 
little  time  and  money  is  generally  devoted  to  surveys.  Too  many  miles 
of  line  are  surveyed,  but  that  which  is  surveyed  is  not  surveyed  as  well 
and  thoroughly  as  it  should  be.  The  perhaps  dangerous  assertion  (dan- 
gerous because  it  may  give  an  excuse  for  hasty  and  over-confident  con- 
clusions) has  already  been  made  (par.  1 128),  that  more  often  than  not  there 
is  only  one  general  route  between  two  points  to  be  connected  by  railway 
of  sufficient  comparative  promise  to  justify  even  a  flying  line  over  it;  but 
good  and  certain  reasons  should  appear  for  failing  to  run  at  least  two 
lines.  Doubtless  sometimes  there  may  be  real  necessity  to  survey  three 
or  more  lines,  but  the  writer  has  never  happened  to  meet  such  a  case. 
Considerations  of  policy,  however,  often  require  the  running  of  numerous 


lines  for  which  no  engineering  necessity  exists;  and  in  the  study  of  the 
details  of  location,  over  distances  of  one  to  twenty  miles,  there  are  often 
a  dozen  or  more  different  lines  or  modifications  of  lines,  which  will  re- 
quire  to  be  attentively  studied. 

1176.  The  true  method  of  determining  whether  or  not  there  is  need 
to  survey  more  than  one  general  route  is  this: 

Having  carefully  examined,  in  the  manner  detailed  at  length  in  the 
preceding  chapter,  every  possible  line,  and  having  gathered  as  full  details 
as  possible  of  the  actual  cost  and  gradients  and  resulting  traffic  and 
earnings  of  other  lines  from  previous  experience  and  study  of  recorded 
results,  a  maximum  and  minimum  estimate  should  be  made  of  each  • 
that  IS  to  say,  it  should  be  said  of  each,  "This  line  will  apparently  af* 
ford  gradients  of  -  per  cent,  which  estimate  cannot  (guarding  well 
the  'cannot')  be  in  error  more  than  -  per  cent  either  way,  giving 
a  range  for  possible  error  of  judgment  of  from  -  to  -  per  cent      Its 

cost  will  apparently  be  about  $ .  and  cannot  range  above  or  below 

this  estimate  more  than  -  per  cent  either  way.     It  will  reach  (such  and 
such)  sources  of  traffic  more  (or  less)  than  the  other  lines,  which  cannot 

add  less  than  $ per  annum  to  the  net  revenues  of  the  company 

and  might  add  as  much  as  % .     In  the  minor  details  of  distance 

curvature,  and  rise  and  fall  it  has  advantages  (or  disadvantages)  which 
may  be  considered  as  liable  to  affect  the  future  revenues  per  annum  of 

the  company  by  from  % to  $ ." 

If.  then  after  making,  with  more  or  less  elaboration,  an  estimate  of 
this  kind  for  each  of  the  various  possible  lines,  it  be  found  that,  taking 
the  most  unfavorable  view  deemed  possible  of  that  line  which  seems  the 
best.  ,t  IS  still  a  better  line  than  the  most  favorable  possible  result  from 
any  of  the  others,  it  is  a  waste  of  time  and  money  to  survey  more  than 
one  Ime. 

1177.  in  the  application  of  this  rule  there  is  real  danger  of  error,  but 
the  danger  l,es.  not  in  the  rule  itself,  but  in  careless  or  over-confident 
appl.cat.on  of  ,t;  not  in  taking  mere  guesses  at  maxima  and  minima  as 
dec.s.ve.  but  .n  failing  to  make  the  limits  wide  enough.     Even  with  the 
most  elaborate  precautions  all  human  judgment  is  fallible.     No  amount 
of  surveys  wdl  do  much  to  prevent  an  incompetent  man  from  selecting 
andbmld.ng  oneof  tl,e  many  possible  wrong  lines  instead  of  the  one 
nght  Ime  which  he  should  have  chosen.     On  the  other  hand,  no  amount 
01  skill  and  experience  will  make  a  man's  unassisted  judgment  as  to  the 
absolute  results  of  a  possible  future  survey  anything  more  than  the  rudest 
ot  rude  approximations.     Nevertheless,  the  most  inexperienced  engineer 


W1 


k 


1  ' 


4 


1611-,; 


^, 


858 


ClfAP.    XXIX.— WHEN   TO  MAKE   SURVEYS. 


knows  that  a  line  in  average  country  cannot  cost  more  than  the  St. 
Gothard  Railway  nor  less  than  the  cheapest  line  he  can  find  record  of 
over  the  Illinois  prairies,  and  that  the  grade  which  he  can  certainly  attain 
lies  somewhere,  say.  between  a  level  and  2  percent.  A  moderate  amount 
of  experience  and  skill  enables  these  limits  to  be  much  contracted,  while 
still  leaving  margin  enough  to  afford  as  nearly  absolute  safety  as  is  pos- 
sible in  human  affairs.  It  is  in  the  rash  and  over-confident  fixing  of  the 
limits  that  the  danger  lies,— Und  it  is  a  great  one,— and  not  in  the  delib- 
erate and  conscious  acting  upon  them  after  once  fixing  them  ;  for  it 
must  be  done  consciously  or  unconsciously  in  any  case,  sooner  or  later. 

1178.  Acting  upon  the  rule  given  will  generally  lead  the  quite  inex- 
perienced man,  moreover,  to  survey  two  lines  at  least,  as  it  is  but  right 
that  it  should,  because  his  limits  of  error  are  so  very  wide.  The  unduly 
great  importance  attached  to  the  minor  details  of  alignment,  distance, 
curvature,  and  rise  and  fall  is  responsible  for  much  unnecessary  survey- 
ing. In  these  details  large  differences  very  often  exist,  and  how  large 
they  are  can  only  be  determined  with  any  degree  of  precision  by  actual 
survey.  But  this  is  not  so  of  traffic  advantages,  nor  even  of  grades,  nor 
do  surveys  help  to  develop  the  former. 

1179.  Even  in  the  case  of  lines  through  difficult  country,  passing  over 
one  or  more  high  summits  and  with  no  local  traffic  to  consider,  connect- 
ing terminals  only,  it  will  in  general— although  with  not  infrequent  ex- 
ceptions— be  found  that  thorough  and  faithful  reconnaissance  will  remove 
all  doubt  as  to  which  is  the  proper  route ;  many  details,  of  course,  requir- 
ing extensive  examination.  The  lowest  pass  or  passes  are  so  commonly 
the  only  proper  place  for  the  line,  that  it  may  almost  be  said  to  be  a  law 
of  nature,  and  the  lowest  pass  can  be  determined  with  close  approxima- 
tion by  the  barometer  and  study  of  the  drainage  lines  alone.  The  natural 
advantages  of  routes  by  the  lowest  pass  result,  not  alone  from  its  lowness, 
but  from  the  fact  that  at  such  points  natural  causes  have  produced  more 
manageable  slopes,  a  greater  proportion  of  good  material,  and  a  shorter 
distance  to  pass  over  before  reaching  the  easier  and  more  practicable 
country,  affording  favorable  grades  and  cheap  construction.  The  lines 
from  Vera  Cruz  to  the  city  of  Mexico,  described  m  Appendix  C,  are  an 
example  on  an  immense  scale  of  the  certainty  with  which  a  single  gen- 
eral route  can  be  picked  out  as  alone  worthy  of  instrumental  examination, 
even  in  regions  of  the  most  extreme  difficulty.  Too  much  is  trusted 
to  surveys,  because  only  the  facts  determined  on  survey  are  taken  into 
consideration.  As  a  rule,  the  general  route  may  safely  be  selected  in 
advance  by  reconnaissance  merely.     If  the  engineer  be  not  able  to  select 


CHAP.   XXIX.— WHEN   TO  MAKE   SURVEYS, 


85^ 


w 

Pi 


wisely  without  surveys,  he  will  be  no  better  able  after  the  surveys  are 
completed.     But  to  this  rule  there  are  exceptions. 

fQ  1180.  In  such  cases  as  Fig.  278,  where  there  is  a  certain 

natural  line  which  manages  to  miss  three  or  four  consider- 
able towns,  CDEF,  lines  running  to  and  into  those  towns 
should  always  be  run,  as  shown  by  the  dotted  lines,  whether 
'••;£  the  other  line  is  run  or  not.  This  is  a  very  common  case, 
because  towns  are  apt  to  be  in  hollows  or  otherwise  incon- 
venient of  access,  and  a  better  grade,  as  well  as  cheaper 
right  of  way,  can  often  be  had  by  keeping  away  from 
them. 
oy  I  The  dotted   line  in  Fig.  278  is  a  very  awkward  looking 

line  by  comparison  with  the  solid  one,  but  if  its  comparative 
length  be  carefully  measured,  it  will  be  found  to  differ  but  a 


>C 


,0 

V; — .c? 

v° 

*%      N 

\  *^ 

%^      *^ 

*      \ 

•-      *-    -. 

C----V-.S 

%               V     Mr 

''•..    f 

*%       • 

% 

*..    ' 

Vv* 

Fig.  279. 


Fig.  380. 


trifle  in  length  while  its  operating  advantages  are  materially  greater, 
unless  its  grades  should  be  decidely  against  it. 

1181,  In  such  cases  as  Figs.  279,  280,  the  line  running  through  BC 
should  likewise  be  always  run.  This  is  more  likely  to  be  done  with 
Fig.  279  than  with  Fig.  280.  In  each  the  distances  AB,  BC,  and  CD  are 
precisely  the  same;  but  the  angular  deviation  from  the  desired  direction 
is  greater  in  Fig.  280,  making  it  correspondingly  repellent.  By  varying^ 
the  intermediate  distances,  leaving  the  aggregate  the  same,  much  greater 
contrasts  can  be  obtained,  as  the  reader  can  find  out  in  a  rather  in- 
structive way  with  a  piece  of  black  thread  and  a  few  pins. 


86o 


CHAP.    XXX.— THE  FIELD-WORK  OF  SURVEYS. 


CHAP.    XXX.— THE  FIELD-WORK  OF  SURVEYS. 


86  r 


■*^( 


S' 


'^  r*^- 


CHAPTER  XXX. 

THE   FIELD-WORK   OF   SURVEYS. 

1182,  In  general,  the  economical  manner  of  making  surveys  of  a  route 
which  it  has  once  been  decided  to  survey,  and  which  offers  any  appreci- 
able difficulties,  is  as  follows : 

The  surveys  should  be  planned  from  the  beginning  with  the  idea  that 
not  less  than  three,  generally  four,  and  frequently  five,  successive  lines 
will  be  run  over  the  route  for  the  purpose  of  fully  completing  the  final 
location,  viz.:    An    exploration  line,   first    preliminary,    second 

PRELIMINARY,  FIRST    LOCATION,    FINAL    LOCATION.      The  attempt  tO  do 

with  less  than  this  on  lines  of  any  considerable  difficulty  is  false  economy; 
or  rather,  it  is  an  attempt  at  economy  which  does  not  usually  result  in 
any  real  saving  of  either  time  or  money,  even  in  the  mere  direct  cost  of 
the  survey,  while  it  does  seriously  endanger  the  excellence  of  the  com- 
pleted work.  Running  what  may  appear  to  be  so  many  lines  does  not 
necessarily  involve  devoting  much  more  time  to  surveys,  but  only  dis- 
tributing the  work  somewhat  differently. 

1183.  First,  the  exploration  line,  or  what  is  popularly  called  a 
"shoo-fly"  line,  should  be  run  as  rapidly  as  possible  over  the  entire  route 
which  it  is  contemplated  will  ultimately  constitute  the  road.  In  the 
case  of  very  long  lines,  circumstances  may  make  it  necessary  to  carry  on 
and  complete  the  surveys  by  sections,  but  this  is  to  be  regretted  and 

avoided. 

The  purpose  of  this  first  line  should  be  merely  to  get  a  general  idea 
of  the  topography  of  the  countr>%  and  especially  of  the  gradients,  and  it 
should  be  passed  over  all  alternate  routes  which  it  is  proposed  to  survey 
later  as  tliey  are  encountered.  No  attempt  to  study  the  location  in  de- 
tail should  be  made,  except  to  make  sure  that  the  line  being  passed  over 
is  certainly  feasible,  and  probably  on  the  most  favorable  ground  in  the 
vicinity,  especially  in  respect  to  gradients. 

For  this  line  a  mere  compass  line  will  not  only  answer  as  well,  but  is 
in  general  decidedly  preferable  to  a  transit  line,  except  in  easy  open  coun- 


try, for  reasons  discussed  in  par.  1185.  It  gives  a  mere  string  of  distances 
and  elevations  from  which  to  construct  a  scheme  of  grades  and  lay  out 
the  line  as  a  whole.  The  following  line  is  not  guided  by  it  in  any  ac- 
curate way,  nor  is  even  a  map  of  it  to  a  large  working  grade  generally 
worth  the  making. 

The  limit  of  speed  will  lie  in  the  levelling,  and  accordingly  two  rodmen 
should  be  used  if  there  be  only  one  leveller,  or  better,  two  complete  level 
parties  (especially  if  the  country  is  at  all  rough),  to  be  jumped  over  each 
other's  heads.  This  extra  force  does  not  expedite  the  work  enough  to 
pay  if  the  levelling  only  were  to  be  considered,  but  as  the  time  of  the 
whole  party  is  to  be  considered,  it  does  pay,  and  it  is  to  some  extent  a 
safeguard  against  errors,  as  the  levellers  are  not  so  hurried.  Sometimes 
an  e.xtra  man  to  keep  notes,  with  two  rodmen,  may  be  preferable  to  two 
level  parties. 

A  full-scale  profile  of  the  ordinary  form  mayor  may  not  be  made: 
it  will  probably  be  a  waste  of  time  to  make  it  for  the  entire  distance; 
but  a  small  scale  profile,  to  about  one  tenth  the  usual  horizontal  scale 
and  one  fifth  the  usual  vertical  scale  (par.  905),  should  by  all  means  in  all 
cases  be  made.  Fig.  281  shows  one  form  of  such  profile  for  a  completed 
road,  to  a  scale  of  about  one  inch  per  mile,  as  engraved,  which  was  origi- 
nally 4000  feet  per  inch,  or  ten  times  the  usual  profile  scale.  It  is  un- 
necessary to  encumber  a  similar  profile  for  location  purposes  with  details 
of  the  minor  structures. 

Following  this  line  comes — 

1184.  Secondly,  THE  PRELIMINARY  line  proper  (which  may  be  two 
successive  lines),  which  is  to  serve  as  the  basis  for  the  final  location.  On 
this  line,  in  all  but  very  easy  country,  careful  topography  should  be  taken, 
and  taken  in  the  field,  in  the  manner  considered  in  Chap.  XXXI.  The 
purpose  of  the  preliminary  is  to  serve  as  a  framework  for  this  topog- 
raphy and  the  located  line,  and  it  is  run  to  follow  closely  the  ground 
where  the  location  is  likely  to  lie,  as  nearly  as  the  eye  can  estimate  it„ 
using  any  angles  which  come  handy  for  this  purpose.  Fig.  282  shows 
how  a  very  well  located  preliminary  is  apt  to  lie  with  relation  to  the  lo- 
cated line,  being  very  close  to  it,  and  yet  entirely  independent  of  it.  The 
average  preliminary  will  diverge  from  the  location  more  than  that  shown. 

This  line  also  may,  without  any  serious  disadvantage,  and  with  cer- 
tain considerable  advantages,  be  a  compass  line,  if  any  time  is  thereby 
saved  to  be  devoted  to  more  important  matters.  The  only  advantage  of 
a  transit  line  (and  it  is  a  slight  one)  is  that  it  enables  the  map  to  be  some- 
what more  accurately  made.     The  located  line  does  not  coincide  with 


i 


CHAP.  XXX.— TRANSIT  vs.  COMPASS  LINES. 


863 


3 
P 

•O     —    f6 
3      W      W 

2    5    "^ 

a   -•  rt 
P  3  » 

*^  -  2* 


the  preliminary  at  any  point,  unless  by  accident,  nor  is  there  any  inten- 
tion that  it  should,  nor  is  the  location  checked  by  the  preliminary,  to  any 
great  extent,  but  by  the  profile  and  topography. 


Fig.  282. — Preliminary  and  Located  Line. 
TRANSIT  7/J.  COMPASS   LINES. 

1185,  An  unreasonable  prejudice  exists  in  the  minds  of  some  engi- 
neers against  compass  lines,  because  of  a  false  assumption  that,  because 
there  is  a  certain  lack  of  precision  in  it,  the  work  is  therefore  inaccurate. 
On  the  contrary,  the  chances  of  substantial  accuracy  in  the  final  result, 
considered  as  a  whole,  are  better  with  the  compass  than  with  a  hasty 
transit  line  (it  being  assumed  that  no  local  attraction  exists),  since  large 
cumulative  errors  cannot  occur  in  the  one  case,  while  they  can  in  the 
other.     This  is  evident  if  we  consider  how  the  two  lines  are  run. 

A  compass  line,  strictly  so  called,  is  run  entirely  by  foresight,  guided 
by  the  needle  alone.  The  chief  of  party  goes  first,  accompanied  by  the 
"  back  flag,"  who  is  now  a  front  flag,  and  picks  out  the  points  to  which 
to  run  (unless  a  straight  line  is  being  run,  where  the  line  is  given  from 
the  instrument  as  soon  as  the  compass  has  come  to  rest).  The  chain- 
men  follow,  the  head  chainman  behind,  chaining  in  a  straight  line  as 
nearly  as  the  eye  can  determine  from  the  point  where  the  instrument  is 
standing  toward  the  flag.  As  the  line  is  sighted  in  by  foresight  this  is 
near  enough  for  all  practical  purposes,  since  more  than  two  or  three 
inches  deviation  is  not  probable. 

The  transitman,  or  rather  compassman,  is  at  the  rear  of  the  whole 
party,  and  simply  takes  the  bearing  of  each  line  by  the  needle,  or,  if  a 
given  line  is  to  be  continued,  gives  the  proper  line  to  the  flagman  in  ad- 
vance as  nearly  as  it  can  be  determined  from  the  needle.  If  a  tree  or 
other  obstruction  is  met,  the  instrument  is  simply  moved  to  the  other 
side  of  it.  placed  on  the  same  line  prolonged  as  nearly  as  may  be  (it  may 
be  a  foot  or  even  two  or  three  feet  off),  and  reset  to  the  same  bearing.  If 
accurately  reset,  it  will  give  a  line,  not  the  same  as  the  original,  but  par- 
allel thereto.     Usually  there  is  a  few  minutes*  error  in  each  bearing  to 


864 


CHAP.  XXX  — TRANSIT  vs.   COMPASS  LINES. 


< 


one  side  or  the  other.  On  the  other  hand,  when  the  line  behind  is* 
visible,  it  is  very  common,  even  in  running  compass  lines  to  run  by  back 
sight  for  considerable  distances,  as  on  a  transit  line,  or  at  least  to  check, 
the  bearings  thereby.  This  practice  does  not  especially  conduce  to  real 
accuracy,  however,  but  rather  the  contrary. 

1186.  A  transit  line,  on  the  other  hand,  is  run  entirely  by  back  sight, 
from  an  accurate  sight  on  a  plug,  and  all  angles  are  measured  exactly  by 
the  vernier.  It  is  very  much  more  precise  than  a  compass  line,  and  is 
the  only  suitable  method  for  running  in  location  lines,  and  the  only 
method  now  practised,  although  it  was  not  used  in  the  earlier  days  of 
railways.     It  has  these  disadvantages : 

1.  It  requires  the  cutting  away  of  all  obstructions,  or  tedious  offsets 
around  them,  thus  causing  great  loss  of  time  and  needless  destruction  of 
vegetation. 

2.  Any  error  in  measuring  or  laying  off  an  angle  is  cumulative,  or 
continued  indefinitely  in  plotting  the  notes.  To  guard  against  this,  the 
angles  in  well-conducted  transit-work  are  always  checked  by  the  needle,, 
but  nevertheless  this  danger  causes  frequent  annoyance  in  practice. 

3-  The  angles  measured  are  never  used  as  such  in  properly  conducted 
mapping,  but  have  to  be  reconverted  into  bearings.  This,  however,  is  a 
small  matter, and  may  and  should  be  avoided  in  the  manner  described  in 
par.  1242. 

1187.  On  the  other  hand,  there  is  this  to  be  said  for  the  transit  line — 
that  it  is  not  unfrequently  the  case  that  no  time  is  saved  by  using  the 
compass  instead  of  the  transit,  since  the  level  limits  the  rate  of  progress 
in  any  case.  When  this  is  so,  it  is  undoubtedly  as  well  to  run  the  more 
accurate  line,  and  wherever  there  is  danger  of  local  attraction  it  is  the 
only  proper  one  to  run.  But  it  should  be  clearly  recognized  that  the 
transit  line  is  to  be  preferred  only  for  these  reasons,  and  that  wherever 
they  do  not  obtain,  the  true  engineer  will  immediately  adopt  the  compass 
instead.  The  not  infrequent  notion  that  the  use  of  the  compass  is  de- 
rogatory to  his  skill  and  unworthy  of  him,  simply  because  it  is  less  pre- 
cise, is  absurd.  Under  the  doctrine  of  chances,  which  is  as  well  estab- 
lished as  the  law  of  gravitation,  the  probable  average  error  in  a  series 
of  observations  decreases  as  the  square  root  of  their  number.  If  in  a 
single  observation  it  be  10  ft.,  in  100  observations  it  will  be  only  i  ft. 
each,  and  in  10,000  observations  only  o.i  ft.  For  all  the  legimate  uses 
of  preliminary  lines  (they  are  sometimes  used  illegitimately)  such  errors- 
in  no  way  detract  from  its  value  and  utility. 


CHAP.  XXX.— TRANSIT  vs.   COMPASS  LINES. 


865 


1188.  The  writer  has  not  foqnd  that,  even  when  the  imperfections  of 
mappmg  are  reduced  as  they  should  be  by  the  use  of  large  scales  the 
superior  precision  of  the  transit  is  of   much  practical   moment,  and   he 
feels  a  preference  for  the  use  of   the  compass  on  preliminaries,  other 
things  being  equal,  believing  that  it  is  easier  for  all  concerned,  and  that 
there  is  less  danger  of  giving  thought  to  splitting  tacks  with  the  cross- 
hairs which  might  better  be  given  matters  of  importance.     It  is  well  for 
the  locating  engineer  to  be  frequently  reminded,  especially  in  acquiring 
his  traming,  that  instrumental  accuracy  is  not  an  end  in  location  as  in 
ordinary  surveying,  but  simply  a  means  to  an  end;   that  a  thoroucrhly 
excellent  location  may  be  made  with  the  level  and  chain  alone  with- 
out  other  instruments,  and  that  a  bad  line  is  not  a  whit  better  for  bein^ 
mstrumentally  precise.     No  angular  or  lineal  error  which  is  not  great 
enough  to  affect  the  riding  of  the  locomotive  over  the  track  is  of  ulti 
mate  importance,  while  on  the  other  hand  errors  of  judgment,  or  unwill- 
ingness  to  disturb  an  accurately  run  line  with  a  "  good  "  profile  are  evils 
of  great  importance.     As  it  is  always  easier  and  in  the  end  less  costly 
to  be  accurate  than  inaccurate,  the  good  engineer  always  will  be  accu- 
rate in  all  essentials,  but  he  will   not  waste  time  in  attempting  unneces- 
sary precision  which  does  not  add  appreciably  to  the  final  value  of  his 
work. 

1189.  The  levels  should,  on  the  preliminary  lines,  be  kept  correct  by 
checking  on  the  exploration-line  benches  and  re-running  all  doubtful 
sections,  at  any  seeming  cost  to  the  progress  of  the  survey  No  time  is 
saved  in  the  end  by  doing  otherwise.  No  time  should  be  wasted  in  try- 
ing to  keep  the  stationing  continuous. 

1190.  Whenever   the   country  becomes   quite   rough,  and   especially 
where  a  grade-l.ne  is  to  be  fitted  to  the  ground,  the  preliminary  line 
should  from  the  beginning  be  divided  up  into  two  by  running  a  first  and 
second  preliminary.     It  might  seem  a  better  way  of  expressing  the  same 
truth  to  say  that  whenever  it  is  found  that  any  section  of  the  preliminary 
does  not  come  sufficiently  near  to  where  the  final  line  will  be  it  should 
be  run  over;   but  that  is  not  true,  and  that  plan  of  conducting'surveys  is 
more  likely  to  result  in  loss  of  time  and   bad  work.     The  true  way  of 
conducting  surveys.from  beginning  to  end.  is  to  recognize  in  tiie  begin- 
ning where  there  is  likely  to  be  difficulty  and  to  run  additional  preliminary 
lines  COMPLETE  over  those  sections,  thus  gaining  opportunity  for  more 
careful  study  and  more  thorough  knowledge.     Even  then,  there  will  be 
occasions  enough  when  it  will  be  necessary  to  "back  up"  and  correct 
false  steps  from  time  to  time  on  all  the  lines,  to  doing  which  occasionally. 

33 


866 


CHAP.  XXX.— TRANSIT  vs.  COMPASS  LINES. 


CHAP,  XXX.^IWNNING  IN   THE  LOCATION. 


867 


I 


of  course,  it  is  not  intended  to  object;  but  in  cases  where  there  seems 
more  than  an  even  chance  that  the  "backing  up"  will  be  a  large  fraction 
of  the  advance,  it  is  always  good  practice  to  give  up  from  the  first  all 
idea  of  completing  the  preliminary  work  with  one  line. 

1191.  When  two  preliminaries  are  thus  run  in  succession,  they  should 
in  general  be  frequently  tied  together  and  plotted  on  the  same  sheets  so 
as  to  give  continuous  topography,  all  errors  in  the  plotting  (which  with 
good  work  should  be  small)  being  left  in  the  tie-lines,  and  the  angles 
and  distances  of  the  second  preliminary  not  distorted  to  make  a  fit. 

1192.  In  extreme  cases,  as  in  that  shown  in  Fig.  216  and  others,  the 
difficulties  of  location  are  so  great,  for  short  distances,  that  all  idea  of 
determining  the  final  location  from  lines  must  be  abandoned,  and  a  com- 
plete topographical  study  of  the  difficult  section  made,  after  the  fashion  of 
what  was  formerly  customary  on  surveys  for  English  railways.  But  such 
cases  are  very  rare,  and,  in  general,  working  from  single  lines  is  all- 
sufficient. 

1193.  Thirdly.  The  location  line.— This  line  also  should  in  general 

be  divided  into  two  and  done  twice  over,  complete. 

It  will  save  time  often  and  money  always,  and  is  the  only  safe  way  to 
insure  good  work,  especially  where  it  is  necessary  to  entrust  a  part  of  the 
work  to  men  of  little  experience.  The  first  location  should  be  made  ap- 
proximately correct  as  it  goes  along,  by  backing  up  to  correct  the  more 
serious  and  evident  defects,  but  it  is  far  better  that  all  minor  changes 
and  modifications  should  be  merely  studied  and  thought  over  as  the  first 
location  advances,  and  that,  after  completing  the  first  line  and  taking 
adequate  cross-sections  of  it  or  of  a  considerable  part  of  it,  the  party 
should  be  recalled  to  run  the  whole  of  it  over  again,  aided  by  its  plotted 
cross-sections. 

1194.  This  results  not  only  from  the  direct  advantage  of  having  the 
details  of  the  whole  line  at  once  to  study,  but  from  the  fact  that  the 
problem  is  studied  more  coolly  and  dispassionately,  with  the  aid  of  more 
extended  knowledge  and  experience  (the  whole  party  being  now  skilled 
in  their  work),  and  without  that  strong  inducement  to  tolerate  bad  work 
and  "let  well  enough  alone"  which  is  derived  from  the  tedious  and  fret- 
ting process  of  "  backing  up."  A  little  consideration  of  the  weaknesses 
of  human  nature  will  make  it  clear  why,  for  many  reasons,  this  should  be 
so  ;  and  the  writer  cannot  urge  too  strongly  that  really  good  work  can- 
not be  otherwise  secured,  under  the  conditions  which  usually  prevail. 
Unnecessarily  sharp  and  frequent  curvature  will  be  left  in  the  line;  side- 
hill  work  on  steep  slopes  will  have  its  centre  line  a  foot  or  two  out  of  its 


proper  place,  and  be  unnecessarily  heavy  •  rock  cut<;  w.li  k. 
save  fills,  and  many  similar  imper'fection's'  be  left    n  T      hneThlch  ar^ 
no  ,  mdeed  of  great  comparative  moment  to  the  line   tsel    sLe  thev  do 
not  rnpre  Us  earning  capacity,  but  which  are  often  o'f  se   L    momen't  to 

1  itrfTh^mTarso^h^^^^^  \i  '---'-^ '''  ^-  --  ="th: 

uneir  means,  so  that  it  finally  passes  out  of  their  hands. 

ORGANIZATION  OF  PARTY. 

ranks'^'r^.n"'!!!^''^"^.'''""''^  ""  f"l'-handed,  especially  i„  the  lower 
ranks.      To  do  otherwise  s  false  economy      tk«  ^         •      •  lower 

general  be  as  follows  :  ^^onomy.     The  organization  should  in 

I.   Chief  of  Party,  with  nothing  to  do  excent  tn  t^^r.  u- 

even  where  there  is  no  clearing  ^"  "  ^""''"''"y  ^~"°'"y. 

3-   The  level  party,  consisting  of  leveller    rf>Hmo„    ^  a    ■ 

..its  the  Jee.  .  the  wloTetrS^to"  r^tercaT.et^lirhVr 
ployed  to  advantage  since  they  expedite  the  work  someXt      '        """ 

4.    I  he  topographical  Party,  varying  from  one  to  tlir^«  ^    t 
according  to  the  country.    This  pa^yl  usuairno"  ri'lTno^glrLr; 

in/of  rtr;rr  o':  roiTis  itV:'' ''-''  -^-^"^  '^°-'^'- 

after  all  can.p  movements  and  Censes  '^°'"™--y-  -'-  'ooks 

conSt^^uI^a^yTsttlr'""  T'  '"  "'''=""  ^°"""^ -"  °''- 
...regionsan^ea-c— :.-^^^^^^^^^^^^ 

RUNNING   IN  THE   LOCATION. 

nne"'!/h"erarupro:r^:::f  ::!?  '•',^  "°'-  forthe,ocatio„ 
-thout  capping  th^e.  at  ai^r^Iii^  w^i^il'va'arr^gtS 


868 


CHAP.  XXX.-KUNNING  IN    THE  LOCATION. 


CHAP.  XXX.— RUNNING  IN   THE  LOCATION. 


869 


Ordinarily,  however,  a  narrow  belt  of  topography  is  both  expedient  and 
necessary.  If  the  preliminary  work  has  been  skilfully  conducted,  it  will 
need  to  be  but  narrow.  On  this  topography  a  "  paper  location  is 
made,  in  the  manner  we  shall  consider  later;  full  notes  of  the  projected 
alignment,  and  of  the  points  of  curve  and  tangency  taken  off,  and  a  pro- 
file  of  the  paper  location  made. 

The  purpose  of  the  location  field-work  is,/rj/,  to  put  this  paper  loca- 
tion on  the  ground  so  as  to  afford  at  least  as  good  a  profile  as  the 
"  paper"  profile,  and,  secondly,  to  study  the  line  thus  put  upon  the  ground 
in  more  detail  than  was  possible  before  the  precise  position  of  the  line 
had  been  so  accurately  fixed.  , 

In  running  in  the  notes  of  such  a  paper  location,  the  most  experienced 
chief  of  partv  never  expects  that  the  notes  can  be  followed  in  the  held 
without  some  slight  correction  at  almost  every  curve.  The  profile  will 
be  found  to  be  running  too  high  or  too  low ;  errors  in  the  field-work  and 
the  topo-raphy  will  be  discovered  ;  new  changes  of  alignment  will  sug- 
crest  themselves,  and  in  other  ways  changes  will  be  made.  Nevertheless 
The  correspondence  in  general  will  be  very  close  ;  so  much  so  that  it  will 
be  difficult  to  distinguish  the  paper  and  actual  location  profile.  They 
may  both  be  wrong  and  bad,  but  they  are  apt  to  agree  with  each  other 

quite  closely.  . 

1197.  No  new  topography  should  be  taken  with  this  line,  but  instead 
of  it  cross-sections  only,  extending  from  30  to  100  feet  on  each  side, 
according  to  locality.  These  cross-sections  should  be  plotted  as  closely 
together  as  clearness  permits,  WITH  THE  even  stations  at  uniform 
DISTANCES  APART,  even  at  the  expense  of  crowding  the  sections  so  that 
they  overlap  each  other  greatly,  which  does  no  particular  harm.  The 
character  of  the  material,  and  especially  the  precise  limits  of  the  rock, 
should  be  carefully  determined.  Boring  tools  of  many  different  forms 
(the  simplest  of  which  is  the  common  post-augur)  are  readily  obtained,, 
by  which  it  may  be  positively  determined  where  the  rock  lies,  at  no  great 
cost,  and  much  perhaps  needless  expense  saved.  It  rs  »very  common 
thing  to  have  shallow  rock-cuts  turn  up  in  the  bottom  of  excavations, 
which  are  always  disproportionately  expensive,  and  often  might  as  well 
as  not  have  been  avoided  altogether. 

Aided  by  these  cross-sections,  the  location  should  be  carefully  re- 
studied,  not' by  the  construction  parties,  who  have  other  things  to  think 
of  and  are  often  incompetent  for  the  work,  but  by  a  location  party  who 
re-run  the  entire  line  complete.  There  will  still  be  chances  enough  for 
the  construction  engineer  to  improve  on  it. 


1198.  This  last  work  especially,  and  in  fact  all  running  of  curves  and 
tangents,  is  greatly  facilitated  by  the  use  of  a  proper  system  of  transition 
curves.  What  transition  curves  are,  and  why  they  can  never  be  omitted 
if  an  easy-riding  road  is  to  be  obtained,  have  been  already  stated  (pars. 
279-81).  and  the  proper  method  of  running  them  in  is  given  in  the  field- 
book  which  follows  this  volume.  It  would  lead  us  too  far  to  attempt  it 
in  this.  The  nature  of  the  advantage  which  they  give  in  making  a  good 
location  is  this  : 

Ail  transition  curves,  by  whatever  method  they  are  run,  must,  from 
their  very  nature,  have  the  form  shown  in  Fig.  283.     The  actual  tangent 

must  lie  parallel  with 
and  outside  of  (at  a 
given  offset  from)  what 
would  be  the  tangent  if 
the  main  curve  were 
prolonged  to  include 
the  whole  angle  turned. 
In  all  the  systems  of 
transition  curves  which 
have  been  put  before  the 
public  by  others  than 
the  writer,  so  far  as  he 
knows,  these  offsets  are 

Fig.  283.— Typical  Transition  Curve.  «-„.^^    .„u-^u  i 

nxed,  which  makes  run- 
ning them  in  a  considerable  addition  to  the  field-work,  but  even  then 
they  are  likely  to  have  a  certain  beneficial  effect  on  the  construction,  for 
the  reason  that  the  curves  of  natural  slopes  generally  ease  themselves  off 
in  this  manner. 

1199.  But  in  any  entirely  satisfactory  system  of  transition  curves  any 
offset,  great  or  small,  within  wide  limits,  should  be  capable  of  use  with 
any  curve,  because  it  will  very  materially  add  to  the  flexibility  of  the  line 
and  facilitate  its  adaptation  to  the  topography.  If  we  consider  the  tran- 
sition curve  as  a  cubic  parabola,  the  only  difference  which  the  offset 
makes  in  the  curve  is  to  increase  its  length  in  proportion  to  the  square 
root  of  the  offset,  so  that  if  the  latter  be  four  times  as  great  the  curve 
will  be  twice  as  long.  In  any  case,  the  curve  remains  a  cubic  parabola, 
and  is  readily  put  in,  either  directly  with  the  transit,  as  the  line  reaches 
it,  by  methods  similar  in  their  nature  to.  and  quite  as  simple  and  easily 
remembered  as,  those  for  running  circular  arcs,  or  by  offsets,  after  run- 


8/0 


CHAP.  XXX.— K [/NAMING  IN   THE  LOCA  TION. 


CHAP.  XXX.— RUNNING  IN    THE  LOCATION 


871 


I 


ning  in  the  full  circular  arc  from  an  offsetted  tangent,  as  indicated  in 
Fig.  283. 

Tlie  former  of  these  methods  is  generally  preferable  for  large  offsets, 
and  the  latter  for  small.  The  immense  advantage  which  the  method' 
gives  for  making  the  finer  adjust- 
ments of  the  line  may  be  made 
evident  by  one  or  two  illustrations, 
but  it  should  be  remembered  that 
the  chief  object  of  the  curves  is 
not  to  facilitate  location,  but  to 
obtain  a  line  which  trains  will  run 
over  smoothly. 

1200.  Example  i.  It  is  found 
to  be  desirable  to  swing  a  located 
tangent.  Fig.  284,  in  2  ft.  at  a  and 
out  3  ft.  at  b. 

The  angle  between  the  old  and 
new  tangent  can  be  at  once  calculated.  Then  the  two  adjacent  curves 
must  be  extended  (in  Fig.  284— or  cut  off,  had  the  change  of  tangent 
been  in  the  other  direction)  by  the  same  angle.  This  can  be  done  at 
once;  the  offset  determined  by  measure,  whatever  it  may  be.  and  the 
corresponding  transition  curve  put  in  by  offsets  from  the  curve  and  the 
new  tangent;  or  the  tangent  points  /  and  /  of  the  new  curve  may  be 
determined  and  the  transition  curve  run  in  by  the  transit. 

1201.  Example  2.  It  is  desired  to  take  out  a  "  broken-back"  curve. 
Fig.  285.     Governing  points  which  it  seems  desirable  the  curve  should 


Fig.  984. 


-^■~ 


I 

I 


pass  through  are  a  and  b,  at  any  off- 
set from  any  point  on  the  tangent. 

The  angle  between  the  new  and 
old  tangent  can  be  calculated  as  be- 
fore ;  the  curves  extended  or  retraced 
by  an  equal  angle,  the  actual  offsets 
measured,  and  the  proper  transition 
curves  put  in.  If  the  change  has  been 
well  planned  and  the  conditions  are 
at  all  favorable,  the  two  curves  will  come  very  near  to  meeting  at  some 
point  near  the  middle  of  the  tangent. 

If  it  leaves  a  little  tangent  between  the  two  curves  it  will  not 
greatly  matter.  The  two  desired  ends  will  have  been  accomplished, 
viz.: 


Fig.  185. 


I.  The  two  shocks  to  the  train  in  entering  and  leaving  the  tangent 

will  have  been  avoided. 

2.  The  ugly  appearance  of  a  broken-back 
curve,  which,  owing  to  the  abrupt  transition 
from  curve  to  tangent,  always  has  the  appear- 
ance of  being  out  of  line  and  somewhat  re- 
versed, will  have  been  corrected. 

If  the  two  transition  curves  of  the  required 
lengths  for  the  offset  chance  to  overlap  each 
other  even  by  a  considerable  distance  it  will 
not  much  matter.  It  simply  introduces  (for 
reasons  which  cannot  be  given  here  without 
discussing  the  whole  theory  of  the  curve)  a 
short  CIRCULAR  ARC  of  very  long  radius  be- 
FiG.  286.  tween  the  two  transition  curves. 

1202.  Example  3.  A  curve  is  found  not  to  lie  on  precisely  the  right 
ground.  It  is  desired  to  throw  it  out  two  feet  at  a,  and  in  3  feet  at  b^ 
Fig.  286. 

This  implies  that  there  will  be  a  certain  point  c,  at  which  the  new  and 
old  curves  will  coincide.  The  whole  curve,  radii,  centres  and  all,  will  be 
practically  rotated  around  c.  The  distances  ca  and  cb  can  be  deter- 
mined by  the  proportion 

« 

ca  \cb  w  offset  a  :  offset  b. 

The  angle  of  rotation  is  readily  calculated  by  computing  the  change 
in  position  of  the  chord  ab,  and  from  these  notes  we  may  either  start  at 
c,  and  run  in  the  new  curve,  or  start  at  a  or  b,  or  compute  the  new  posi- 
tions of  the  original  P.  C.  and  P.  T. 

If  the  new  curve  is  found  to  crowd  too  closely  upon  or  to  overlap  the 
tangents  we  must  change  the  latter  also.  This  we  do.  however,  entirely 
independent  of  the  curve,  if  it  appears  desirable  to  do  so  ;  putting  the 
tangent  upon  the  ground  which  will  suit  it  best,  measuring  the  actual 
offset  which  the  locations  chosen  give,  and  then  putting  in  the  corre- 
sponding transition  curves. 

1203.  These  examples  will  illustrate,  as  well  as  more,  the  peculiar  ad- 
vantage of  transition  curves,  thus  used  ;  that  they  enable  each  part  of  the 
line  to  be  studied  and  modified  in  detail,  independently  of  the  rest;  and 
the  new  and  old  lines  to  be  then  connected  together  in  what  is  at  once 
the  very  best  possible  and  the  simplest  possible  way.  without  any  of 
the  puzzling  geometrical  problems  and  the  confusing  field-work  which 


872 


CHAP.  XXX.-^RUNNING  IN    THE  LOCATION. 


CHAP.  XXXI.— TOPOGRAPHY:  ITS  USES  AND  ABUSE,     873 


1 


1 


# 


0 


\ 
I 


are  as  apt  to  result  from  slight  changes  as  great,  if  certain  geometrically 
exact  connections  at  all  points  of  circular  arcs  are  taken  as  essential. 

Differences  of  offsets  of  20  ft.  or  more  are  readily  admissible  under 
this  plan,  and  in  projecting  location  it  is  unnecessary  to  consider  what 
the  actual  offsets  will  be.  Figs.  208,  216,  and  others  illustrate  how  this 
is  done.  The  advantages  of  the  method  in  such  rough  localities  are  evi- 
dent from  those  engravings,  and  these  advantages  become  even  greater 
if  one  knows  how  to  save  unnecessary 
trouble  in  field-work,  which  will  not  - 
tell  beneficially  in  the  final  result. 

1204.  As  a  single  example,  if  one 
has  a  curve  formerly  terminating  at 
T,  Fig.  287,  which  is  to  be  extended 
to  T'  in  order  to  connect  with  the  tan- 
gent 00  ;— to  determine  the  offset  O  it 

is  quite  unnecessary  to  run  in  T'  with  Fig.  287. 

a  transit.  The  offset  Oo  to  the  old  point  T  may  be  measured  instead. 
Then  will 

0=00  —  0,        and  |^"o  -^  ^D, 

in  which  D  =  the  degree  of  the  curve,  n  =  the  distance  in  stations  from 
the  tangent  point  T'  to  the  point  where  the  offset  to  the  curve  is  de- 
sired, and  O  =  the  desired  offset.  • 

1206.  This  latter  formula  is  one  of  the  most  useful  of  all  location 
formulae,  being  almost  indispensable  for  the  correct  and  expeditious 
conduct  of  field-work.  It  is  closely  approximate  (in  all  cases  sufficiently 
so  for  what  is  required)  within  the  widest  possible  range  of  values  of  D 
and  n,  and  it  is  one  of  the  few  formulae  which  should  be  indelibly  en- 
graven in  the  memory  of  every  locating  engineer,  ready  for  instant  use. 
It  applies  equally  well  for  offsets  from  one  curve  to  another  having  a 
common  tangent  point,  letting  Z>=  the  difference  in  the  degree  of  cur- 
vature. 


CHAPTER  XXXI. 

topography:  its  uses  and  abuse. 

1206.  Topography,  in  the  limited  technical  sense  of  the  word  which 
is  given  to  it  in  railway  location,  is  the  representation  upon  a  map  by 
"contour  lines"  of  the  comparative  or  absolute  elevations  on  the  area 
covered  by  the  map.  In  a  broader  and  more  literally  correct  sense,  it  in- 
cludes the  representation  of  all  the  details  of  the  surface  by  any  method 
whatever,  including  its  form,  character,  and  artificial  structures. 

Topography,  in  the  broader  sense,  may  be  represented  approximately 
either  by  hatchings  or  "  hacliures,"  or  by  washes  of  color.  Very  beauti- 
ful effects  may  be  produced  in  this  way  by  skilled  and  patient  work  but 
the  results  are  only  of  pictorial  value,  to  give  a  general  idea  of'  the 
region,  and  are  of  no  assistance  for  the  details  of  location.  Topography 
when  spoken  of  in  connection  with  the  latter,  means  an  exact  repre- 
sentation of  the  form  of  the  surface,  so  that  the  elevation  of  any  point 
can  be  determined  from  the  map,  and  hence  a  line  be  drawn  on  the  map 
and  a  profile  of  it  called  off,  as  well  (barring  a  margin  of  error)  as  if  the 
line  had  been  run  in,  and  levels  run  over  it,  in  tlie  field.  Figs.  208,  216 
and  others  are  representations  from  actual  practice  of  such  maps,  re- 
duced photographically  from  the  working  scales. 

1207.  The  nature  of  contour  lines  may  be  thus  explained  :  Conceive 
a  certain  area,  the  topography  of  which  is  to  be  taken,  to  be  entirely 
flooded  with  water.  Conceive  the  level  of  the  surface  of  this  water  to 
be  lowered  by  a  certain  fixed  distance,  say  ten  feet  at  a  time.  At  each 
lowering  of  the  water  a  new  shore-line  would  be  developed  :  The  con- 
tour lines  are  these  imaginary  shore-lines.  If  the  slopes  be  very  steep 
these  successive  shore-lines  will  be  at  small  distances  from  each  other 
horizontally.  If  the  slopes  be  flat  they  will  be  at  greater  horizontal  dis- 
tances, and  if  the  slopes  are  very  flat  they  will  be  at  very  great  distances 
apart,  and  only  a  few  will  appear  on  a  moderate  area.  Thus  the  lower 
part  of  Fig.  288  shows  a  contour  map  of  a  slightly  oblique  cone,  and  the 
lower  part  of  Fig.  289  a  similar  contour  map  of  a  hemisphere.  In  each 
case,  if  the  nature  of  contour  lines  has  been  grasped,  they  enable  the 
mind  to  form  a  very  correct  picture  of  the  form  of  the  surface. 


I* 


874     CHAP.  XXXL— TOPOGRAPHY :  ITS  USES  AND  ABUSE. 


S-: 


i\ 


1208.  It  will  be  obvious  that  working  with  such  topographical  maps 
has  both  advantages  and  disadvantages.     The  advantages  are  : 

I.  The  eye  is  able  to  take  in  a  large  surface  at  once,  with  exact  in- 
formation as  to  the  form  of  every  part  of  it,  and  without  those  confusing 
optical  illusions  which  result  from  looking  at  a  natural  surface  horizon- 
tally instead  of  from  above,  and  in  successive  bits  instead  of  all  at  once. 


,,T-'-"--"^ 


Fig.  288. 


Fig.  289. 


2.  Various  projects  can  be  studied  with  great  ease,  and  the  effect  of 
different  changes  considered  at  once.  A  curve  can  be  struck  in  with  a 
compass  in  a  moment,  and  three  or  four  different  ones  in  as  many  differ- 
ent positions  almost  as  quickly,  each  one  of  which  would  take  perhaps  a 
day's  hard  work  to  run  in  on  the  ground,  with  the  chance  after  they 
were  run  that  they  would  lie  considerably  out  of  the  position  intended. 

3.  By  dotting  on  the  grade-contour  (pars.  1246-8)  or  line  where  the 
plane  of  the  road-bed  cuts  the  natural  surface,  it  can  be  seen  almost  at 
once  whether  the  alignment  is  as  favorable  as  the  topography  permits, 
or  not. 

1209.  Each  one  of  these  advantages  is  a  great  one.  On  the  other 
hand  the  disadvantages  of  working  from  contours  are  : 

1.  The  making  of  good  contour  maps  is  expensive — which  is  a  very 
weak  objection,  even  if  their  cost  were  much  greater  than  it  is. 

2.  It  is  difficult  to  insure  accuracy. 


C//AP.  XXXL— TOPOGRAPHY :  ITS  USES  AND  ABUSE.     875 


3.  They  afford  no  evidence  of  material. 

4.  They  do  not  impress  upon  the  mind  the  magnitude  of  the  works^ 
projected,  as  it  does  to  study  the  actual  surface. 

5.  They  are  of  assistance  only  for  doing  the  least  important  part  of 
the  work,  making  the  first  approximation  to  the  detailed  location  of  the 
line. 

These  and  other  difficulties  which  we  shall  shortly  consider  are  like- 
wise great  and  valid  ones.  They  indicate  what  is  the  fact,  that  topog- 
raphy has  both  its  uses  and  abuses,  and  which  predominates  is  often, 
the  subject  of  heated  discussion. 

1210.  In  such  discussions  one  is  reminded  of  the  old  fable  of  the  two- 
knights  who  fell  to  fighting  over  the  shield  which  seemed  gold  or  silver 
according  to  the  "point  of  view  ;"  for  the  disputed  question  is  emphati- 
cally  one  of  the  same  kind.  It  is  only  by  losing  sight  of  one  side  or  the 
other  that  one  becomes  a  strong  partisan  of  either  view. 

The  difference  between  the  two  views,  in  fact,  is  more  imaginary  than 
real.  On  the  one  hand,  there  are  no  engineers  of  any  standing  or  ex- 
perience who  believe  that  location  offering  any  difficulties  can  be  made 
to  advantage  in  any  other  way  than  from  topographical  notes  embodied 
in  a  more  or  less  elaborate  topographical  map;  while,  on  the  other  hand,, 
there  are  no  engineers  of  experience  who  would  think  of  claiming  that 
more  topography  than  is  really  necessary  for  intelligently  completing  the 
location,  and  making  sure  that  it  is  correct,  should  be  taken. 

The  true  question  to  be  decided,  therefore,  is  simply  how  mucft 
topography  should  be  taken,  and  where  the  line  should  be  drawn.  There 
is  no  such  difference  of  opinion  as  would  appear  from  an  error  into  which 
many  have  fallen— an  error  which  well  shows  how  completely  the  views 
of  those  who  take  one  side  of  this  question  are  misapprehended  by  those 
who  think  they  disagree  with  them  ;— that  is  to  say.  there  is  no  class  of 
engineers  who  attempt  to  make  a  final  location  assisted  by  the  natural 
eyesight  alone,  or  in  any  other  way  than  by  working  from  a  preliminary 
line  as  a  basis,  which  is  intended  to  lie,  and  if  skilfully  run  does  lie,  very 
close  to  the  line  on  which  the  final  location  is  placed,  as  in  Fig.  282. 

1211.  To  mark  the  limits  of  the  debatable  ground  still  more  closely, 
it  cannot  be  reasonably  questioned  (i)  that  in  proportion  to  the  skill  of 
the  engineer  the  preliminary  line  (often  at  difficult  points,  necessarily,  the 
result  of  two  or  three  trials)  will  approximate  more  and  more  closely  to- 
where  the  final  location  will  ultimately  lie;  (2)  that  it  should,  and  in 
general  will,  lie  nearer  than  300  or  400  feet  as  an  outside  limit;  (3)  that 
the  placing  of  this  preliminary  line  upon  the  ground  is  and  must  be 


4 


^7^    CHAP.  XXXI.-TOPOGRAPHY. 


ITS  USES  AND  ABUSE. 


r 


purely  a  matter  of  individual  "  eye  for  country"  and  good  judgment;  and 
(4)  that  the  really  vital  and  dangerous  errors  of  location,  the  selection  of 
the  general  route,  the  system  of  gradients,  the  going  to  or  passing  by  the 
local  towns,  etc.,  etc.,  are  committed,  if  committed  at  all.  before  any  to- 
pography whatever  has  been  taken,  in  locating  this  preliminary  line  •  the 
usefulness  of  the  topography  beginning  only  after  the  more  momentous 
question  of  where  TO  PUT  THE  PRELIMINARY  has  been  decided,  and 
serving  only  for  the  more  ready  and  perfect  adjustment  of  details-de- 
tails which  have  an  important  effect  upon  the  cost  of  construction,  in- 
deed, but  do  not  otherwise  seriously  modify  the  earning  capacity  of  the 
line. 

1212.  The  remaining  ground  for  difference  between  extreme  advo- 
cates of  either  view  is  this  :  The  extreme  believer  in  topography  is  indif- 
ferent  to  getting  his  preliminary  very  near  to  its  ultimate  location,  look- 
ing upon  400  or  500  feet  average  distance  apart  as  near  enough,  and 
takes  or  causes  to  be  taken  a  wide  belt  of  accurate  topography  to  save 
the  need  of  a  new  or  a  better  preliminary.  But  the  advocates  of  the  other 
view  say.  "No;  the  engineer  who  can  be  trusted  to  put  a  preliminary 
line  within  even  500  feet  of  the  true  location  can  and  ought  to,  in  gen- 
eral, put  it  much  nearer ;  or  if  not.  it  is  cheaper  to  put  a  new  line  through 
5till  closer  to  the  ultimate  location  than  to  take  so  wide  a  belt  of  topog- 
raphy. By  one  method  or  the  other,  the  good  engineer  can  and  will 
bring  the  line  so  near  to  where  his  location  should  lie,  that  the  topog- 
raphy which  he  will  really  need  will  be  only  a  very  narrow  belt— usually 
tio  more  than  a  few  series  of  cross-sections,  and  hardly  amounting  to  a 
topop^raphical  map  at  all." 

1213.  The  truth  lies  between  these  two  limits.  Since  the  amount  of 
topography  ultimately  needed  and  used  (when  its  use  is  not  abused  by 
making  it  serve  as  a  substitute  for  the  careful  placing  of  the  preliminary) 
can  be  seen  on  any  location  map  to  be  very  little,  covering  a  map  all 
over  with  accurate  topography  is  a  sign  of  weakness  and  not  of  strength. 
On  the  other  hand,  accurate  topographical  contour  lines  for  a  reasona- 
ble and  moderate  distance  on  each  side  of  the  line  are  an  immense  as- 
sistance for  the  ready  projection  of  lines,  and  at  points  can  hardly  be 
dispensed  with.  It  is  also  an  important  truth  that  the  usefulness  of 
tO[)ography  is  not  confined  simply  to  that  portion  of  it  which  is  used  to 
project  the  line  adopted,  but  extends  also  to  the  portion  which  enables 
one  to  make  sure  that  no  other  and  better  alignment  might  have  been 
adopted.  However  confident  an  engineer  may  feel  that  he  has  in  fact 
studied  his  work  to  the  best  of  his  ability,  he  owes  it  to  himself  and  to 


CHAP.    XXXI.— TOPOGRAPHY :   ITS  USES  AND  ABUSE.    877 


his  employers  to  have  the  ocular  evidence  of  that  fact  before  him,  to  be 
placed  before  others  if  need  be;  and  it  is  but  reasonable  that  no  study  of 
the  ground  alone,  unassisted  by  accurate  maps,  can  be  as  complete  as 
one  which  has  been  so  assisted.  Yet,  on  the  other  hand,  it  is  even  more 
emphatically  true  that  no  study  of  maps  alone,  unassisted  by  study  of  the 
ground  in  detail,  both  before  and  after  the  making  of  the  maps,  can  be 
as  complete  as  it  should  be. 

1214.  No  skilled  engineer,  even  among  those  who  are  strong  believers 
in  the  proper  use  of  contour  maps  will  approve  of  such  elaborate  reli- 
ance upon  maps  alone,  as  is  sometimes  taught  and  advocated ;  such  as; 
taking  the  nicest  precautions  for  computing  notes  for  8  or  10  miles  of 
location  at  once,  so  that  it  shall  fit  geometrically  onto  the  preliminary,, 
and  so  dispense  with  renewed  and  more  detailed  study  of  the  ground. 
Not  but  that  the  field-work  and  mapping  might  be  done  so  accuratel5r 
that  this  would  be  all  that  would  be  necessary,  and  not  but  that  much  of 
a  location  so  made  may  prove  on  examination  to  be  beyond  improve- 
ment, at  least  by  the  same  engineer ;  but  that  for  practical  reasons  it  is- 
inexpedient  to  rely  so  largely  upon  paper  location.  Among  these  rea- 
sons are — 

1215.  I.  As  above  suggested,  the  length  and  depth  of  cuttings,  and 
especially  the  classification,  do  not  impress  themselves  upon  the  mind  so 
forcibly  in  studing  a  topographical  map  as  in  studying  the  ground,  and 
hence  as  great  efforts  will  not  be  made,  practically,  to  avoid  this  danger 
when  the  principal  study  of  the  details  of  the  line  is  made  upon  the  maps 
as  when  the  paper  location  is  looked  upon  as  at  best  nothing  more  than 
a  close  approximation,  and  the  last  study  of  the  ground  is  made  with, 
the  rock-cut  staring  one  in  the  face,  or  on  large  scale  cross-sections. 

1216.  2.  A  very  dangerous  error,  which  the  best  engineers  find  it  hard 
to  avoid  altogether,  is  especially  hard  to  avoid  in  making  paper  loca- 
tions, which  is,  to  regard  a  certain  horizontal  approximation  to  the 
GRADE-POINTS  as  about  the  proper  thing,  thus  leading  to  altogether  too> 
much  curvature  and  respect  for  the  contours  in  easy  country,  and  alto- 
gether too  little  of  both  at  the  more  diflficult  points.  The  watchful  en- 
gineer finds  himself  drifting  into  this  error  continually,  guard  against  it 
as  he  will.  It  results  in  part  from  a  natural,  but  evidently  erroneous, 
tendency  to  look  on  a  certain  percentage  of  decrease  of  curvature,  for 
example,  as  worth  a  certain  percentage  of  increase  in  the  work  (pars.  14, 
15),  instead  of  being  merely  worth  a  certain  absolute  sum,  which  on  easy 
work  justifies  great  disregard  of  contours,  and  on  heavy  work  requires, 
close  accordance  with  them. 


- 


'1; 


jmjmM- 


I 


878     CHAP.  XXXr.  — TOPOGRAPHY :  ITS  USES  AND  ABUSE. 

1217.  3.  The  best  topographical  maps  wliich  it  is  either  expedient  or, 
in  general,  possible  to  make,  with  the  time,  money,  and  men  at  command, 
cannot  by  any  means,  as  is  sometimes  foolishly  claimed,  be  relied  on 
within  a  foot,  nor  even  5  or  10  feet,  at  critical  points,  especially  if  extend- 
ing to  any  great  width  on  each  side.  Over  most  of  their  area,  if  well 
made,  they  will  be  trustworthy,  but  minor  irregularities  of  considerable 
importance,  if  nothing  more  than  a  few  big  boulders,  get  smoothed  out  of 
the  map  or  misplaced  or  exaggerated,  so  that  tlie  only  safe  rule  is  to  look 
on  the  iirst  location,  however  carefully  studied,  as  still  open  to  much 
improvement — an  expectation  which  will  rarely  be  disappointed.  But 
if  frequent  minor  changes  are  to  be  made,  much  of  the  advantage  of 
computing  field-notes  from  a  paper  location  so  precisely  as  is  often  at- 
tempted is  lost.     It  is  not  in  fact  good  practice  to  do  so. 

1218.  4.  To  run  in  long  stretches  of  location  successfully  without 
further  topographical  tests,  but  only  the  geometrical  test  of  a  "tie"  to  a 
preliminary,  requires  the  nicest  field  and  office  work  from  the  beginning 
to  the  end  of  the  survey.  It  is,  of  course,  only  a  question  of  degree.  No 
one  would  advocate  anything  but  good  work  of  the  kind,  but  it  is  obvious 
that  less  precision  is  required,  if  it  is  fully  understood  and  expected  that 
the  paper  location  will  be  topographically  tested  throughout,  than  if  it  is 
expected  to  be,  in  the  main,  a  finality.  This  saving  of  needed  precision 
means  some  corresponding  saving  of  time  and  money,  which,  as  Mark 
Twain  said  of  his  profanity,  "can  then  all  be  saved  and  devoted  to  some 
other  end,  where  it  will  do  more  real  and  lasting  good." 

1219.  Another  objection,  which  is  perhaps  the  strongest  of  all,  against 
too  great  reliance  on  contour  maps,  is  founded  rather  on  the  foibles  of 
human  nature  than  on  any  purely  technical  reason  :  It  encourages  a  dis- 
position in  the  higher  engineering  officers  to  throw  the  field-work  of 
location  into  incompetent  hands,  and  to  assume  to  themselves  the  func- 
tion of  fixing  the  petty  details  of  location,  and  hence  (since  the  whole  is 
only  equal  to  the  sum  of  all  its  parts)  to  control  the  whole  location  from 
their  office  chair,  without  giving  to  it  that  careful,  thorough,  and  con- 
tinued study  on  the  ground  which  alone  will  qualify  the  ordinary  man  to 
wisely  exercise  such  control.  This  practice  works  injuriously  in  several 
ways: 

I.  It  deadens  the  perceptive  faculties  of  the  engineer  in  charge  of  the 
party  and  transforms  him  into  a  mere  machine.  He  may,  if  an  unusually 
skilful  and  faithful  man,  go  over  the  paper  line  with  a  microscope  and 
improve  its  details,  but  he  will  not  be  watching  out  for  and  thinking  of 
the  larger  details,  especially  as — 


CHAP.   XXXI.-TOPOGRAPHY :  ITS  USES  AND  ABUSE.    879 

2.  The  practice  leads  to  the  engagement  of  poorer  men  for  the  field- 
work  ;  and 

3.  The  engineer  who  puts  in  the  paper  location,  and  conirols  the 
work,  never  qualifies  himself  by  familiarity  with  the  ground  to  do  well 
even  that  minor  duty,  and  is  so  little  in  the  field  that  the  far  more  im- 
portant end  of  avoiding  the  larger  errors  is  not  duly  insured. 

1220.  The  "conclusion  of  the  whole  matter" therefore  is,  that  accu- 
rate topography  for  a  certain  narrow  strip  is  a  highlv  useful  adjunct  to 
practical  location,  which  should  never  be  omitted  altogether  and  should 
generally  be  very  carefully  taken  and  studied  ;  but  that  it  is  in  no  way  a 
safeguard  against  anything  but  minor  errors  of  location,  and  is  not  a  safe 
nor  expedient  reliance  for  giving  the  last  degree  of  perfection  even  to  the 
-details  of  alignment. 

Great  differences  in  natural  aptitude  for  location  exist,  and  among 
the  strongest  believers  in  the  absolute  necessity  of  elaborate  topography 
may  well  be  some  who  have  less  of  this  natural  aptitude,  and  hence  will 
not  make  very  good  use  of  the  best  of  maps.  In  fact,  although  we  should 
not  allow  this  to  prejudice  us  against  topography,  it  is  beyond  doubt  that 
those  of  least  natural  aptitude  for  location  rely  most  on  topography,  and 
are  the  most  helpless  without  it.  On  the  other  hand,  those  who  have  or 
thmk  they  have  such  aptitude  may  be  led  thereby  to  be  over-confident, 
and  commit  errors  which  good  topography  would  reveal  to  them.  It  is 
certain  that  the  better  natural  qualifications  a  man  has  for  the  work  the 
less  topography  he  will  take,  because  he  will  see  in  advance  where  it  is 
and  is  not  important.  He  will  always  take  some,  however,  and  what  he 
does  take  will  be  correct. 

1221.  Another  truth  may  appropriately  be  added  here.  It  is  easier  to 
put  A  line,  of  some  kind  or  other,  on  a  topographical  map  than  on  the 
ground  ;  but  to  do  the  best  that  the  ground  admits  is  almost  as  hard,  and 
takes  almost  as  much  study  and  skill,  on  the  contour  map  as  on  the 
ground.  This  the  inexperienced  projector,  of  good  natural  parts,  will 
soon  find  out  if,  after  having  put  in  a  paper  location,  which  he  thinks  is 
very  gpod.  he  will  start  in  over  again  on  the  assumption  that  it  is  all  very 
bad.  and  give  two  or  three  times  more  thought  and  care  than  before  to 
finding  out  wherein  it  is  bad.  He  will  probably  soon  be  satisfied  that 
his  assumption  was  correct,  by  finding  his  curvature  and  quantities 
simultaneously  diminishing. 

1222.  There  is  a  tendency  in  discussing  this  question,  as  in  many  others  to 
fall  back  upon  the  singular,  yet  in  a  sense  natural,  argument  which  seeks  to 
defend  some  one  way  of  doing  things  by  showing  that  some  of  those  who  take 


83o 


CHAP.   XXXI.— TOPOGRAPHY :  ITS  USES  AND  ABUSE. 


CHAP.   XXXI— TOPOGRAPHY :  ITS  USES  AND  ABUSE.    88 1 


another  way  do  work  badly.     On  the  one  hand,  we  have  pictured  the  "born- 
engineer"  spending  days   in  fitting  a  bad  line  to  the  side  of  a  hill  with  his- 
•'  practised  eye,"  when  hours  would  have  sufficed  with  the  assistance  of  a  little 
well-taken  topography;  and,  on  the  other  hand,  a  man  studying  over  topographi- 
cal maps  of  a  line  in  the  wrong  place,  missing  the  salient  features,  and  perpet- 
uating on  the  ground  errors  of  the  maps.     Either  picture  may  well  be  drawn 
from  life,  for  out  of  a  hundred  men  doing  anything  which  requires  skill,  more 
than  half  will  do  it  but  indifferently  well,  a  considerable  fraction  wretchedly  ill, 
and  only  a  small  proportion  thoroughly  well.     This  fact  insures  a  supply  of 
ready  weapons  for  supporting  either  side  of  any  argument,  yet  it  is  strange  that 
they  should  be  so  often  chosen,  since  it  is  clear  that  they  prove  nothing.     But 
as  evidence   of  this   inconclusive  character  seems  sometimes  to  carry  undue 
weight,  we  may  add  a  few  words  further  as  to  certain  details. 

1223.  The  fact  that  the  actual  profile  of  a  line  run  from  a  "paper  location" 
agrees  so  precisely  with  the  latter  that  the  two  cannot  be  told  apart,  is  no  proof 
of  the  excellence  of  the  system,  for  both  profiles  may  be  bad.  It  proves  the- 
geometrical  excellence  of  the  work,  but  it  also  proves,  or  tends  to.  that  the 
whole  process  is  too  mechanical,  unless  the  "  paper  location"  has  been  at 
least  so  improved  or  modified  in  detail  as  to  be  distinguishable  from  the  other. 

1224.  On  the  other  hand,  fixing  the  details  of  the  alignment  in  the  office, 
to  be  put  on  the  ground  by  other  men  of  less  skill,  while  never  a  desirable,  is. 
not  necessarily  a  wrong,  way  of  doing  things.     We  are  often  compelled  to  do, 
not  what  we  would,  but  what  we  can.     If  there  be  but  one  skilled  man  to  look 
after  half  a  dozen  parties,  and  perhaps  look  after  other  work  as  well,  it  is  im- 
possible that  he  should  do  much  more  than  put  the  line  on  paper,  and  he  is  far 
more  likely  to  project  a  good  line  in  that  way  than  an  inexperienced  man  is  to 
reach  the  same  end.  either  on  paper  or  on  the  ground,  or  both.     When,  how- 
ever, one  ceases  to  look  on  this  practice  as  merely  a  necessary  evil,  and  begins- 
to  look  on  it  as  an  ideal  state  of  things,  so  that  on  a  difficult  line  it  is  "  re- 
quired" that  the  projected  location  should  be  "  strictly  followed"  and  "no  cut- 
and-try  permitted,"  as  is  sometimes  done,  then  the  abuse  of  topography— and  a 
dangerous  abuse,  sure    to  waste  more  or  less  money— has  begun.     The  better 
course  in  such  cases  is  to  require  the  engineers  in  the  field  to  make  the  first, 
projection,  which  is  simply  sent  in  for  examination  and  revision  if  necessary, 
so  as  to  compel  them  to  rely  on  their  own  intelligence  and  not  on  another  s,  and 
especially  to  give  an  indication  of  the  extent  to  which  their  own   skill  can  be 
relied  on.     For  if  unequal  to  making  a  tolerably  correct  projection  in  the  first 
instance,  they  will  probably  be  still  more  unequal  to  the  more  responsible  duty 
of  putting  in  the  final  line. 

1225.  To  mention  one  instance  among  many,  of  the  evils  of  too  great  re- 
liance on  maps:  an  unusually  accurate  paper  location,  on  a  very  steep  side-hill,, 
gave  a  beautiful  profile,  which  no  one  could  delect  in  the  office  to  have  any  fault. 
The  cut  averaged  about  a  foot,  which  was  what  prudence  seemed  to  require^. 


\ 


and  what  no  one,  certainly,  in  the  office  would  have  thought  of  objecting  to. 
But  just  below  the  earth  was  rock,  as  a  "  practised  eye"  might  have  detected  in 
the  field,  and  the  earth  itself  was  such  as  to  make  an  unusually  solid  bank,  so 
that  when  the  line  came  to  be  constructed  there  was  an  ugly  shallow  rock-cut 
on  the  inner  edge  and  a  broad  solid  platform  for  the  road-bed  nearly  twice  too 
wide,  due  to  the  unnecessary  amount  of  excavation,  which  involved  a  loss  of 
some  $8ooo  in  much  less  than  a  mile,  all  of  which  might  have  been  saved  by 
throwing  the  line  out  three  or  four  feet  beyond  the  paper  location. 

Such  cases  occur  so  frequently  that  the  engineer  who  does  not  feel  the  limi- 
tations of  the  map  and  wish  that  he  had  the  ground  before  him  in  making  a 
paper  location,  and  who  does  not  feel  that  it  may  be,  and  probably  is,  suscepti- 
ble of  further  improvement  by  further  study  in  the  field,  will  probably  be  wise 
to  leave  "  topography"  alone,  both  in  the  field  and  in  the  office. 

1226.  In  some  cases  the  larger  errors  of  location,  such  as  putting  a  line  on 
the  hill-side  with  a  short  tunnel,  instead  of  in  the  bottom  of  the  valley  with  a 
long  tunnel,  are  very  unreasonably  advanced  as  an  effect  of  neglecting  topog- 
raphy;  whereas  it  is  precisely  such  errors  which  over-reliance  on  topography  is 
apt  to  lead  to.  The  result  depends  chiefly  on  the  man.  A  good  man  will  use 
every  tool  that  will  serve  his  end,  and  one  of  these  tools  is  topography.  Another 
one,  at  least  equally  essential,  is  shoe-leather. 

1227.  If  topography  is  to  be  taken  at  all  it  should  be  taken  accurately, 
and  to  combine  this  end  with  reasonable  rapidity  the  limits  within  which 
accurate  topography  is  taken  should  be  restricted  as  closely  as  possible. 
Beyond  these  limits  a  skilful  topographer  will  sketch  in  by  the  eye  the 
general  form  of  the  ground,  with  sufficient  accuracy  to  give  a  better 
general  idea  of  the  form  of  the  country,  and  occasionally  to  serve  a  use- 
ful purpose  in  a  rough  study  of  some  considerable  change  of  line. 

1228.  Topography  is  taken  from  the  preliminary  line  as  a  base-line, 
with  the  elevations  on  it  given,  by  determining  the  slopes  on  each  side  as 
far  out  as  seems  necessary.  Four  methods  for  taking  slopes  are  more  or 
less  practised : 

1.  By  a  slope-level  and  board  straight-edge,  with  or  without  a  tape- 
line. 

2.  By  a  hand-level  and  tape-line. 

3.  By  cross-sectioning  rods. 

4.  By  using  a  stadia  telescope  and  rod  to  measure  distances  in  place 
of  a  tape-line,  in  either  the  first  or  second  methods. 

To  these  may  be  added— 

5.  By  using  an  altazimuth  in  place  of  the  slope-level  or  hand-level  in 
the  first  or  second  methods.  It  may  also  under  special  circumstances  be 
used  to  advantage  with  cross-section  rods. 

56 


882   CHAP.   XXXL— TOPOGRAPHY :  ITS  USES  AND  ABUSE. 


CHAP.   XXXI.— TOPOGRAPHY :  ITS  USES  AND  ABUSE.    883 


Fig.  agow 


1229.  In  rugged  and  broken  topography,  as  where  there  is  much  rock 
and  large  scales  are  to  be  used,  the  third 
method,  by  cross- section  rods,  is  much 
the  best.  These  rods  are  in  principle 
nothing  more  than  a  horizontal  measur- 
ing-rod of  a  fixed  length,  sometimes  10 
but  better  12  ft.,  carrying  a  level  bubble, 
so  that  it  can  be  set  exactly  horizontal. 
This  is  carried  by  one  assistant  while  an- 
other reads  with  a  light  vertical  rod,  B, 
Fig.  290,  the  rise  or  fall  of  the  ground 
in  the  given  distance.  In  practice,  to  prevent  warping  of  the  rod  A,  it 
is  usually  made  in  one  of  the  forms  shown  in  Fig.  291. 

These  rods  are  convenient  to  have  with  a  locating  party  in  rough 
country,  and  they  are  especially  suitable  for 
cross-sectioning  a  located  line,  but  the  pro- 
cess' is  much  slower  than  any  of  the  others 
specified,  which  are  in  general  better  for 
ordinary  topography. 

1230.  A  wise  choice  between  the  slope- 
level  and  hand-level  methods,  also,  depends  a 


Fig.  291. 


good  deal  upon  circumstances,  and  the  character  of  the  topography  to  be 
taken,  although  each  method  has  its  partisans  who  will  rarely  use  any 
other.  By  the  use  of  the  altazimuth  either  method  can  be  used  at  will, 
which  is  one  of  the  distinguishing  merits  of  that  instrument.  Much 
more  depends,  however,  upon  the  individual  skill  of  the  topographer  than 
upon  the  use  of  any  particular  method.  Where  the  country  is  rough, 
with  irregular  slopes,  the  hand-level  method  is  to  be  preferred,  since  it  is 
more  positive.     Otherwise,  the  slope-level  is  best. 

1231.  The  topography  based  on  these  slope-notes,  by  whatever 
method  taken,  should  invariably  be  drawn  in  the  field  directly 
UPON  the  working  maps  of  the  line,  which  should  be  the  first  and 
only  direct  use  made  of  the  cross-section  notes.  As  a  safeguard  in  case 
of  doubt,  the  rodman  may  well  keep  a  note-book  record  of  them,  but  this 
should  be  strictly  restricted  to  such  use  only.  The  habit  of  taking  the 
cross-sections  in  the  field  and  drawing  in  the  topography  in  the  office 
cannot  be  too  strongly  discouraged.  It  is  certain  to  result  in  more  or 
less  imperfect  work,  as  well  as  loss  of  time.  After  a  little  practice  a 
skilled  topographer  ought  to  be  able  to  keep  up  with  a  transit  and  level 
party  without  much  difficulty,  unless  circumstances  require  a  wide  belt 


-of  exact  topography  to  be  taken,  when  he  should  be  furnished  with  a 
double  cross-section  party.  The  main  requirement  for  doing  work 
quickly  and  well  is  to  train  the  eye  and  judgment  so  that  needless  cross- 
section  work  need  not  be  done  while  yet  taking  all  that  is  essential. 

1232.  The  topographer  is  provided  with  a  thin  drawing-board,  hav- 
ing a  leather  or  oil-cloth  pocket  on  the  back,  in  which  are  carried  the 
sheets,  about  19  X  24  inches  in  size  (par.  1240),  on  which  the  line  has  been 
plotted  the  night  before,  the  stations  marked  of!,  and  the  elevation  of 
each  station  and  plus,  as  taken  by  the  level,  lightly  pencilled  on  it.  The 
topographer  must  thus  work  behind  the  level,  but  a  good  topographer 
will  endeavor  to  keep  very  close  up  to  it.  One  sheet  at  a  time  is  pinned 
upon  the  board  for  use.  A  6-in.  scale,  preferably  of  paper,  lead  pencils, 
and  rubber  complete  his  outfit.  His  two  assistants  (or  four  if  need  be) 
have  nothing,  necessarily,  but  tape  and  hand-level,  with  a  small  hatchet. 
A  small  compass  for  taking  bearings  is  in  general  desirable. 

1233.  In  taking  cross-sections,  the  elevation  of  each  station  is  given 
to  the  rodman  (or  has  been  previously  taken  off  by  him),  and  an  offset 

measured  off  to  a  point,  as 
indicated  by  the  hand-level, 
where    the     contour    next 
above  or  below  the  eleva- 
tion  of  the    given   station 
falls.      Thus,   in   Fig.    292, 
with  contours   10  ft.  apart, 
elevation  of   station   704.2, 
contour  710  is  5.8  ft.  above 
it,  and  contour  700  4.2  ft. 
below  it.    The  distance  out 
in  which  the  ground  rises  or 
falls  these  amounts  should 
in  general,  on  rough  ground, 
be  directly  determined,  and 
then  the  distances  to  a  suc- 
cession of  other  points,  fall- 
ing 5  ft.  at  a  time,  as  far  out  as  accurate   topography  is  taken.    On 
smoother  country  a  little  trouble  may  be  saved  as  below  spoken  of. 

The  points  where  the  contours  cut  the  centre-line  are  also,  at  the 
same  time,  noted  by  the  topographer.  He  then  makes  a  light  pencil 
guess  at  the  course  of  the  contour  lines  ahead,  and  passes,  perhaps,  two 
stations  ahead,  to  "  17.4,"  Fig.  292.  and  repeats  the  process,  the  rodmen 
in  the  mean  time  cross-sectioning  the  intermediate  station  if  it  seems 


Fig.  292. 


884   CHAP.    XXXI.— TOPOGRAPHY :  ITS  USES  AND  A  BUSK. 


I 


essential,  or  more  properly  speaking,  unless  it  seems  unessential.  Until 
the  topographer  has  acquired  well-founded  confidence  by  practice  he  will 
save  nothing  by  taking  chances.and  be  liable  to  throw  discredit  on  his  work. 
Here  the  previous  guesses  are  checked  by  the  cross-sections  and  the 
course  of  the  contours  sketched  in  backward,  exactly  and  finally,  and 
lightly  ahead,  with  further  pencilled  guesses.  In  this  way  the  topographer 
trains  his  eye  and  his  hand,  and  forms  an  idea  of  where  accuracy  is  and 
is  not  essential,  and  if  he  be  once  properly  instructed,  and  has  a  capable: 
assistant,  it  is  not  at  all  difficult  to  take  a  mile  or  two  of  topography 
a  day  in  ordinary  country.  When  he  has  to  take  more  than  200  to  300  ft. 
on  each  side  it  becomes  a  different  matter,  and  progress  is  much  slower. 

1234.  If  slopes  are  determined  by  a  slope-level  it  is  still  simpler  work. 
A  scale  is  then  constructed,  showing  for  a  series  of  different  slopes  from. 
1°  to  20°,  the  horizontal  distance  apart  of  lo-ft.  contours,  which  is  10  x  cot 
5.  From  this  the  contours  can  be  put  down  upon  the  map  at  once,  at 
the  proper  distances  apart,  or  as  far  out  as  the  slopes  are  taken, 

1235.  Time  is  lost  and  accuracy  sacrificed  in  many  surveys  by  using 
too  small  scales.  The  standard  working  scale  may  be  said  to  be  400  feet 
per  inch,  or  jnrW  (nearly  the  same  thing)  when  the  metre  is  used ;  but 
this  scale  is  adhered  to  far  too  strictly.  In  rough  country  it  should  be 
at  once  doubled,  and  in  very  rough  country  should  be  increased  to  100  ft. 
per  in.  or  ^-^Vo  (83i  ft.  per  in.).  These  latter  are  the  only  suitable  scales 
when  there  is  any  considerable  proportion  of  rock-work.  It  rather  saves 
work  in  taking  topography,  adds  but  little  to  the  drafting  work,  and 
adds  immensely  to  the  practical  value  of  the  maps  when  made. 

1236.  The  following  cautions  will  assist  in  taking  topography  correctly : 
I.  One  contour  line  can  never  run  into  another  and  either  disappear 

altogether  or  afterwards  depart  from  it,  in  the 
manner  shown  at  AA,  Fig.  293,  but  must  always 
be  everywhere  a  separate,  distinct,  and  continu- 
ous line  until  it  either  runs  off  the  map  or  closes 
on  itself  so  as  to  form  an  irregular  ring  or  circle,- 
as  at  B,  Fig.  293. 

There  is,  indeed,  one  case  in  which  two  or  a 
dozen  contours  may  so  run  together  into  a  single 
-line,  viz.,  when  an  absolutely  vertical  slope  is  to 
be  represented.  There  is  even  a  possible  case- 
that  of  an  overhanging  cliff— in  which  the  con- 
tour lines  may  cross  over  each  other  and  back 
again,  as  in  Fig.  294.  But  both  of  these  cases 
are  so  rare,  although  they  do  occur,  that  it  is  unnecessary  to  coneides 
them  as  normal  types  of  topography. 


Fig. 293. 


CHAP.   XXXI.— TOPOGRAPHY :  ITS  USES  AND  ABUSE.   885 

1237.  2.  It  is  impossible  for  a  contour  line  to  split  into  two  parts  which 
sooner  or  later  reunite  again,  in  the  manner  shown  in  Fig.  295.     It  is  a 

frequent  error  of  young  topographers,  and  an 

immediate  evidence  of   inexperience,  to  be- 

r^^^_       _^^  lieve  the  contrary.     It  is  indeed  theoretically 

conceivable  that  a  surface  should  have  such 
'°*  ^^'  form  as  to  make  a  sketch  like  Fig.  295  topo- 

graphically correct.     Thus,  if  we  imagine  it  to  be  a  representation  of  the 
.crest  of  a  hill,  it  might  come  to  so  sharp  and  regular  a  ridge,  if  made  of 

dressed  stone  for  example,  that  only  a  single  mathe- 
matical line  at  the  peak  or  ridge  of  the  slope  should 
appear  above  the  water,  and  yet  that  the  ridge  should 
so  appear  above  the  water  for  a  considerable  distance, 
being  precisely  level,  and  should  at  a  certain  point 
swell  out  into  the  "  island  "  AA.  But  practically,  with 
natural  surfaces  as  they  actually  exist,  this  is  plainly 
impossible,  and  the  true  method  of  representing  the 
natural  surface,  which  is  erroneously  presented  in  Fig. 
295,  would  be  as  shown  in  Figs.  208,  216. 

1238.  Topography,  more  largely  than  almost  any 
other  mechanical  detail  of  engineering  work,  is  a  mat- 
ter of  practice.  The  young  engineer  who  ends  his 
first  day's  work  at  topography  discouraged,  with  but  a  few  stations  taken, 
and  that  so  badly  taken  as  to  be  worthless,  can  by  even  a  few  days'  de- 
termined effort  to  understand  it,  and  do  what  he  does  do  well,  learn  to 
go  over  as  much  ground  as  an  ordinary  transit  party.  It  is  a  valuable 
drill  for  cultivating  the  faculties  most  needed  for  location,  and  good  to- 
pographers generally  make  the  best  chiefs  of  party.  In  country  at  all 
rough  the  topographer  fills  the  most  responsible  position  on  the  party 
below  its  chief,  and  he  should  so  rank.* 


Pic.  295. 


*  The  art  of  taking  topography  should  be  taught  in  schools  more  thoroughly 
than  it  is.  There  is  no  better  drill  for  cultivating  those  faculties  of  mind  which 
make  the  engineer. 


y 


•M 


mmmmat 


886   CHAP.   XXXII,— MAPPING  AND  PROJECTING  LOCATION 


^) 


\ 


CHAPTER    XXXII. 

MAPPING    AND    PROJECTING    LOCATION. 

1239i  But  two  methods  of  mapping  railroad  surveys  are  to  be  com- 
mended, which  are : 

1.  For  large-scale  working  maps :  plotting  lines  by  bearings  with  a 
large  paper  protractor  and  parallel  ruler. 

2.  For  small-scale  maps :  by  latitudes  and  departures. 

Plotting  lines  of  any  length  by  laying  off  successive  angles — a  favor- 
ite way  of  laboriously  making  a  bad  map  among  inexperienced  men — 
should  never  under  any  circumstances  be  permitted.  All  work  should! 
be  plotted  by  bearings  from  a  constant  North  and  South  line,  which  is 
transferred  from  sheet  to  sheet  by  prolongation  or  with  a  parallel  ruler. 
Cumulative  errors  are  thus  avoided. 

1240.  Except  in  cases  where  fully  8o  per  cent  of  a  line  is  tangent,  and 
there  is  little  topographical  detail,  a  survey-line  should  never  be  plotted 
on  long  strips  or  rolls  of  paper,  but  always  on  small  sheets,  about  19X  24 
inches  in  size,  or  larger  if  there  be  little  curvature  and  topography — say^ 
19X  36  inches.  These  sheets  are  added  one  after  another  as  the  plotting 
progresses,  lapping  one  side  or  corner  always  under  the  preceding  sheet, 
and  giving  its  axis  any  random  direction,  compared  with  the  other,  which 
will  best  serve  to  keep  the  centre  line  of  the  survey  in  the  middle  of  the 
sheets,  as  shown  in  Fig.  296.  The  two  sheets  are  pinned  together  with 
thumb-tacks,  and  two  or  three  X  marks  made  at  the  lap,  so  that  they  can 
be  replaced  at  any  time  in  exactly  the  same  position. 

A  North  and  South  base-line  should  then  be  laid  down  the  full  length 
of  the  sheet,  nearly  in  its  middle,  and  a  consecutive  number  for  the  sheet 
and  the  name  of  the  line  pencilled  on,  always  in  the  same  corner. 

1241.  The  large  paper  protractor  should  then  be  laid  down  in  the 
middle  of  the  sheet  on  the  North  and  South  lines,  from  a  clearly-marked 
permanent  centre-point,  and  the  computed  or  actual  bearings  of  ALL 
the  lines  which  are  likely  to  fall  on  the  sheet  laid  off  at  once.  If  omis- 
sions  are   discovered,  the   same   process   should   be   repeated  ;    lightly 


CHAP.   XXXII.— MAPPING  AND  PROJECTING  LOCATION.   88/ 


pencilling  in  the  degrees  and  minutes 
of  each  bearing  laid  off,  and  per- 
mitting the  points  thus  marked  to 
remain  permanently,  except  as  they 
interfere  with  the  mapping.  Should 
any  subsequent  error  be  discovered, 
they  may  then  all  be  checked  at 
once,  saving  much  time. 

With  a  good  parallel  ruler  (not 
the  cheap  and  poor  ones  which  are 
most  used,  but  a  heavy  metal  rule 
about  18  inches  long),  or,  failing 
that,  a  couple  of  triangles,  it  is  then 
but  a  few  moments'  work  to  transfer 
each  bearing  in  succession  to  its 
proper  point,  draw  in  the  line,  and 
plot  its  length.  The  angles  should 
then  be  roughly  checked  with  a 
small  protractor  to  guard  against 
the  large  errors  which  are  alone 
likely  to  occur.  The  bearing  of 
each  line  and  the  plus  at  each  angle 
should  then  be  pencilled  on. 

Every  station  should  then  be 
pricked  off  and  indicated  by  a  light 
check-mark,  and  every  fifth  station 
should  be  numbered. 

Opposite  each  station  on  a  di- 
agonal line  should  then  be  lightly 
pencilled  in  the  elevation,  and  also 
the  elevation  of  any  pluses  taken. 
The  sheets  are  now  ready  to  turn 
over  to  the  topographer. 

This  work  should  be  done  every 
night.  It  takes  but  a  short  time 
after  a  little  practice.  The  lines  may 
be  inked  in  on  rainy  days  or  at  any 
convenient  time.  The  centre  line 
should  be  in  red. 

1242.  For  the  same  reason  that 


Fig.  296. 

plotting  should  be  done  from  bearings,  it  is  well  to  do  all  the  transit 


888   CHAP.   XXXII.^MAPPING  AND  PROJECTING  LOCATION. 

work,  on  preliminary  lines  at  least,  by  reading  BEARINGS  instead  of 
ANGLES  from  the  vernier.  In  starting  the  survey  the  vernier  is  set  at  o, 
and  the  lower  limb  clamped  on  a  North  and  South  line,  or  as  near  to  it 
as  possible.  Unclamping  the  upper  limb,  we  may  then  read  the  bearing 
of  the  line  eklier  with  the  compass  or  the  vernier,  and  the  two  should 
approximately  correspond.  Retaining  the  verniers  at  the  same  reading 
for  talcing  a  back-sight  at  the  next  angle,  and  unclamping  above  to  take 
the  next  sight,  we  obtain  the  bearing  of  the  new  line,  likewise  either  by 
the  compass  or  the  vernier— the  one  approximate,  the  other  exact.  Thus 
we  may  continue  throughout  the  survey,  with  the  advantage  (i)  that  we 
can  check  our  work  at  any  time  by  simply  dropping  the  needle,  since 
the  needle  and  vernier  readings  should  always  correspond,  and  (2)  that 
our  *'  computed  bearings"  are  already  computed.  We  should  work,  how- 
ever, by  1 80°  on  each  side  of  the  North  point,  and  not  be  troubled  by  the 
transition  from  N.  E.  to  S.  E.  This  is  the  best  way  to  do  in  any  case, 
and  it  is  easy  to  read  the  needle  so. 

1243.  In  inking  in  the  topography,  every  fifth  line  should  in  all  cases 
be  made  heavier  or  a  different  color.  Black  or  brown  for  every  fifth 
line,  and  brown  or  orange  for  the  intermediates,  does  very  well.  Where 
possible,  contours  should  only  be  five  feet  apart,  although  ten  feet  is 
usual.  The  values  of  every  fifth  line  should  be  frequently  written  on 
them,  in  rows  one  above  the  other,  preferably  by  leaving  a  gap  in  the 
line  for  inserting  the  figures,  or  otherwise  by  writing  them  directly  over 
and  across  the  line.  Much  of  the  prejudice  against  working  with  con- 
tour topography  arises  from  the  prevalent  neglect  of  these  simple  direc- 
tions, which  seem  almost  too  simple  to  mention.  Such  a  map  as  Fig. 
297,  for  example,  is  an  abomination.  It  reflects  just  discredit  on  any 
engineer  to  turn  in  one  in  that  condition,  which  makes  it  almost  worth- 
less to  the  engineer  and  incomprehensible  to  the  mere  observer.  It  should 
be  finished  up  as  shown  in  Fig.  298. 

A  light  case,  provided  with  three  or  four  drawers  of  the  proper  size 
to  hold  the  sheets,  should  be  provided  for  field  use.  Light-yellow  de- 
tail paper  makes  very  good  sheets,  and  is  less  trying  to  the  eyes  than 
white. 

1244.  Experience  has  clearly  shown  this  system  of  mapping  survey- 
lines  to  be  far  better  than  any  other.     Its  advantages  are : 

1.  But  a  small  amount  of  paper  is  in  use  at  once  in  plotting,  while 
any  number  of  sheets  that  there  is  table-room  for  may  be  put  together 
if  desired. 

2.  A  very  small  table  is  all-sufficient. 


"~r~niiM 


F.G.ag7.-AN  IMPROPERLY  FINISHED  CONTOUR  MAP.    (A  spiral  located  on  the  Connellsville  &  Southern  Pennsylvania  RaHroad.)    'lilt 


(A  map  left  in  this  condition  is  almost  wholly  useless  for  practical  work,  or  for  giving  a  definite  idea  of 


I     I     I, 


J 1000  FT. 


the  line  to  a  casual  examiner,  while  it  is  nearly  as  much  work  to  make  it  as  to  finish  it  properly,  as  shown  on  the 
plate  which  faces  this  one.] 


Fig.  298.-THE  SAME   MAP,  PROPERLY  FINISHED. 


J 1000  FT. 


I 


added  on  a  full-scale  map.     Centre  line  and  radii  of  curves  should  be  in  red.] 


v' 


CHAP. 


XXXII.— MAPPING  AND  PROJECTING  LOCATION.    889 


3.  No  time  need  be  lost  in  studying  how  to  keep  the  line  on  the 
paper,  or  in  rubbing  out,  or  in  pasting  on  extensions. 

4.  The  map  need  not  be  covered  over  with  prolonged  lines  for  laying 
off  angles,  but  only  the  actual  length  needed  is  drawn. 

5-  Great  accuracy  is  secured  without  effort,  and  cumulative  errors  are 
impossible.  If  an  error  is  made  on  one  sheet  it  in  no  way  injuriously 
affects  the  work  on  the  adjacent  sheets,  except  that  two  of  them  will 
have  to  be  re-matched. 

6.  If  matched  properly  the  greatest  precision  is  possible  in  laying  them 
together  again  whenever  desired.  For  all  practical  purposes  they  are  as 
-a  single  sheet. 

7-  There  is  no  waste  paper,  and  the  line  is  always  in  the  middle  of 
what  is  used,  readily  accessible  for  office  work.  The  awkwardness  of 
working  with  wide  rolls  is  entirely  saved. 

8.  The  paper  is  never  rolled,  but  always  flat  and  clean,  in  good  con- 
dition for  working  on. 

9.  For  projecting  location,  the  ease  with  which  any  part  of  the  line 
desired  can  be  worked  with,  without  annoyance  from  what  is  not  wanted 
and  from  change  of  scale  due  to  rolling,  gives  it  very  great  advantage. 

10.  The  maps  are  readily  stowed  away  in  dust-tight  boxes  or  drawers 
and  in  very  small  compass,  instead  of  taking  up  a  great  deal  of  room  and 
getting  into  a  practically  unserviceable  condition  in  a  short  time,  as 
rolled  maps  usually  do. 

^45.  For  making  small-scale  maps,   plotting   by  latitudes    and  " 

DEPARTURES  is  the  most  satisfac- 
tory way.     The   latitude   and   de- 
partures should   not  be  computed, 
however   (or  the   labor   would   be 
prohibitory),  but  read  off  mechanic- 
ally from  a  diagram  similar  to  Fig. 
299,  which  shows  the  principle  of 
an  apparatus  for  the  purpose  de- 
vised by  Mr.  Chas.  Francis.  Chief 
of  Office  on  the  Pacific  Branch  of 
the  Mexican  Centra!  Railway.    Any 
one  can  readily  make  it.    The  base 
is  a  sheet  of  accurate  cross-section 
paper,   10  or  20  squares  per  inch, 

^ff     .-  ,    ,  on  which  angles  are  accurately  laid 

Off,  either  around  the  ^d.^^,  as  shown,  or  on  a  circular  arc  of  as  large  a 


•  i^ 


Fig. 


299. 


..-mmK. 


f 


890 


ClfAP.   XXXIT.^PROJECTING  LOCA  TION. 


radius  as  possible.     Values  are  given  to  the  lines  from  zero  to  100  or 
more.     The  straight-edge  is  laid  off  with  the  same  scale. 

We  have  then  only  to  set  the  edge  of  the  straight-edge  at  the  angle 
corresponding  to  any  bearing ;  place  a  needle-point  or  sharp  pencil  at 
the  point  on  it  representing  the  length  of  a  given  line,  and  we  read  off 
from  the  sheet  below,  at  once,  latitudes  and  departures  for  the  line.  Lati- 
tudes and  departures  for  miles  of  line  can  thus  be  called  off  and  tabulated 
in  a  day  by  two  men,  and  the  absolute  position  of  every  point  on  the 
survey,  by  rectangular  coordinates  from  any  fixed  origin,  determined 
once  for  all.  From  these  notes  as  many  or  as  few  points  can  be  trans- 
ferred to  the  map  as  seems  desirable,  according  to  its  scale,  and  the  re- 
mainder sketched  in.  When  several  alternate  lines  are  to  be  mapped 
together  this  method  is  especially  useful,  as  the  trouble  of  closing  ac- 
curately is  so  greatly  reduced. 

PROJECTING  LOCATION. 

1246.  To  make  a  really  good  projection  on  a  topographical  map  in- 
volves a  great  deal  of  work  and  study,  and  errors  are  almost  as  easy  as 
they  are  on  the  ground.  In  fact  the  writer  has  no  belief  that  any  one 
ever  projected  a  location  on  paper  which  could  not  be  materially  improved 
by  study  on  the  ground. 

The  most  difficult  case  is  projecting  a  final  grade-line  in  which  curve 
compensation  is  to  be  introduced  as  it  advances.  In  very  difficult  coun- 
try a  first  projection  on  an  estimated  average  "  straight "  grade-line  is  often 
advantageous,  saving  time  and  giving  a  better  final  result  because  of  the 
double  study.  The  lower  (dotted)  spiral  of  Fig.  216  was  projected  in 
this  way. 

The  projection  should  begin  at  the  summit  or  other  fixed  point 
which  the  line  must  make.  Assuming  a  starting-point  and  elevation, 
take  in  a  pair  of  dividers  the  distance  on  the  map  which  the  given  grade- 
line  takes  to  fall  10  ft.,  or  better  yet,  5  ft.  When  curve  compensation  is 
introduced  this  distance  will  be  different  on  a  tangent  and  on  every  curve.^ 
and  should  be  laid  off  on  a  strip  of  paper  so  that  the  dividers  can  be  set 
and  reset  without  trouble. 

With  the  dividers  thus  set,  step  off  a  distance  of  10  or  12  inches  on 
the  map,  following  as  nearly  as  may  be  where  it  is  thought  the  line 
will  lie.  On  favorable  topography  this  will  be  very  closely  along  tlie 
GRADE  CONTOUR,  or  line  where  the  plane  of  the  grade  strikes  the  natural 
surface.     In  that  case  we  can  step  off  quite  a  distance  at  once,  stepping 


CHAP.  XXXII.^PROJECTING  LOCA  TION, 


891 


down  a  contour  or  half-contour  at  a  time,  and  marking  by  a  small  cross- 
mark  wiiere  the  grade-line  crosses  each. 

1247.  The  grade-contour  should  then  be  very  lightly  pencilled  in,  and 
a  curve  or  two,  or  a  long  tangent  and  the  beginning  of  one  curve,  pro- 
jected. Then,  setting  the  dividers  for  the  proper  distance  for  a  L\\  of 
I,  2,  or  5  ft.  on  the  given  curve  or  tangent,  and  starting  from  the  fixed 
point,  step  along  the  projected  location  to  the  first  point  of  curve  and 
determme  and  write  down  its  elevation  to  the  nearest  foot  and  tenth  ; 
paying  no  attention  as  yet  to  stationing,  but  simply  to  determining  points 
where  the  grade-line  reaches  certain  even  elevations,  and  to  determining: 
the  grade  at  the  points  of  curve. 

Having  reached  a  curve  from  a  tangent,  reset  the  dividers  for  the 
proper  distance  for  the  given  fall  on  the  curve  ;  start  from  the  P,  C.  cor- 
rectly by  straddling  the  dividers  over  it  according  to  its  fractional  eleva- 
tion ;  step  around  the  curve  to  the  P.  T.,  and  determine  and  lightly  note 
Its  elevation.  Reset  the  dividers  for  the  next  tangent  or  curve,  and  so  on 
to  the  end  of  the  section  projected. 

1248,  Then  return  and  correct  the  grade-contour  according  to  the 
precise  points  at  which  the  elevation  of  each  contour  or  half-contour  is 
reached  on  the  actual  projection,  sketch  every  bit  of  it  in,  and  see  if  the 
projection  corresponds  to  the  corrected  grade-contour  as  well  as  is  possi- 
ble.    Consider  everything  :  the  material  (above  all);  the  surface  slope  ; 
the  water-ways ;  whether  the  line   should  be  preferably  in  cut  or  fill, 
whether  the  tangent  or  the  centre  of  a  curve  cannot  be  slightly  changed 
so  as  to  fit  the  grade  contour  better,  or  avoid  a  rock-cut ;  whether  the 
form  of  the  gulches  is  correctly  represented  and  there  is  not  a  crossing 
point  slightly  more  favorable  above  or  below,  which  the  topography  does 
not  clearly  show  ;  whether  the  tangent  cannot  be  broken  up  by  a  slight 
curve  and  save  work  which  will  be  more  conspicuous  on  the  ground  than 
on  the  map ;  or,  on  the  other  hand,  whether  the  line  cannot  be  thrown  out 
here  and  in  there,  so  as  to  take  out  curvature  and  yet  give  as  good  a  pro- 
file.    Probably  some  little  modification,  at  least,  will  be  at  once  seen  to 
be   desirable,  and  the  whole  work  will  have  to  be  done  over,  perhaps 
three  or  four  times.     If  not.  it  may  be  for  the  time  being  left  behind. 

1249.  A  short  stretch  more  should  now  be  projected  in  the  same 
manner  as  before,  and  now  only  will  it  be  possible  to  give  proper  study 
to  the  first  section  ;  for  the  whole  relations  of  the  line  to  the  ground  can- 
not be  taken  in  until  the  projection  is  complete  for  a  considerable  dis- 
tance on  each  side  of  the  point  studied.  It  is  now  more  likely  than  be- 
fore that  modifications  will  suggest  themselves  in  the  first  section.    The 


tr.}-    — - 


I 


«92 


CHAP.  XXXIL— PROJECTING  LOCATION. 


reader  who  is  quite  satisfied  with  his  first  or  second  or  third  trial  may 
justly  fear  that  he  is  doing  bad  work.  The  projection  in  Fig.  216,  for 
example,  while  good  enough  for  an  approximation,  is  by  no  means  good  for 
a  final  one,  being  capable  of  considerable  improvement  at  several  points. 

After  completing  several  miles  the  whole  should  be  studied  over  again, 
and  corrections  unnoticed  before  are  pretty  sure  to  suggest  themselves. 
Very,  often  long  stretches  of  the  grade  can  be  raised  or  lowered  somewhat 
to  advantage,  at  the  expense  of  a  slight  break.  It  is  difficult  to  point 
out  every  danger  in  advance,  but  it  is  a  fact  that  men  will  differ  in  their 
projections  almost  as  much  as  in  field  location,  and  the  most  obvious  im- 
provements will  not  suggest  themselves  until  some  one  else  points  them 
out.  Without  an  accurate  personal  knowledge  of  the  ground,  it  is  folly 
for  any  one  to  attempt  to  make  a  really  good  final  projection,  although 
contour  maps  have  the  great  negative  merit  that  glaring  errors  or  gen- 
eral incompetency  may  be  detected  at  sight  by  any  one  of  experience. 

Before  the  projection  is  considered  final  the  corrected  grade-contour 
should  be  made  exactly  right,  and  sketched  in  clearly  and  complete.  It 
is  very  bad  practice  to  sketch  in  only  certain  grade-points.  A  great  check 
acfainst  error  is  thus  lost. 

1250.  The  line  should  now  be  stationed  and  a  profile  and  field-notes 
called  off.  The  latter  are  readily  made  up,  since  the  length  and  degree 
of  each  curve  is  known,  but  they  should  be  checked  and  corrected 
throughout  by  determining  the  bearings  of  every  projected  tangent  from 
the  original  North  and  South  line.  Except  when  errors  are  seen  to  be 
compensatory  the  bearings  thus  read  will  be  more  trustworthy  than  the 
stepped-off  lengths  of  the  curves,  and  the  latter  should  be  modified  to 
correspond. 

1251.  Curves  may  be  projected  either  (i)  by  compasses,  (2)  by  wooden, 
rubber,  or  metal  curves,  or  (3)  by  a  curve- protractor  made  on  a  large  clear 
sheet  of  isinglass  by  scratching  on  the  curves  and  rubbing  ink  in  the 
scratches.  The  latter  is  a  very  convenient  and  desirable  adjunct  to  the 
work,  but  not  essential  when  the  radii  are  not  too  large  for  compasses. 
With  cut  curves  it  is  far  more  important.  The  writer  personally  prefers 
a  pair  of  compasses  to  anything  else  when  the  radii  admit  of  their  use. 
The  transition  curves  should  be  projected  at  the  same  time  as  the  curves 
by  drawing  in  the  latter  not  quite  tangent  to  the  tangents,  but  at  a  slight 
offset  to  them,  as  in  Figs.  208  and  216.  What  this  precise  offset  may  be 
does  not  matter.  It  may  vary  from  0.5  to  3.0  or  4.0  feet  per  degree  of 
curve. 

1252.  Having  made  the  profile,  the  GRADES  should  be  put  on  it.     Re- 


CIIAP.  XXXII.— PROJECTING  LOCATION. 


\ 


895 

member  in  putting  grades  on  a  profile  that  it  is  a  great  deal  easier  to- 
stretch  a  thread  to  cover  two  or  tliree  feet  of  a  profile  than  to  execute 
with  shovel  and  crow-bar  tlie  work  which  it  calls  for.     Long  shallow  cuts 
are  generally  a  mistake  of  judgment.    The  grade  sliould  rather  be  broken 
and  thrown  up  into  fill.    As  a  rule,  apices  in  grade-lines  should  never 
meet  on  a  fill  nor  a  hollow  in  them  appear  in  a  cut,  since  the  extra  depth 
of  the  cut  or  height  of  the  fill  is  so  much  work  thrown  away  in  order  to 
do  a  bad  thmg-bring  grade-lines  to  a  sharp  intersection  ;  but  there  are 
exceptions  as  respects  fills,  when  it  is  desirable  (as  it  alwavs  is)  to  give 
abundant  water-way  for  streams  without  carrying  the  whole  fill  on  too 
high  a  bank.    It  is  a  common  error  of  inexperienced  projectors  to  lav 
the  grade-lme  too  near  to  the  supposed  high-watermark.  It  is  not  worth 
while  to  take  chances,  and  it  should  be  several  feet  above  all  the  an 
parent  possibilities.  P 

1253.  It  is  always  desirable,  except  on  steep  side-hills,  to  have  the 
fills  exceed  the  cuts.  Heavy  fills  can  be  gotten  at  from  a  good  many 
points,  or  temporarily  trestled  and  filled  by  train,  but  large  cuts  are  very 
apt  to  delay  progress  (they  are  generally  the  last  work  finished),  and  give 
trouble  for  maintenance  later.  Long,  low  fills  should  never  be  laid  out 
to  average  less  than  two  feet  high.  The  temporary  economy  is  a  dear 
one.  Grades  can  in  general  be  laid  out  just  as  well  as  not  at  some  evea 
rate  and  starting  from  some  even  station,  but  the  trouble  often  taken  to 
this  end  IS  perhaps  rather  worse  than  thrown  awav,  as  it  is  a  simple 
matter  to  compute  the  grade  elevations,  and  economy  is  very  apt  to  be 
sacrificed  to  no  real  advantage.  Full  allowance  for  vertical  curves  should 
IooITh    ff'  ..  progresses  and  the  grades  for  stations  carefully 

looked  after,  especially  m  projecting  long  grades.  Table  125,  page  388  ■ 
will  facilitate  doing  so.  The  original  grades  should  be  studied  ovi  and 
revised,  aided  by  the  cross-sections  of  the  final  location.  It  is  costlv 
business  to  attempt  to  make  the  latter  without  accurate  knowledge  of  the 
material  under  the  surface,  but  this  trouble  is  too  frequentiv  not  taken 
Simple  boring  and  drilling  appliances  for  investigating  the  material  now 
exist  in  plenty,  and  the  expense  is  very  slight.     Whenever  and  wherever 

or  1',%  T^^""-  ^^'"^'J  '""^  "^"""'^  "'^  ^"^f^''^^'  *ere  is  little  excuse 
for  not  determining  its  depth  and  limits,  as  it  can  often  be  avoided  with 
ease. 

the'f  *;  T''"'}^^^.  ^'^t'  '>>=  P™fi'^  and  field-notes  of  the  paper  location 
he  final  location  is  proceeded  with.    The  profile  is  kept  close  up  to  the 

chert'/  ,'  r""°".  °/  "''  ^°'^  ^'  ^"'P^^^'^  ^'*  '"^  projection 

checked  mainly  by  it.    A  few  tie-notes  with  the  preliminary  are  usually 


894 


CHAP.  XXXII.— PROJECTING  LOCATION. 


% 


mt 


taken  off  for  each  day's  work,  but  it  is  not  worth  while  to  attach  much 
weight  to  them.  The  question  is  only :  Does  the  line  as  run  on  the 
ground  give  as  good  a  profile  as  was  expected  and  desired,  and  can  any 
improvements  be  made  in  it  ?  That  chief  of  party  is  not  a  very  good  one 
who  will  not  see  many  improvements  as  he  progresses.  Aided  by  the 
system  of  transition  curves  referred  to  in  the  previous  chapter,  these 
changes  are  rapidly  made;  but  if  there  be  any  doubt  at  all  about  them, 
they  should  be  left  for  a  later  revision.  In  fact,  the  better  way  is  always 
to  run  the  whole  location  over  twice  (par.  1193).  The  money  spent  will 
be  well  invested. 


\ 


\ 


CHAP.  XXXIII.— THE  ESTIMATION  OF  QUANTITIES. 


895 


CHAPTER  XXXIII. 

THE    ESTIMATION    OF    QUANTITIES. 

1255.  The  purpose  of  preliminary  estimates  is.  first,  to  arrive  at  an 
approximate  idea  of  the  cost  of  the  work ;  secondly,  to  compare  alternate 
lines  together;  and  thirdly,  to  assist  in  fixing  the  grades.     For  neither  of 
these  purposes  is  any  great  exactitude  necessary,  especially  if  there  is 
certamty  of  having  the  quantities  at  least  large  enough.    For  estimating 
the  cost  of  the  work  an  excess  of  two  or  three  per  cent  is  rather  an  ad 
vantage.     For  comparing  alternate  lines  the  error,  whatever  it  is.  will 
make  no  difference   unless  there  are  causes  why  it  should  exist  on  one 
Ime  and  not  on  the  other.     For  fixing  grade-lines  a  slight  percentage  of 
error  ,s  equally  unimportant,  since  it  is  rarely  good  engineering,  under 
modern  "methods  of  construction,  to  attempt  any  very  exact  balance  of 
cut  and  fill,  the  fill  bemg  always  laid  out  in  excess,  and  long  cuts  avoided 
as  much  as  possible.     The  only  exceptions  to  this  rule  are  when  both  the 
cuts  and  fills  are  short  and  heavy,  so  that  the  haul  will  not  be  long  or 
on  a  steep  side-slope,  so  that  throwing  the  line  in  to  decrease  the  ci^ts 
will  increase  the  fills,  or  vice  versa.     Even  then  the  possibility  of  using 
temporary  or  permanent  trestles,  the  size  of  water-ways  required,  and  the 
.differences  in  classification  will  ordinarily  have  more  effect  on  where  the 
hne  IS  laid  than  the  mere  question  of  balancing  the  profile. 

1256.  For  these  reasons  it  is  an  absurd  waste  of  time  to  use  the  pris- 
moidal  formula,  or  any  other  method  but  that  of  averaging  end-areas 
for  making  preliminary  estimates,  and  this  method  should  be  used  in  the 
simplest  way  of  ail-that  of  determining  centre-heights  directly  from  the 
profile,  unless  the  ground  is  quite  rough  and  irregular.     In  that  case 

des^rable^  '^  ^^^  ™^'^''^^  ^^  '''''^'  ^^"""^"^  cross-sections  may  appear 
In  working  merely  from  the  profile  centre-heights,  without  takin<r  the 
^trouble  to  compute  them,  there  is  a  certain  lack  of  precision  which  o"n  an 
individual  solid  may  introduce  a  considerable  error,  but  we  introduce  no 
tendency  to  error  in  either  direction.  Our  readings  are  as  likely  to  be 
too  great  as  too  small,  and  when  that  is  so  we  know  from  the  theory  of 


896     CHAP.  XXXUI.—  THE  ESTIMATION  OF  QUANTITIES, 


probabilities  that  if  the  average  error  on  each  individual  solid  be  i,  with 
no  tendency  to  either  excess  or  deficit,  the  probable  net  error  per  solid 
on  1000  such  solids  will  be  only  0.0316  cubic  yards,  and  on  10,000  solids- 
only  o.oi  cubic  yards.     Thus  there  is  no  real  objection  to  working  from 
a  well-made  profile  for  any  preliminary  purpose. 

1257.  The  nature  of  the  error  in  the  method  of  computing  by  averag- 
ing end-areas  is  this  :  The  error  increases  as  the  square  of  the  difference 
in  centre-height,  and  is  not  in  the  least  affected  by  the  absolute  volume 
of  the  solid.  The  heavier  the  work,  therefore,  or  the  less  the  sudden 
changes  of  profile,  the  less  the  proportionate  error.  That  cut  is  an 
unusual  one  in  which  the  error  is  more  than  5  per  cent,  and  that  section 
of  road  would  be  very  unusual  on  which  the  error  was  more  than  i  per 
cent,  and  this  error  is  always  in  excess.  There  are  indeed  certain  pos- 
sible solids  in  which  the  error  will  be  in  deficiency,  and  certain  others 
(those  whose  width  on  top  is  the  same  while  the  centre-heights  differ,  or 
vice  versa)  in  which  the  end-area  method  is  precisely  correct,  while  cer- 
tain methods  by  the  prismoidal  formula  which  appear  much  more  exact 
will  give  a  deficiency;  but  except  on  perhaps  one  solid  in  a  thousand, 
averaging  end-areas  always  gives  an  excess  of  volume. 

1258.  All  methods  of  computing  volume  by  first  transforming  the 
end  sections  into  equivalent  level-sections  introduce  a  constant  tendency 
to  deficiency,  and  for  that  and  other  reasons  are  a  worse  than  useless- 
labor,  far  simpler  methods  giving  a  more  accurate  result.  The  proper 
method  of  computing  earth-work  in  construction  is  to  compute  by  end- 
areas  only,  and  then  at  any  later  time  when  convenience  serves,  to  deter- 
mine prismoidal  corrections  for  those  solids  which  need  it  only,  which 
are  those  differing  by  more  than  two  or  three  feet  in  centre-height. 
These  corrections  are  then  added  together  for  each  cut  or  section  and 
deducted  in  gross  from  the  end-area  volume.  The  reasons  which  make 
this  method  at  once  the  simplest  and  the  most  accurate  of  all,  and  the 
evidence  from  experience  that  it  is  so,  are  given  at  length  in  the  writer's 
treatise  on  the  computation  of  earth-work,  referred  to  elsewhere  in  this 
volume,  and,  so  far  as  he  knows,  are  given  nowhere  else. 

1259.  In  computing  quantities  from  profiles  for  preliminary  purposes 
the  cut  or  fill  should,  as  a  rule,  be  assumed  to  terminate  at  the  nearest 
half-station  to  where  it  actually  does  terminate,  as  shown  in  Fig.  300, 
whether  its  actual  length  be  a  little  more  or  less.  This  introduces 
another  element  of  slight  uncertainty,  but  it  is  justified  by  the  fact, 
which  it  is  sometimes  difficult  for  young  engineers  to  realize,  that  the 
end  of  a  cut  makes  a  very  small  part  of  its  total  volume,  so  that  very 


\ 


CHAP.  XXXIII.^THE  ESTIMATION   OF  QUANTITIES.     897 

trifling  errors  in  the  centre-heights  at  the  middle  of  the  cut  will  have  far 
more  effect.    Moreover,  as  the  error  is  as  likely  to  be  one  way  as  another, 

it  will  be  in  the  end  com- 
pensatory, and  no  good  end 
will  be  attained  from  the 
considerable  extra  labor  of 
taking  account  of  such  de- 
tails, unless- the  material  is 
rock,  and  not  always  then, 
except  in  the  final  adjust- 
ment of  the  line. 

The    centre-heights  are 
then  read  off  at  each  sta- 
tion and  the  corresponding 
Fig.  300.  •  •      J  .      ,         ^ 

tShowin^  the  manner  in  which  a  profile  cut  is  assumed   ^^^ntlties  determmed.  This 

l?miJary  eltrmTtetr°  ^"^"'^  ^"    ^^^^^    equivalent    to 

...  .     _..        '  assuming  that   the    actual 

solid  m  Fig.  300  may  be  transformed  into  the  series  of  prisms  bisected 
by  the  dotted  lines. 

1260.  It  is  not  usual  nor  necessary,  in  preliminary  estimates  of  earth 
to  make  any  part  of  the  estimate  for  fractional  stations.  When  neces- 
sary It  IS  allowed  for  by  taking  the  centre-heights  a  little  higher  or  lower 
as  IS  also,  in  fact,  any  excess  or  deficiency  in  the  length  of  the  end  sec- 
tion. In  this  way,  with  a  little  practice,  closely  approximate  results  to 
what  the  most  careful  work  will  give  can  be  readily  obtained.  There 
can  be  no  better  practice  for  the  student  than  to  determine  this  practi- 
cally. 

1261.  One  source  of  error  must  be  allowed  for  when  it  exists,  however 
-the  SURFACE  SLOPE.  This  may  be  done  either  by  using  a  coefficient 
to  multiply  the  quantities  when  obtained,  or  bv  working  from  adiacrram 
like  those  devised  by  the  writer,  which  give  quantities  at  once  for  any 
surface  slope.  When  the  surface  slope  is  level  or  under  10°,  a  table  of 
level-section  quantities  may  be  conveniently  used,  or,  still  better,  plotted 
as  a  diagram,  as  in  those  of  the  writer,  and  the  successive  quantities 
taken  off  by  an  odometer  or  on  a  strip  of  paper.  The  trouble  and  chance 
of  error  in  addition  is  thus  saved. 

1262.  In  ROCK-WORK,  or  wherever  these  methods  are  not  accurate 
enough,  by  far  the  better  way  is  to  plot  the  surface,  draw  in  the  road-bed 
and  slopes  with  a  template,  and  determine  the  areas  with  a  planimeter. 
which  is  a  very  rapid,  simple,  and  accurate  method.     Before  the  final 

$7 


f" 


SgS     CHAP.  XXXIII.—  THE  ESTIMATION  OF  QUANTITIES. 

location  is  regarded  as  complete,  it  is  in  every  way  desirable  tliat  such 
sections  should  be  plotted  complete  for  the  entire  line  and  carefully 
studied. 

1263.  Culverts. — It  is  always  a  mistake  to  make  separate  estima- 
tions of  each  of  the  minor  masonry  structures.  It  is  but  two  or  three 
hours' work  to  construct  a  diagram  on  a  single  sheet  of  cross-section 
paper,  which  will  enable  the  quantities  for  any  standard  type  of  culvert 
to  be  read  off  at  once  for  any  given  centre-height,  to  a  tenth  of  a  cubic 
yard  if  desired,  but  the  nearest  cubic  yard  is  sufficiently  precise  for  the 
requirements.  The  surface  slopes  would  inake  a  material  difference 
with  the  length  of  these  structures,  except  that  when  the  surface  slope 
is  steep  it  is  rarely  good  practice  to  lay  a  culvert  in  the  deepest  hollow 
of  a  gulch.  It  may  usually  be  placed  somewhat  higher  and  at  one  side, 
and  often  well  up  toward  sub-grade,  with  very  great  advantage  and 
economy,  the  only  important  point  being  to  absolutely  secure  the  lower 
end  of  the  culvert  against  wash,  which  is  readily  done.  Therefore,  if  a 
culvert  be  taken  as  the  equivalent  of  one  under  the  deepest  centre  fill 
with  a  level  surface  slope,  it  will  ordinarily  be  sufficient.  If  not,  it  can  be 
taken  as  much  deeper  as  seems  necessary. 

1264.  To  construct  the  diagram,  the  volume  of  any  box  or  arch  cul- 
vert whatever  (assuming  it  to  be  level)  is  expressed  by  the  equation 

in  which  // =  the  centre  height, /=  a  coefficient  depending  on  the 
cross-section  of  the  main  body  of  the  culvert,  and  C=  a  constant  (which 
may  be  either  plus  or  minus),  which  includes  the  modifying  effect  on 
volume  of  the  ends  of  the  culverts.  To  substitute  actual  values  in  the 
equation  for  any  given  type  of  culvert:  Compute  its  volume  complete 
with  an  average  depth  of  foundation,  under  any  height  of  fill  from  the 
natural  surface — say  lo  feet.  Compute  also  the  addition  to  its  volume 
by  lengthening  it  3  feet  (with  i^  to  i  side  slopes),  or  by  whatever  other 
length  is  added  to  the  culvert  by  increasing  the  fill  i  foot.  We  then 
have  values  of  v,f,  and  Hto  substitute  in  the  equation,  and  Ccan  be  de- 
termined at  once. 

Such  a  diagram  has  another  value  than  merely  to  save  labor.  It  keeps 
before  the  mind  the  proportionate  quantities  in  culverts  of  different  sizes, 
although  it  this  should  lead  to  using  smaller  ones  it  would  ordinarily  be 
unfortunate.  No  dry  work  should  be  estimated  for  if  cement  is  rcason- 
5ibly  accessible.     It  is  costly  economy. 

1265.  Bridge  Piers.— Any  bridge  pier  may  be  resolved  into  certain 


CHAP.   XXXIII.— THE  ESTIMATION  OF  QUANTITIES.     899 

parts  independent  of  height;  a  rectangular  solid  varying  directly  with 
height,  and  a  pyramid  or  cone.  In  other  words,  its  equation  of  volume 
is  of  the  form 

'V=fH^f'H^ArC, 

with  values  of  letters  as  above.  Numerical  values  may  likewise  be  deter- 
mined  in  the  same  way.  With  a  batter  of  \  inch  per  foot,  the  value  of 
J  ,  for  volumes  m  cubic  yards,  will  be  only  .00103.  For  a  pier  lo  ft  high 
this  gives  1.03  cubic  yds.  as  due  to  the  batter;  for  a  pier  100  ft.  hi-h  10^0 
■cubic  yards.  **   '      ^ 

1266.  Bridge  abutments  and  open  culverts  may  have  their 
volume  expressed  for  constructing  a  diagram  in  precisely  the  same  way 
as  may  also  pile  or  other  foundations.  It  may  not  save  any  great  amount 
of  labor  to  do  this,  but  it  does  furnish  a  check  against  errors  in  single 
computations,  and  is  information  which  it  is  very  convenient  to  have 
ready  for  instant  reference. 

1267.  Wooden  trestles  are  cheap  affairs.  The  effort  should  be  to 
estimate  them  liberally,  but  it  is  quite  unnecessary  in  a  preliminarv  esti- 
mate to  waste  time  on  a  careful  design,  merely  for  the  purpose  of  getting 
quantities.  «>         & 

In  any  wooden  trestle,  the  caps  and  all  the  floor  system  above  it  as 
also  the   minimum   length   of  sill  and   all  wooden    parts  below  it  are 
directly  as  the  length  of  the  structure  and  independent  of  its  height 
The  same  is  true  of  the  cost  of  digging  foundations,  and  the  piling  or 
masonry  if  used  (as  one  or  the  other  always  should  be). 

At  a  certain  distance  below  the  cap,  say  10  feet,  there  is  a  system  of 
longitudinal,  transverse,  and  diagonal  ties  and  sway-brace  running  the 
entire  length  of  the  structure  on  a  line  about  10  feet  below  the  caps  and 
^constructively)  a  certain  addition  to  the  length  of  the  sill.  All  this* may 
be  expressed  at  so  much  per  lineal  foot  on  a  horizontal  line  10  feet  below 
the  grade-line. 

Ten  feet  farther  down  there  is  a  similar  system,  nearly  duplicating  the 
first,  but  a  little  larger,  which  may  be  all  expressed  at  so  much  per  lineal 
foot  on  a  horizontal  line  20  feet  (or  whatever  the  distance  may  be)  below 
the  grade-line. 

So  we  may  proceed  until  we  have  provided  for  the  highest  trestles 
likely  to  occur  on  the  line  of  the  given  type,  and  we  shall  have  expressed 
the  feet  board  measure  in  any  width  in  an  equation  of  the  following 
lorm :  ^ 

F/.  B.  M.  =/L  +fL'  +f'L"  -f  etc., 


w\  I 


f 


a 


I 


900     C//AP.  XXXIII.— THE  ESTIMATION  OF  QUANTITIES.. 

in  which  L,  L',  L"  =  the  respective  lengths  of  the  structure  on  the* 
grade-line  and  on  parallel  lines  10, 20,  30  feet,  etc.,  below  it,  and /,/*,/"=. 
the  corresponding  measurement  per  lineal  foot. 

1268.  The  length  of  each  of  these  lines  below  the  grade-line  ought,  in 
theory,  to  be  measured  a  little  short  on  the  profile  to  allow  for  any  bents 
which  may  extend  below  one  system  and  not  quite  down  to  another,  but 
such  nicety  may  be  neglected.  At  the  bottom  of  the  trestle  there  will 
be  an  irregular  area  of  greater  or  less  extent.  To  include  this  in  the 
estimate,  transform  it  by  eye  into  a  rectangle  10  feet  high  and  of  equal 
area.  Any  one  familiar  with  the  construction  of  trestles  will  do  this 
with  great  accuracy;  and  the  results  of  this  method,  in  which  no  account 
is  taken  of  the  particular  number  or  position  of  bents,  come  surprisingly 
close  to  the  ultimate  measurement,  as  the  writer  has  tested  on  many 
structures. 

1269.  Trestles  should  invariably  be  built  with  side  stringers  and  ties- 
about  12  ft.  long,  capped  with  a  guard  rail,  as  a  safeguard  against  de- 
railed trains,  foot-passengers  caught  on  the  structure  by  a  train,  and  the- 
insidious  effect  of  decay,  as  well  as  for  its  material  addition  to  the  strength, 
of  the  structure  even  when  new.  "  Split  "  stringers,  breaking  joints  with 
each  other,  are  invariably  used  in  good  practice,  and  split  caps  and  sills- 
boxed  into  the  posts  and  bolted  through  make  a  far  stiffer,  better,  and 
more  easily  renewable  structure  than  the  common  form  of  mortise 
joints.  "  Cluster-bent"  trestles  made  of  8  x  8  inch  timber  are  the  best- 
for  high  structures. 

The  ends  of  all  trestles  and  bridges  should  be  protected  by  Latimer's 
rerailing  safety  frogs,  a  cheap  cast-iron  watchman  which  may  be  relied 
upon  to  put  derailed  wheels  back  upon  the  track,  if  not  too  far  displaced, 
as  has  been  proven  by  many  instances. 

1270.  Iron  Trestles.— Iron  trestles  may  be  estimated  in  much  the 
same  way  as  wooden  trestles,  and  it  is  of  practical  value  to  do  so  to 
bring  out  how  little  the  height  of  trestles  has  to  do  with  their  weight  or 
cost, — a  fact  which,  if  it  be  fully  realized  and  taken  advantage  of,  may 
often  be  an  immense  assistance  in  obtaining  a  favorable  line,  by  enabling 
it  to  be  carried  high  above  what  are  apt  to  be  the  most  serious  obstacles — 
the  deep  gorges. 

Iron  trestles,  for  some  occult  reason,  are  usually  planned  for  bents  30 
feet  apart,  each  successive  pair  of  bents  being  braced  together  into  a 
kind  of  pier.     Sometimes  the  intermediate  spans  are  made  45  or  60  feet, 
and  occasionally  the  bents  are  60  feet  apart,  continuously.     Sometimes* 
the  intermediate  spans  are  mcreased  to  loaor  more  feet. 


\ 


'CHAP.  XXXIII.—  THE  ESTIMATION  OF  QUANTITIES     9OI 

1271.  However  these  details  are  varied,  there  is  wonderfullv  little  dif- 
ference m  the  total  weight  of  the  structure,  which  usually  comes  out  much 
the  same,  barring  a  slight  percentage,  as  if  the  simple  type  of  30-foot  bents 
had  been  used  throughout.  What  is  gained  in  the  bents  is  lost  in  the 
floor-system,  or  vice  versa.  This  is  strikingly  illustrated  even  in  so  widely 
different  a  structure  from  the  ordinary  trestle  as  the  Kentucky  River 
bridge.  The  total  weight  of  iron  corresponds  very  closelv  with  what 
would  have  been  required  to  cross  the  gorge  with  a  trestle  with  30-ft 
bents— not  equally  safe  by  any  means,  but  of  the  same  average  weight 
per  lineal  and  vertical  foot  as  in  the  minor  structures  on  the  same  road 
built  to  sustain  the  same  rolling  load ;  so  that  in  estimating  structures 
for  large  and  small  gorges,  by  the  same  rule,  we  do  not  go  far  astray 

1272.  This  fact  has  led  Mr.  Geo.  H.  Pegram  to  propose  the  followin^r 
lornmla  for  the  weight  of  iron  trestles,  which  he  states  that  he  has  found 
to  give  close  results  when  tested  on  a  considerable  number  of  actual 
structures : 

IVt.  in  lbs.  =  (3Z  +  2H)  no  for  Mogul  engines  and  1820  lbs.  per  ft  • 
m  which  L  =  the  total  length  of  the  structure  between  centres  of  end- 
pins  and /r=  the  sum  of  the  total  bent  heights  from  top  of  masonry 
pedestal  to  top  of  columns,  taken  as  30  feet  apart,  whatever  they  may 
actually  be.  For  Consolidation  engines  we  may  take  W=(xL  +  2H) 
125  to  130.  ^ 

These  formulae  give  the  total  shipping  weight  of  iron,  and  will  ordi- 
narily  approximate  within  5  to  10  per  cent.  They  will  be  most  in  error 
<too  small)  for  very  large  structures. 

1273.  To  this  estimate  is  to  be  added  the  timber-floor  system  and  the 
pedestals.  The  pedestals  are  usually  of  the  best  quality  of  cut  stone 
masonry,  and  on  the  Cincinnati  Southern  Railway,  where  all  such  details 
were  very  carefully  looked  after,  averaged  1.6  cubic  yards  per  lineal  foot  of 
trestle  and  ranged  from  4  to  8  ft.  high,  above  the  natural  surface  The 
floor  system  is  readily  estimated  according  to  the  design  adopted  which 
should  include  plenty  of  timber. 

On  the  Cincinnati  Southern  Railway  (Mogul  rolling-load,  which 
proved  too  small  almost  before  the  road  was  opened)  the  average  con- 
tract prices  for  viaducts  were  $25  per  foot  horizontal  and  $10  per  foot 
vertical,  including  the  floor.  Adding  to  this  the  cost  of  masonry  pedes- 
tals,  we  have,  by  a  similar  method  of  estimation  to  that  recommended 
lor  wooden  trestles  ; 

Per  foot  horizontal  at  grade-line $40  00 

Per  foot  horizontal  at  intervals  of  lo-ft.  below  grade... .         3  ^;i 


r 


902     CHAP.  XXXIII.— THE  ESTIMATION  OF  QUANTITIES. 

1274.  We  may  see  from  this   method  of  expressing  the  cost  more 
clearly  than  otherwise  how  little  the  height  of  trestles  has  to  do  with 


I 

f 
I 

I 
I 
I 
I 
I 


C*-^-".--.'--r-- 


jprj; 


ir..'!L_JEpC 


I 
-I- 


59300      ^O^TRAIW  OF  BOX  aRS 

^  44600 '^fortrajn  of  coal  cars 
toVoVjuTls 


I  I 


WEIGHT  7,4000 


■! 


\ 


-UWC 


Fig.  301.— Main  Pier  of  Niagara  Cantilever   Bridge,  showing  the  Slight  Effect  of 

Height  on  the  Total  Cost  of  the  Structure. 

TOTAL  WEIGHT  OF  STRUCTURE. 
Span,  248  ft.  (2920  lbs.  f>er  ft.) 724,000  lbs. 


Pier,  130  ft.  4  in.  (1304  lbs.  per  ft.), 


lyOjCxxj 


Total  of  pier  and  cantilever  span,        894,000  lbs. 

Additional  per  ft.  extra  height,  about, 1,500  '* 

or  \  of  one  per  cent. 


CHAP.  XXXIII.— THE  ESTIMATION  OF  QUANTITIES.     903 

their  cost.  Singularly  enough,  it  appears  from  comparisons  of  the  con- 
tract  prices  on  that  road  that  it  has  more  effect  on  the  cost  per  foot 
horizontal  than  per  foot  vertical,  which  latter  were  very  little  affected ; 
in  part,  no  doubt,  because  erection  is  much  more  expensive  per  pound 
with  low  trestles.  Fig,  301  will  show  how  little  the  height  has  to  do  with 
the  cost  of  even  the  largest  structures. 

1275.  It  is  probable  that  pedestals  of  very  superior  concrete  would  be 
cheaper  as  well  as  better  than  masonry.  One  difficulty  in  the  use  of  concrete 
which  is  a  very  serious  one  with  masonry  also,  is  that  under  the  usual  form  of 
contract  the  contractor  furnishes  his  own  cement.  He  is  therefore  under  a  con- 
stant temptation  to^ skimp  the  work  in  that  vital  detail,  both  in  quantity  and 
quality.  The  true  way  is  for  the  company  to  purchase  its  own  cement,  furni«;h 
It  to  the  contractor  liberally,  and  require  him  to  use  it  so.  He  will  then  be  as 
anxious  to  make  the  work  good  in  that  respect  as  he  is  now  to  make  it  poor. 
Much  dispute  and  inspecting  annoyances  will  thus  be  saved,  the  cost  of  the 
work  little  if  any  increased,  and  its  quality  materially  benefited. 

1276.  Bridges.— In  Fig.  247,  page  767,  there  has  alreadv  been  given 
a  diagram  prepared  by  the  writer,  mainly  from  the  formula  determined 
by  George  H.  Pegram.  C.E.,  and  given  in  a  paper  before  the  American 
Society  of  Civil  Engineers.  In  addition  to  what  is  stated  in  connection 
with  the  diagram,  it  may  be  added  that  the  West  Shore  specifications 
called  for  rolled  I-beams  up  to  20  ft.  span,  plate  girders  from  20  to  50 
feet,  lattice  girders  from  50  to  75  ft.,  and  thereafter  pin-connected  trusses. 
There  was  naturally  a  slight  jump  in  passing  from  one  to  another.  The 
weights  of  bridges  of  various  spans  were  computed  to  be  of  first-class 
construction,  without  any  additions  of  doubtful  utility,  so  that  while  a 
bridge  might  weigh  more  than  that  given  through  some  special  excel- 
lence, it  should  not  weigh  much  less.  The  following  are  the  formulae 
deduced  by  Mr.  Pegram,  in  all  of  which 

5  =  the  span  centre  to  centre  of  bed-plates  or  end-pins,  as  the  case 
may  be. 

W  rr  the  total  or  "  shipping"  weight  of  iron  or  steel  in  pounds. 
For  iron  bridges  under  200 ft.  span  : 

in  which 

c-    7  for  Class  T,  Fig.  248,  page  769. 

<^  =    9  for  Class  C, 

a  =  12  for  Class  M.         "  " 

For  Class  N,  three  fourths  of  the  weight  as  given  for  Class  T  was 
taken — a  very  rough  process. 


if 


I 


I 


] 


904     C//AP.  XXXI1I,—  THE  ESTIMATION  OF  QUANTITIES, 
For  iron  bridges  over  200  ft.  span  : 

»-=  (5  +  1)5-. 


in  which 


b  —  100  for  Class  C,  • 
^  =    80  for  Class  T. 


For  steel  bridges  aver  yooft.  span  : 

W  =  cS\ 


in  which 


c  —  d  for  Class  C, 
^  =  6.7  for  Class  T. 


1277i  The  type  of  bridge  assumed  was  as  follows : 

For  spans  below  75  ft. :  deck-plate  girder  bridges,  8  ft.  wide,  con- 
nected with  angle-iron  bracing,  and  with  cross-ties  resting  on  the  top 
chords. 

Above  75  ft.  up  to  150  ft.:  through  truss  bridges,  Pratt  or  single 
quadrangular  trusses. 

Over  150  ft.:  Whipple  or  double  quadrangular  trusses. 

The  widths  assumed  were:  For  standard-gauge  spans  under  255  ft., 
14  ft.  in  the  clear;  for  320-ft.  span,  18  ft.  centre  to  centre  of  trusses; 
for  420-ft.  span,  21  ft.  centre  to  centre,  and  for  520  ft.  span,  25  feet  centre 
to  centre.  The  floors  of  the  spans  consisted  of  cross  floor-beams  at  the 
panel  points,  with  a  line  of  iron  stringers  under  each  rail,  except  for  spans 
over  300  ft.,  which  had  three  lines  of  stringers. 

Differences  in  depth  affect  the  weight  less  than  would  be  supposed. 
Thus  in  a  6o-ft.  girder  span,  for  Class  T,  the  difference  in  total  weights 
between  depths  of  5  ft.  and  5^  ft.  was  practically  nothing,  and  for  an 
80-ft.  girder  span,  calculated  for  Class  C,  with  depths  of  6  ft.,  6^  ft.,  and 
7  ft.,  the  difference  was  less  than  i  per  cent.  In  a  1 80-ft.  truss  span,  the 
difference  in  weights  between  depths  of  26  and  28  ft.  was  less  than  2  per 
cent. 

In  a  520  ft.  steel  span,  for  Class  T,  the  difference  in  weight  between  a 
depth  of  50  ft.  and  one  of  58  ft.,  was  about  3  per  cent. ;  a  depth  of  56  ft. 
was  finally  taken  in  this  case. 

1278.  Modifications  for  other  conditions  than  those  specified  may  be 
made  as  follows : 

If  wooden  stringers  are  used,  deduct  195  lbs.  per  ft.  for  Classes;  M.  and 
C,  210  lbs.  for  Class  T,  and  140  lbs.  for  Class  N. 

For  safety  stringers  add  100  lbs.  per  ft.  for  all  classes. 


CHAP.  XXXIIL^THE  ESTIMATION  OF  QUANTITIES.    905 

For  deck-truss  bridges  add  10  per  cent,  and  for  double-track  bridges 
90  per  cent,  to  the  formula  weight. 

Through-plate  girder  bridges  will  not  differ  materially  from  deck 
bridges  m  weight,  where  the  cross-ties  are  made  to  serve  as  floor  beams. 
When  an  iron  stringer  floor  is  used,  it  will  be  a  close  approximation  to 
add  200  lbs.  per  foot  to  the  weight  given  by  the  formula. 

For  bridges  of  less  than  150  ft.  span,  the  only  part  of  the  rolling  load 
which  affects  the  weight  of  the  bridge  greatly  is  the  engine  load.  For 
spans  of  over  200  or  250  ft.,  an  average  of  the  engine  and  car-load  per 
loot  will  come  nearer  to  expressing  the  ratio  by  which  the  weight  of  the 
bridge  is  affected. 

1279.  The  weight  of  a  drawbridge,  including  turn-table,  wheels  and 
machinery  to  turn  by  hand,  will  be  very  nearly  the  same  as  for  a  fixed 
span  of  the  same  total  length  to  carry  the  same  live  load.  This  rule  is 
stated  by  Mr.  Pegram  to  have  been  remarkably  exact  in  tests  on  a  num- 
ber of  drawbridges  of  150  to  400  feet,  both  single  and  double  track. 

1280.  The  cost  of  bridges  per  pound  is  far  from  fixed  for  all  classes 
of  structures,  but  may  be  said  to  be  made  up  as  follows : 

•n  .    .  Cts.  per  lb 

1.  Raw  material,  rolled  and  plate  iron 2^  to  3 

2.  Work  on  same  in  shop '  b  |.q  j  1 

3.  Transportation  by  rail 1  ^^    1 

4.  Falseworks  and  erection i  to  i 

<;.  Profit  and  administration i  to  i4- 

"^^^^^ 4""^ 

The  lowest  of  these  prices  are  sometimes  cut  under,  especiallv  in  dull 
times  and  for  large  orders  of  a  simple  class  of  work.  For  example  on 
the  Manhattan  Elevated  Railway,  involving  immense  weights  of  a  very 
simple  class  of  work,  contracts  were  let  at  2  to  3  cents  per  pound  while 
on  the  other  hand,  fat  contracts  at  much  higher  rates  than  those  given 
above  are  not  uncommon  ;  but  these  are  fair  averages  for  average  work 
in  moderately  good  and  bad  times. 

It  will  be  seen  that  only  items  i  and  3  above,  and  not  always  even 
those,  increase  directly  with  the  weight  of  the  bridge.  We  may  say  in  a 
general  way  that  10  per  cent  increase  iri  weight,  with  its  several  times 
greater  increase  in  safe  rolling  load,  will  mean  not  more  than  5  or  at 
most  6,  per  cent  in  the  cost  of  the  bridge  to  the  company,  and  propor- 
tionately for  greater  or  less  differences  of  weight. 


90^     LHAP.   XXXIII.^THE  ESTIMATION  OF  QUANTITIES. 


1281.  Station  buildings,  yards,  track  and  track-laying,  and  many  other 
minor  details  of  construction,  must  likewise  be  included  in  any  complete 
estimate,  but  to  consider  them  here  would  lead  us  too  far  from  our  sub- 
ject, which  has  had  to  do  with  those  details  only  which  are  connected 
with  and  affected  by  the  location  of  the  road. 

In  all  such  details,  it  has  been  intended  to  go  far  enough,  and  not  toa 
far,  to  at  least  fairly  prepare  the  patient  reader  to  make  a  decent  approxi- 
mation to  the  true  economy  of  alignment.  To  do  more  than  this  can 
only  be  a  happy  accident  with  any  one.  To  do  less  than  this  the  writer 
hopes  he  may  have  rendered  unnecessary.  He  has  not  spared  his  own 
labor  to  do  so,  and  for  wherein  he  may  have  fallen  short  he  can  only  say 
with  the  heroine  of  "  A  Winter  s  Tale  :  I  speak  as  my  understanding, 
instructs  me,  and  as  mine  honesty  puts  ii  to  utterance.' 


APPENDICES. 


APPENDIX    A. 


] 


EXPERIMENTS    ON    THE    RESISTANCES    OF    ROLLING-STOCK 

The  mode  of  test  was  by  what  may  be  termed  the  "  drop  test  •"  start- 
ing car^  from  a  state  of  rest  down  a  known  grade,  and  deducing t^e 
resistances  from  the  velocity  acquired.  The  principle  of  this  method  ht! 
of  en  been  employed  before,  sometimes  merely  to  determine  comparati^ 
resistances,  w,thout  attempting  to  measure  their  absolute  amount  and 

wi  r^it^       "  °"  ''"'"'•     '"  '"^  P^^^^"*  ^-'^  ■'  »-  "temped! 
with  entire  success,  to  extend  this  method  to  the  determination  of  a  serie^ 

pa  h  of  the  vehicles,  dunng  which    their  velocity  varied  /rom  o  to  ,o 
miles  per  hour      Great  accuracy  in  time  observations  was  necessa^  for 

tSTT,u  "^'  ""^  '^""'^'^  "y  "'^  ^'d  °f  electricity,  so  Tully 

m  fact  that  the  margin  for  error  in  the  latter  half  of  the  experiment 

I     luVr  "'^"  ^'^  '"•  ^'  *°"-    I'  ™"^'  be  added,  however  that 
about  half  the  tests  were  made  before  the  apparatus  was    ully Trfeaed 
and  are,  hence  less  minutely  accurate,  but  the  maximum  erro'^s'Tn  these 

atter  can  hardly  exceed  i  lb.  per  ton  in  any  case,  as  will  be  evident  from 
the  record  plates,  and  all  errors  of  any  kind  in  this  mode  of  test  ar" 
necessarily  compensatory,  any  excess  in  one  resistance  causing  a  corri! 
spond.ng  deficiency  in  the  succeeding  one,  and  v^ce  versa. 

It  IS  believed  that  equal  accuracy  is  unattainable  by  any  other  mode 
of  test,  sirfce  it  is  plain  that  every  step  in  this  process'^is  free  from  any 
^nsible  source  of  error  other  than  carelessness.  The  accelerating  force 
(gravity)  is  uniformly  applied,  and  exactly  known  from  formula  without 
measurement.  This  force  is  necessarily  all  consumed  (.)  in  ov;rI^ming 
he  resistances  to  be  measured,  or  (2)  in  communicating  velockyThf 
amount  of  force  represented  by  a  given  velocity  is  known  by  fo;muli 
without   measurement,  and   the  velocity   itself  is  exactly   record   ^ 


tl 


\. 


] 


910 


APPES'DIX  A. 


electricity,  beside  a  synchronous  record  of  seconds,  from  which  intervals 
of  time  may  be  easily  read  off  to  ^V  second.  Errors  from  carelessness 
in  computation  are  always  possible,  but  three  checks  existed  against  them: 
<!)  All  formulae  used  were  first  tabulated  by  "constant  differences;"  (2) 
most  of  the  resistances  were  computed  independently  by  two  distinct 
methods,  and  (3)  all  the  computations,  when  completed,  were  plotted 
on  the  record  diagrams  (Plate  IX.),  and  so  many  resistances  were  deter- 
mined for  each  test  at  gradually  increasing  velocities,  that  any  consider- 
able error  of  computation  revealed  itself  graphically.  Finally,  any  errors 
which  still  occur  are  not  cumulative,  any  excess  in  one  resistance  causing 
a  corresponding  deficiency  in  the  next  following,  and  vice  versa. 

The  tests  were  made  under  as  great  a  variety  of  conditions  in  respect 
to  load,  number  of  cars  in  a  train,  area  of  cross-section,  etc.,  as  it  was 
possible  to  secure  with  the  limited  time  at  command,  and  give  due  cer- 
tainty to  each.  This  variety  of  conditions  was  secured  in  order  to  facili- 
tate, as  far  as  possible,  one  of  the  objects  which  was  held  especially  in 
view,  viz.,  a  more  correct  separation  than  heretofore  of  the  aggregate 
resistance  from  velocity  only  (excluding  the  normal  axle-friction)  into  its 
constituent  elements,  air  resistance,  oscillatory  resistance,  etc.  This  ob- 
ject, it  is  thought,  has  been  quite  successfully  attained,  and  with  some- 
what surprising  results. 

[The  great  length  to  which  this  volume  has  grown  forbids  the  reproduction 
of  the  body  of  the  paper,  and  those  desiring  to  follow  it  are  referred  to  the 
paper  itself.  The  determination  of  the  possible  air  resistance  especially  is 
believed  to  have  been  sufficiently  exact  to  make  it  certain  that  it  has  less  effect 
on  the  movement  of  trains  than  is  commonly  supposed.  The  following  are  the 
conclusions  of  the  paper:] 

Summary. 

We  may  summarize  the  various  conclusions  reached  in  the  preceding 
paper  as  follows : 

ist.  The  axle  and  rolling  friction  of  empty  freight  cars  may  be  taken 
as  6  lbs.  per  ton  of  2000  lbs.  The  axle  and  rolling  friction  of  coaches 
and  loaded  freight  cars  may  be  taken  as  4  lbs.  per  ton.  The  fluctuations 
from  these  limits  are  small,  rarely  exceeding  i  lb.  per  ton  in  single  cars, 
or  i  to  i  lb.  per  ton  in  a  train. 

2d.  The  initial  resistance  at  the  instant  of  starting  is  several  times 
greater  than  this,  and  greater  for  loaded  than  for  empty  cars,  being  at 
least  18  lbs.  per  ton  for  loaded  cars,  and  14  lbs.  per  ton  for  empty  cars, 
as  an  average,  but  fluctuating  considerably.  Its  amount  probably  varies 
with  the  length  of  stop,  according  to  unknown  laws. 


APPENDIX  A. 


911 

<:onsum!!:Tlf  '^''  initial  resistance  is  almost  wholly  instantaneous,"^ 
consumes  little  power.  Enough  of  it  still  remains,  however  to  increase 
the  normal  axle-friction  in  the  first  few  car-lengths'  by  at  Ie:;t  .  lbs   ;:: 

/  ^.^^'^'7^^  ^'''  ^^s's;^"ce  against  such  a  surface  as  the  end  of  a  box  rpr 

pe^hl';  21'^  '^  '"^  r "  *  '"•  ^'  ^<'--  ^°«  -  ^  veloct  of  ,0  ^ 
per  hour,  and  (presun.ablyj  mcreases  as  the  square  of  the  velocity     The 

current  estimates  of  this  resistance  (J  lb.  to  i  lb.  p^r  square    Lt)  are 

e^^neous  by  fro.  .50  to  500  per  cent,  when  applied'to  surfaces  of  lh« 

5th   About  two  thirds  of  the  velocity  resistance  proper  excluding  th,. 

due  to  th,s  latter  cause  alone  may  be  estimated  at  \  lb.  per  ton  at  a 
velocuy  of  ,0  miles  per  hour,  varying  as  the  square  of  the  vdoci^r 

6th.  The  resistance  of  curves  decreases  materially  with  the  velocity 
and  appears  to  be  greater  by  a  considerable  percentage  in  the  first  2^To 
500  feet  than  on  the  rest  of  the  curve.  t-  ■*  e  nrst  200  to 

„  L"!'  ^^^  '•^^'"^"=«  °f  «  '°  curve  is  over  i  lb.  per  ton  at  a  velocity  of 
.2  m  les  per  hour,  and  decreases  to  about  i  lb.  per  ton  at  a  velocity  o 
22  .n.les  per  hour.    The  resistance  of  an  Z'  curve  is  oyer  8  lbs.  per  to^  a 
a  velocity  of  9  miles  per  hour,  and  decreases  to  about  6*  lbs  '°  ton 
(probably)  at  a  speed  of  19  miles  per  hour.  ^ 

8th.  Tl>e  average  resistance  of  a  1°  curve  to  4-wheel  trucks  having  » 
5- oot  r,g,d  wheel-base,  and  to  6-wheel  tn,cks  haying  aToliVL 
t:t'r?ScaK  '"^  ^'^^  °^  "^^  "--'  -  ''^  Peistal-AsrlpS 
9tli.  It  appears  possible  that  the  act  of  coupling  together  cars  hv  a 
loose  hnk  slightly  decreases  the  axle-friction,  and  hence  presuLblv 
the  oscllating  friction  at  high  velocities.  The  ave  age  reducS 
observed  from  coupling  four  or  five  cars  together  appeaf^d  to  be  a^ 
much  as  i  lb.  per  ton.  [The  tests  appeared  to  indicate  this  but  th^ 
author  now  regards  it  as  very  doubtful.]  ^ 

loth.  There  appear  to  be  good  grounds  for  suspecting  that  a  shVht 
superelevat.on  of  one  rail  on  a  tangent  may  have  the  effect  of  appre 

.TewV:!ir"p!rtur'^"^^ '° '"°"°"  --  -  ->-''-  °^  - :; 


•  This,  of  course,  does  not  include,  nor  in  any  way  refer  to  th-  ,h^-,-  ^i 
power  demanded  to  get  up  speed,  which  is  .  lbs.  per  oV  to  g ";  a  peed' "70 
miles  per  hour   n  3340  feet   or  4  :;  lh«5   n*.r  r«„  »        •  ^  ° 

hour  in  the  same  dfslance  '^        "  '°  ^"'  "  '"""'  "'  '^  ™''«^  P" 


912 


APPENDIX  A. 


ij  1 


I 


\ 


nth.  Roller-journals  of  various  forms  appear  to  be  very  effectual  at 
velocities  of  o  +,  but  lose  nearly  all  their  theoretical  advantage  as  the 
velocity  increases.  Such  journals  appear  to  be  more  effective  as  the 
load  is  decreased,  and  reduce  the  resistances  of  empty  horse  cars  by 
about  one  half. 

1 2th.  Forty-two-inch  wheels  seem  to  be  even  more  effectual  than 
theory  would  indicate  in  reducing  extra  friction. 

13th.  The  equation  of  resistance  for  average  trains  (twenty  cars)  of 
loaded  box  cars  may  be  taken,  approximately,  as 


APPENDIX  B. 


-ff  = +  4; 

130 


or,  for  trains  of  forty  empty  box  cars. 


^  = 


106 


+  6. 


The  velocity  resistances  of  flat  cars  increase  somewhat  more  rapidly^ 
being  for  twenty  loaded  flat  cars  — ,  and  for  forty  empty  flat  cars  -x— . 

These  formulae  are  believed  to  be  closely  approximate  up  to  velocities 
of  thirty  miles  per  hour.     No  tests  were  made  at  higher  velocities. 

14th.  The  coeflicient  of  axle-friction  is  about  .02  for  loaded  freight 
cars  and  passenger  coaches  at  speeds  of  over  five  miles  per  hour,  about 
.03  for  empty  freight  cars,  about  .065  for  horse  cars,  and  about  .12  for 
freight  tmwks  without  load.  The  coefficient  is  two  to  three  times 
greater  at  the  instant  of  starting.  It  decreases  rapidly  as  the  load  per 
journal  increases. 


913 


APPENDIX    B. 


EXPERIMENTS  WITH   NEW  APPARATUS  ON  JOURNAL.FRICTION 

AT   LOW  VELOCITIES. 

[A  Paper  by  the  author,  read  before  the  American  Society  of  Civil  Engineers   Tune  .   x8g. 
Abbreviated  from  Trans.  Am.  Soc.  C.  E.,  Dec,  1884.]  '       '' 

Of  iLT  1''"''''T  experiments  were  undertaken  by  the  writer  in  the  winter 
of  1878.  pr.manly  to  test  the  correctness,  especially  in  respect  to  initial 
fnct.on  at  low  velocities,  of  a  series  of  other  tests  of  rollin^stock  e  t 
ances  (see  Appendix  A)  made  in  a  totally  different  manner,  on  the  Like 
bhore  &  M.ch,gan  Southern  Railway,  under  the  directi;n  of  Charles 
lame.  Member  and  ex-President  of  the  Society,  who  kindly  furnished 
the  writer  all  necessary  facilities.  ^  ^urnisnea 

The  apparatus  used  is  shown  with  sufficient  clearness  in  Ficr  ,0"     It  is 
extremely  cheap  and  simple,  but  fulfils  its  purpose  as  perfectTy  as" could 
be  desu-ed.  and  is  believed  to  be  entirely  novel.'  The  axle  To  b    tes    d 
IS  placed  ,n  an  ordinary  lathe,  having  as  great  a  variety  of  speeds  as 
possible.     The  testmg  apparatus,  as  actually  constructed,  consisted  of  an 
oak  beam.  6.  about  4"x4"  in  size,  and  about  5  ft.  long,  carrying   he  com 
pound   ever.  LU,  each  of  which  multiplies  the  load  applied  about  i    timl 
or.  m  the  aggregate.  ,25  times.    The  yoke  E  encircles  the  axle  and  bea^ 
agamst  the  brass  B  underneath  it.  thus  furnishing  the  necessary  resTs" 
ance  to  the  action  of  the  levers  and  throwing  the  same  load  upon    he 
ower  brass  i?  as  is  imposed  by  the  levers  directly  on  the  upper  brass  by 
transn.ss.on  through  the  pin  D,  the  latter  being  passed  through  Thole 
in  the  beam  C     The  pressure  was  transmitted  to  both  the  upper  and  the 
lower  brass  by  suitable  iron  blocks  (shown  in  the  cut  directly  above  and 
below    he  brasses),  representing  as  nearly  as  might  be  the  ordinary  fo"^ 
of  the  top  of  a  journal-box.  ^       ^ 

As  thus  constructed,  it  will  be  seen  that  the  entire  apparatus  (when 
properly  balanced,  which  is  perfected  by  the  light  counLrpo  se  ml 
poised  in  unstable  equilibrium  on  the  axle  A,  and  opposes  no  esisfance 
to  motion  in  either  direction,  except  such  as  arises  from  frict^n  A  v"^ 
heavy  load  maybe  thrown  on  the  bearings  viz.,  6000  lbs.  Qc^  fbsoT 


^1 


] 


914 


APPENDIX  B. 


each  bearing)  for  every  24  lbs.  of  load,  W  placed  on  the  extremity  of  the 
compound  lever,  but  the  only  weight  thrown  upon  the  lathe-centres 
is  the  dead  weight  of  the  apparatus  itself,  which  was  kept  constant  at 
205  lbs. 

[Some  further  details  are  omitted  here,  and  throughout  the  remainder  of  the 
paper.] 

When  the  axle  A  is  caused  to  revolve,  the  lever  C  is  held  stationary 
by  the  platform -scale,  and  it  is  obvious  that  the  pressure  produced  upon 


w. 


rt 


Fig.  302.— Apparatus  for  Te.sting  Journal-Friction  in  a  Lathe. 

the  scale  furnishes  an  exact  and  direct  measure  of  the  journal-friction 
It  was  found  in  practice  that  this  pressure,  varying  from  10  to  140  lbs., 
with  the  proportions  actually  adopted,  could  be  weighed  with  as  much 
delicacy  and  ease  as  if  it  were  a  material  substance  resting  upon  the 
platform  of  the  scale.  Under  a  given  load  and  speed  of  journal  the 
friction  produced,  although  it  did  not  remain  absolutely  stationary, 
varied  so  very  little  and  so  slowly  that  the  beam  of  the  scale  would 
sometimes  vibrate  slowly  and  gently  between  the  guards  (sometimes 
touching  the  upper  one  and  again  returning  to  the  lower,  but  for  the 
most  .part  touching  neither)  for  10  or  15  minutes  at  a  time.  On  the 
other  hand,  when  the  brass  was  growing  hot,  by  continuing  the  test  for 
a  considerable  time  the  friction  would  continue  to  increase  so  that  the 
scale-weight  had  to  be  continually  moved  ;  but  the  change  was  never  so 
rapid  but  that  it  could  be  easily  followed  and  studied  with  the  scale,  with 
an  absolute  certainty  that  the  friction  existing  for  the  moment  was  being 
accurately  weighed.  The  difference  in  friction  caused  by  temperature 
was  found  to  be  very  great,  but  in  the  absence  of  arrangeinents  for 
accurately  determining  the  temperature  no  very  close  results  as  to  its 
precise  effect  were  attempted. 


APPENDIX  B. 


915 


pends  upon  the  use  of  the  ni.^f.  1       success  of  this  apparatus  de- 

weighing  t„e  :^^  ^^^:^:::::^^z:z zT^  ■ '''"'  '°^ 

-  may  be  absolutely  statical,  no  mo  o  o7  e  bearin  "Zf  "  T'' 
necessary  in  order  to  express  a  variation  ^f  f  .  ^  "'hatever  being 
attempted  to  use  sprina-scale.  t„     ™  u  °"-     "  "'^^  "  ^^^^ 

variations  of  friction  couwL     "'^^''"l'^^  f"«i°n,  with  the  idea  that 

vibration  which  ^u  dTn^^.^iirtW  s  t'u^  '"'  r'"'  '''"■     '''' 

sr  f-r- 4--  rd'xru^t'e-rade  :^-^^^ 

1st.  The  determination  of  these  resistanr^c  o„^      .  . 

the  general  laws  of  all  friction  Zl  ,h!      ^  °'  '"vestigations  of 

2d.  The  coefficient  nrl  '"  '"'="' '"  '''^  experiments. 

imately,  the  journal-speed  in  feet  per  minutf.  "  ^  "PP™^" 

In  the  comparisons  which  follow,  with  vario.i,  ^v„<.,-        .      ^ 
proximate  formula,  .?=  200C,  has  been  used  ^.T    experiments  the  ap- 
efficients  into  pounds  per  ton     ru!t       ,  "'""  "'"  '^'"'"^''^  <=°- 

of  a  railroad  journal   s^ne  tenth  ,h    H  ^  '°7'"  *''""  "'^  '""'""er 

V4  jyjuiiid.1  IS  one-tentn  the  diameter  of  thf-  vvh/:»«i      r 

•at  the  present  time  it  ran^e^  from   i       !.  ^"  general, 

iiaving  been  the  r^tl^  i .  ZT  ^^"  ^  '^  ^^  '''"'^''  '^'^  ^^^^^ 

The  apparatus  heretofore   described   k    mli^r,   ^  i 

Cheap .  the  actual  weights  tTbe^ltdT^d  Z  Z'  sl'JZT^t  ^"' 
readily  changed,  and  but  little  strain  is  produced^oH^e  machri  .74': 


9i6 


APPENDIX  B. 


be  used  in  any  ordinary  lathe  and  with  an  ordinary  platform  scale^ 
enough  varieties  of  which  can  be  obtained  without  special  construction  to 
Satisfy  every  requirement;  it  is  positive  in  its  action  throughout,  and  no- 
delicate  computation  and  construction  of  scales  is  necessary  for  its  use;, 
and  it  admits  of  any  desired  delicacy  of  readings  by  the  simple  substitution, 
of  more  delicate  scales.  The  common  platform-scale  of  the  shop  where 
the  tests  were  made  was  deemed  sufficient  in  this  instance,  since  the 
Stresses  actually  weighed  ranged  so  high  that  the  error  of  observation 
from  lack  of  delicacy  in  the  scales  could  rarely  exceed  a  fraction  of  one 
per  cent.  The  axle  was  set  very  slightly  eccentric,  so  as  to  imitate  the 
effect  of  an  imperfectly  centred  wheel.  This  probably  somewhat  in- 
creased the  coefficient,  although  very  slightly  at  the  low  speed  used. 
The  effect  of  end  play  in  distributing  lubricants  was  imitated  by  the  oc- 
casional use  of  manual  force.  It  was  found  possible  to  do  this  in  great 
degree,  and  it  was  generally  found  to  have  a  slight  beneficial  effect  upon 
the  coefficient,  but  only  slight;  especial  pains  was  at  all  times  taken  to« 
have  the  journal  well  lubricated  before  beginning  each  test.  The  jour- 
nals and  brasses  were  fairly  well  polished  by  use  up  to  their  average  con- 
dition in  service,  but  no  more. 

The  tests  made  are  shown  in  Table  I.  (omitted),  and  graphically  in 
Fig.  303.  Three  different  loads  only  were  used  in  testing,  corresponding 
as  nearly  as  might  be  to  the  loads  on  bearings  of  a  loaded  car,  empty  car 
and  truck  alone.  Each  one  of  these  it  was  designed  to  test  a  number  of 
times  at  all  the  speeds  which  the  lathe  used  admitted  of.  Whenever  a 
bearing  heated  above  150°  F.  the  tests  were  suspended  and  the  bearings 
cooled,  since  no  means  had  been  provided  for  accurate  measure  of  tem- 
perature. Each  test,  at  any  given  speed  and  load,  was  contiimed  for 
from  5  to  even  30  minutes,  when  the  bearings  were  cool,  in  order  to  be 
certain  that  it  was  a  fair  average.  When  the  bearings  were  hot  the  tests 
were  shorter,  and  the  bearings  were  retained  as  nearly  as  might  be  at  the 
same  temperature  by  waiting  a  considerable  interval  between  each  test. 
During  a  test  the  resistance  would  generally  fluctuate,  slowly  and  gently, 
from  10  per  cent  to  sometimes  20  per  cent  higher  or  lower  than  the 
average  afterwards  taken.  This  change  was  considered  normal,  and 
arose  from  no  discernible  cause.  When  the  fluctuations  were  greater 
than  this  they  were  generally  very  much  greater,  and  arose  from  heating 
of  the  bearings. 


APPENDIX  B. 


917 


^^^'^^^i^,t^~!Z2-:.r.szA-s^-s^^., 


\ 


Csq/0002)  uqj.^sd-sq|  -  uoipuj    a,xv 


9i8 


APPENDIX  B. 


\ 


Note. — In  all  the  diagrams  below,  as  also  in  Fig.  303  giving  results  of 
the  writer  s  tests,  the  Journal-speed  has  been  reduced  to  its  equivalent 
train  velocity  in  miles  per  hour  and  the  coefficient  of  friction  to  its 
equivalent  in  pounds  per  ton  tractive  resistance  to  the  locomotive. 

Intensity  of  Load  Per  Sq.  Inch  indicated  by  Thickness  of  Lines. 


%M     \hi.^Ytfv\.       1         1         II,-         III 

_    7F'"-- 

TT  irn  M   \  1   ill   III 

.-  "■       —    - 

■■■■■r;r.7'7:r<'//#^r}r,BBHBBBi 

r                                 —  — 

_,  -' 

M'l. - 

-~      -      ^^'"^ 

, » 

-  "•  ~ 'z ^'f. 

5  iS*  lj_!                                    Z:'^ 

<^    .•-^*5"^"    *■ 

.^    ■ 

^r-:>-_!:; 

b«^--«B    -    ^^- 

lS-i--r    71-                       : 

:S3:!=S!:S:::-i-+ 

i::-^-  — fr— ?r— ih-tH+-tf^ffi=B 

.Vel.  Mites  p«r  hour. 
Fig.  304. 


, ^ ..    _  =  = 

™«H.-'^                                                                                                         ' 

ojohrBtej^bjTBi^ : 

-^     ^jjjH- 

aujBi^siSijaa --^^^-: 

'^-                       -«;'     -*_ 

^                                       * 

"r           "'^           •^' 

2,fi_3-£_Jic: 

S                    ^ZxcssjZ;: 

\11\tAULC 

- -M,  m^if  It.  ^  Li 

^ 

/.c   j_   ^2\'' 

J -_    i^        ...... 

s»^ 

V, 

^  ^ 

s 

_  ^  —  — y"  I"                               ^  ^  ■"  "^ 

/. S_i__''''._2:_    _^i ,„^mc: 

■"                                                ^  —  'i 

\^4!n    _ 

"3^  —  ^~ 

11 

^•"tIT  — '^          *""' 

;*M  /*"4^..-/0? 

.  -  -"^ 

AC     ''        «       '/        ^^^^-^--'i 

<c-''"^c:-'"        sszs:^? 

^zsz^^ii 

rL-^^--'- 1 

c>,  4 ;,.  .^      {'      '^               i4-  -  ■ — 

Egjr =  =  — — -J--- 

--"'""■"  "^~    r--*--"" 

" '"  "T""" 

1 

o\iL fii  M  1  lai?  1  1  1  gy  1  M  g 

21        2r    __E___2L___£! 

Vel.  Miles  per  hour 
Figs.  305,  306. 

Figs.  104-30^,  Results  of  Mr.  Beaitchamp  Tower's  Tests,  ciriNG  Effects  of  Higw 
Vklocitv,  Variation  of  Pressure  and  Differences  of  Lubrication  upon  Coefficient  of 
Friction. 


APPENDIX  B. 


919 


Ve/.  Miles  per  hour. 


creasing  the  pressure  to  ^  lbs.  per  «>  in  cau^d Tmri,^  •  ^'  "'•  ""•  '"' 

Thurston,  test3  and  an  equally  ™Led^*":rr„  Torr^testlT'''''"  "'  '"""'"'  "" 

Deduction  from  the  Tests. 
( Tons  of  2000  Ibs^) 

Initial  FrMiot.-yhe.  writer's  observations  under  this  head  «er<.  ., 
cepttonally  complete,  and  the  conclttsions  reached  were  as  follls  " 

I.  Fnct.on  at  very  low  journal-speeds  of  o  +   is  abnormal  I  v  great 
and  more  nearly  constant  than  any  other  element  of  friction  underf-Tv 
ng  cond.ttons  of  lubrication.  load,  and  temperature.     It  varies  fomfs 
to  24  lbs.  per  ton  (coefficient.  .09  to  .,2)  for  loads  of  from  30  to    ^Ibs 

oTte:rp:::tr-  ^"^'"  -'-  --^^^^^.o.^.^^^,,^^:^ 

2.  This  abnormal  increase  of  friction  is  due  solely  to  the  velocifv  of 
r^olunon  cont.nuing  unchanged  so  long  as  the  velocity  is  unct  1/ 
and  returnmg  to  the  same  amount  whenever  the  velocity  is  reduced  to 
the  same  rate,  barri,,.  exceptionally  slight  variations,  prJbab  y  due    ^ 


;^ 


% 


920 


APPENDIX  B. 


differences  of  lubrication  and  temperature.  It  is  not  appreciably  affected 
by  the  fact  that  the  journal  may  be  just  starting  into  motion,  or  is  just 
coming  to  rest,  or  is  temporarily  reduced  to  a  velocity  of  o  +  during 
continuous  motion. 

3.  At  velocities  higher  than  o  +,  but  still  very  low,  the  same  general 
law  obtains.  The  coefficient  falls  very  slowly  and  regularly  as  velocity 
is  increased,  but  is  constantly  more  and  more  affected  by  differences  of 
lubrication,  load,  and  temperature. 

4.  A  very  slight  excess  of  initial  friction  proper  (varying  from  \  lb. 
to  2  lbs.)  could  generally  (but  not  always)  be  observed  over  that  which 
continued  to  exist  at  the  nearest  approach  to  a  strictly  infinitesimal 
velocity  which  it  was  possible  to  obtain.  This  difference  was,  by  analogy, 
ascribed  solely  to  the  fact  that  the  lowest  continuous  velocity  attainable 
was  nt)t  strictly  infinitesimal,  and  the  final  conclusion  was  drawn  that — 

5.  There  is  no  such  phenomenon  in  journal-friction  as  a  Jrtction  of 
rest,  or  a  friction  of  quiescence,  in  distinction  from  (i.e.,  differing  in 
amount  from)  friction  of  motion  at  slow  velocities,  and  due  to  the  fact 
of  quiescence.  Consequently,  the  use  of  such  a  term,  although  con- 
venient, is  scientifically  inaccurate,  in  that  it  ascribes  the  phenomenon 
to  the  wrong  cause,  and  to  a  cause  which  is  not  necessary  for  its  exist- 
ence. The  fact  that  friction  of  rest,  as  such,  appears  to  exist,  is  due 
solely  to  the  fact  that  no  journal  or  other  solid  body  can  be  instantly 
set  into  rapid  motion  by  any  force,  however  great.  There  must  be  a  cer- 
tain appreciable  instant  of  time  during  which  the  velocity  is  infinitesimal 
and  gradually  increasing. 

This  interesting  fact,  which  is  believed  to  have  been  here  observed 
for  the  first  time  (no  other  apparatus  being  known  to  have  been  used 
suitable  for  determining  it),  was  determined  with  great  completeness  by 
many  tests.  Very  slow  motion  could  be  produced  at  any  time  by  re- 
volving the  driving  pulley  of  the  lathe  by  hand  when  geared  for  a  slow 
speed.  With  a  little  experience,  the  weight  on  the  scale-beam  could  be 
placed  in  advance  at  a  point  which  would  be  a  trifle  less  than  the  initial 
friction  proper,  and  (when  properly  placed)  it  would  barely  lift  when 
motion  first  began,  and  then  have  to  be  moved  back  a  notch  or  two  only, 
to  weigh  the  friction  which  continued  to  exist  indefinitely.  Similarly, 
when  a  test  at  comparatively  high  speed  was  about  to  be  concluded,  the 
scale-weight  would  be  placed  to  measure  the  same  pressure,  or  a  little 
less,  as  existed  in  starting,  and  it  was  always  found  to  indicate  in  stop- 
ping substantially  the  same  friction  as  in  starting.  The  same  test  was 
made  by  interrupting  tests  at  speed,  so  as  to  give  a  continuous  motion. 


APPENDIX  B.  921 

.i)ut  to  suddenly  reduce  the  speed  to  o  +.    These  tests  were  repeated 
-again  and  again,  with  practically  identical  results. 

Comparing  these  results  with  others,  they  agree  very  closely  indeed 
with  the  writer's  conclusions  from  the  results  of  his  gravity  tests,  as  will 
be  seen  below : 

" Initial"  Journal-friction  (i.e.,  at  velocity  of  o  +). 
Writer's  conclusions  from  journal  tests,  above,  say. .     19    to    25  lbs.  per  ton. 
Wriier  s  conclusions  from  gravity  tests  of  rolling-stock 
(see  Trans.  Am.  Soc.  C.  E.,  February,  1879),  "at 

'f^'" 14    to    18     •*       "     «' 

Prof.   R.  H.  Thurston  ("Friction  and  Lubrication," 

page  175).  W.  Va.  oils .'.     22    to    28     "       «     « 

Prof.  R.  H.  Thurston  ("Friction  and  Lubrication." 

page  175).  sperm ;       j^    ^^    ^8     "       "     «« 

Prof.  R.  H.  Thurston  ("  Friction  and   Lubrication  " 

page  175).  lard \^     ^^    ^^    ^2     "       «     •• 

Prof.  Kimball  {Am.  Jour.  Sci.,  March,    1878,  or  Fr. 

and  L.,  page  186) ^^    ^^^^     „       ,.     „ 

In  addition,  it  may  be  noted  that  the  writer  has  taken 
pains  to  observe  with  some  care  at  various  times 
that  in  ordinary  service  no  railroad  cars  can  start 
themselves  from  rest,  nor  can  they,  in  general,  be 
started  without  the  use  of  much  force,  on  a  grade 
of  .7  per  cent  (=  14  lbs.  per  ton.  36  ft.  per  mile), 
but  that  they  will  generally  (but  not  always)  start 
of  themselves  on  a  grade  of  i.i  to  1.2  percent 
(=  22  to  24  lbs.  per  ton.  58  to  63  ft.  per  mile),  in- 
dicating an  "  initial"  friction  of 20    to    24     "       "     « 

These  results  agree  wonderfully  well  with  each  other,  the  averages 
running  18,  16,  25,  20,  18,  25^,  and  22  lbs.  per  ton.  the  average  of  all  bein- 
18.0  to  25.0  lbs.  per  ton.  or  20^  lbs.  as  the  general  average  of  all  This 
corresponds  to  the  accelerating  force  of  gravity  on  a  i  per  cent  (52.8  ft 
per  mile)  grade,  and  that  being  also  the  lowest  grade,  by  universal  rail- 
road experience,  upon  which  cars  can  be  relied  on  to  start  off  from  a 
state  of  rest  with  little  or  no  assistance,  the  correctness  of  this  coefficient 
may  be  considered  as  well  determined.* 

♦  On  a  0.7  per  cent  grade  (14  lbs.  per  ton)  the  writer  found  it  impossible  in 
several  instances  for  six  men  pushing,  two  with  pinch-bars.  to  start  two  loaded 
box  cars  into  motion.  In  no  single  instance  out  of  over  sixty  did  cars  start 
"Without  some  assistance. 


\ 


^\:i\ 


4 


Iff 


] 


922 


APPEKDIX  B. 


Normal  Coefficient  of  Journal-friction  at  Ordinary  Operating  Veloci- 
ties.— Certain  general  facts  seem  to  be  clear  from  all  the  various  tests 
here  considered : 

The  first  of  these  is,  that  (i)  the  character  and  completeness  of 
lubrication  seems  to  be  immensely  more  important  than  the  kind  of 
the  oil,  or  even  pressure  and  temperature,  in  affecting  the  coefficient. 

This  is  very  clear  from  the  diagrams  (Figs.  303  to  307)  showing  the 
various  results.  Mr.  Tower  found  that  lubrication  by  a  bath  (whether 
barely  touching  the  axle  or  almost  surrounding  it)  was  from  six  to  ten 
times  more  effective  in  reducing  friction  than  lubrication  by  a  pad.  By 
this  method  of  lubrication  Mr.  Tower  succeeded  in  reducing  the  co-^ 
efficient  in  a  large  number  of  tests  to  as  low  a  point  as  .001,  equivalent 
to  only  0.2  lb,  per  ton  of  tractive  resistance,  and  the  general  average  in 
the  bath  tests,  under  all  varieties  of  load  and  speed,  is  given  as  only 
.00139  or  0.278  lb.  per  ton,  against  1.96  to  1.95  lbs.  per  ton  with  siphon- 
lubricator,  or  pad  under  journal.  These  results  are  very  far  below  any 
heretofore  reported,  as  will  be  seen  from  the  following  general  average- 
of  results;  not  considering  now  the  comparatively  minor  variations  pro- 
duced by  ordinary  working  differences  in  temperature,  load,  etc. 

The  normal  journal-friction,  under  favorable  conditions,  deduced 
from  various  series  of  tests,  may  be  summarized  as  follows  for  velocities- 
greater  than  10  miles  per  hour,  or  90  ft.  per  minute,  journal  speed  : 

Beauchamp  Tower,  bath  of  oil . . , 278  lbs.  per  ton*. 

'*  **        pad  or  siphon 1.9 

Thurston,  light  loads 2.75 

**  heavy  loads 1.75 

Wellington  (gravity  tests  of  cars  in  service),  light  loads  ....  6.0 

heavy  "     ....3.9 

*•  direct  tests  (as  shown  in  Fig.  2) \      ^'^ 

'      3-7 

Thurston,  inferior  oils  (Fr.  and  Lub.,  p.  173). \     ^' 

<      30 

Morin,  continuous  lubrication 6.0  to  10.8 

These  discrepancies,  especially  as  they  are  accompanied  by  many 
minor  ones,  are  very  instructive,  as  showing  that  the  character  of  lubri- 
cation is  the  great  cause  of  variation  of  coefficient. 

Resistance  of  Freight  Trains  in  Starting. — It  will  be  seen  in  Fig.  303 
that  the  abnormally  high  coefficient  of  friction  at  starting  continues 
during  the  period  of  getting  up  speed,  and  thus  constitutes  an  extra  tax 
upon  tractive  power  for  some  little  distance  after  getting  under  way. 


<< 


«< 


(« 


<« 


•« 


APPEiVD/X  B. 


923 


The  following  conclusions  may,  it  is  believed,  be  drawn  (already  sum- 
marized in  par.  635).  v  ^        n 

Effect  of  Temperature  on  Coefficient  of  Friction.-So  far  as  can  be 
estimated,  the  results  agree  very  closely  with  Prof.  Thurston's  formula 
that  the  coefficient  increases  as  the  square  of  the  increase  of  heat  over 
90    to  100    F.  at  speeds  under  12  miles  per  hour. 

Effect  of  Load  per  Square  Inch  of  Bearing  on  Coefficient  of  Friction  - 
Comparison  of  the  results  obtained  by  the  writer,  and  by  Messrs  Thurs- 
ton and  Tower  and  others,  as  shown  in  Figs.  303  to   307.  develop  this 
curious  fact :  that  while  the  results  differ  quite  widely,  in  fact  by  several 
hundred  per  cent,  in   what  may  be  called  the   typical  or  average  co- 
efficient of  friction,  they  all  agree  quite  closely  in  finding  that  the  effect 
of  increased  load  within  working  limits,  is  to  very  materially  diminish 
the  coefficient.     Mr.  Tower,  in  fact,  goes  so  far  as  to  state,  as  one  of  the 
results  of  his  tests,  that  it  almost  seemed  at  times  as  if  it  was  approxi- 
mately true  that  the  absolute  loss  by  friction  was  entirely  independent  of 
load,  the  coefficient  falling  almost  to  half  when  the  load  was  doubled 
But  It  seems  plain,  from  the  diagrams  given  herewith,  that  this  result  is 
only  true  on  account  of  the  unprecedentedly  low  coefficients  which  he 
obtained  by  his  very  perfect  lubrication.    Inspection  of  the  diagrams  will 
show  that  the  general  law  of  variation  from  increase  of  load  is  not  mate- 
rially different  in  the  different  tests,  despite  the  wide  variations  in  the 
average  coefficients. 

^      Effect  of  Velocity  over  Twelve  Miles  per  Hour.~^\^^.  303  to  307  taken 
in  connection,  seem  to  show  the  following : 

'•  w^Vu  ""u'^  ""^  ^'''^^''  journal-friction  is  10  to  15  miles  per  hour 
^      2.  With  bath  or  other  very  perfect  lubrication  there  is  a  verv  slight 
increase  of  journal-friction  accompanying  velocities  up  to  55  miles  per 
hour  (Figs.  306  and  307).  ^ 

3.  With  less  perfect   lubrication,    as   with   pad   or   siphon,   greater 
velocity  ,s  as  apt  to  decrease  as  to  increase  the  coefficient  (Figs  ^04  .0; 
and  307).     The  latter  being  more  like  the  ordinary  lubrication  in  railroad 
service,  we  may  say.  without  sensible  error,  that  the  coefficient  of  journal- 
fnct^ion  IS  approximately  constant  for  velocities  of  15  to  50  miles  per 

This  has  been  the  assumption  which  all  investigators  of  railroad  fric- 
tion, to  date,  have  been  compelled  to  make,  and  it  is,  in  some  respects 
fortunate  that  it  proves  not  far  from  true. 

Higley  Roller.  Journal  Bearings.~The  direct  tests  of  this  apparatus 
confirmed  exactly  the  correctness  of  the  writer's  previously  stated  con^ 


'924 


APPENDIX  B. 


elusions,  that  the  Higley  bearing  was  nearly  as  efficient  as  theory  would 
indicate  in  reducing  initial  friction,  but  loses  nearly  all  of  this  advantage 
under  speed. 

[The  paper  was  followed  by  a  long  discussion,  which  it  is  necessary 
.to  omit,  bringing  out  many  further  points  of  interest.] 


) 


APPENDIX  a 


92S- 


APPENDIX  C 


THE  AMERICAN  LINE  FROM  VERA  CRUZ  TO  THE  CITY  OF 
MEXICO.  F/A  JALAPA,  WITH  NOTES  ON  THE  BEST  METHODS 
OF  SURMOUNTING  HIGH  ELEVATIONS  BY  RAIL. 

[Read  by  the  author  at  the  Annual  Convention  of  the  American  Society  of  Civil  En«. 
neers,  July  3,  1886.     See  Trans.  Am.  Soc.  C.  E.,  Nov.  1886.] 

The  line  described  in  this  paper,  and  illustrated  in  the  accompanying 
maps  and  profiles,  is  one  located  by  the  writer,  as  consulting  and  after- 
ward chief  engineer,  from  the  Port  of  Vera  Cruz  to  the  city  of  Mexico 
vm  the  city  of  Jalapa.  being  a  parallel  line  to  the  existing  Mexican  Rail- 
way—the first  railway  built  in  Mexico— in  the  sense  of  connecting  the 
same  termini,  although  following  a  very  different  route  and  of  a  very 
different  character. 

All  the  features  of  interest  and  of  difficulty,  both  in  the  line  here  de- 
scribed and  in  the  line  of  the  Mexican  Railway,  are  confined  to  the 
mountam  grade  by  which  the  necessary  abrupt  ascent  from  the  level  of 
the  sea  to  the  level  of  the  plateau.  8000  feet  above  the  sea.  is  accom- 
plished. Once  on  the  plateau  there  is  no  great  difficulty  in  going  almost 
anywhere  with  very  light  work ;  many  high  mountains  being  scattered 
around,  even  on  the  plateau,  but  disconnected,  with  flat  lands^etween 

The  elements  which  appear  to  make  the  mountain  grade  of  this  line 
particularly  worthy  of  description  are  these  : 

J^trs/.  It  is  believed  to  be  by  far  the  longest  continuous  grade-line 
ever  located;  116.9  kilometres  (72.64  miles)  having  been  located  on  an 
unbroken  2  per  cent  grade  (105.6  feet  per  mile),  rising  in  that  distance 
from  elevation  600  4  feet  (183  metres)  to  elevation  7923.3  feet  above  the 
sea  (241 5  metres).  The  accompanying  plate  (Fig.  232)  shows  graphically 
the  extent  of  the  contrast  in  this  respect  with  some  of  the  other  great 
inclines  of  the  world. 

Secondly.  It  is  believed  to  be  on  the  lowest  rate  of  grade,  by  about 
2  per  cent,  ever  successfully  attempted  for  accomplishing' within  a 
limited  distance,  either  by  a  continuous  grade-line  or  otherwise,  a  rise 


■926 


APPENDIX   C. 


APPENDIX  C. 


of  over  one  half  as  much  as  was  attained  on  this  line.     The  grounds  for 
this  belief  also  are  shown  in  the  accompanying  plate  (Fig.  232). 

Thirdly.  The  line  is  believed  to  be,  by  probably  one  half  at  least, 
the  cheapest  line  per  mile  which  has  ever  been  actually  located,  with 
equally  favorable  alignment,  for  attaining  within  a  limited  distance  as 
much  as  one  half  the  rise  actually  attained  by  this  line,  either  by  con- 
tinuous or  broken  grade-lines,  on  any  rate  of  grade.  As  for  this.  Table 
190,  Figs.  309  and  310,  and  the  general  knowledge  of  engineers  are  the 
only  evidence  that  can  conveniently  be  appealed  to,  or  which  it  is  worth 
while  to  attempt  to  present. 

Finally.  It  appeared  that  the  manner  in  which  the  line  was  obtained 
might  have  a  certain  instruction  and  encouragement  to  those  who  may 
be  dismayed,  as  was  the  writer,  by  having  similar  problems  of  unusual 
difficulty  suddenly  thrust  upon  them,  and  it  was  also  desired  to  give,  in 
connection  with  the  description  of  the  line,  certain  conclusions  which 
the  observation  and  experience  of  the  writer  has  indicated — not  only  on 
this  incline,  but  on  eight  or  ten  others  of  considerable  rise,  which  have 
been  located  or  relocated  in  part  or  whole  under  his  supervision,  aggre- 
gating over  24,000  vertical  feet — in  regard  to  the  most  advantageous  and 
economical  manner  of  dealing  with  great  inclines,  under  which  may  be 
classed  anything  exceeding  1200  to  1500  feet  of  vertical  rise. 

It  is  one  of  the  unfortunate  features  of  the  department  of  engineering 
to  which  this  paper  refers — that  of  laying  out  railway  lines  to  the  best 
economic  advantage — that  a  mere  description  of  a  located  line  has 
usually  little  technical  interest  or  instruction,  since  it  is  ordinarily  im- 
possible to  so  carefully  describe  any  line  on  paper  as  to  enable  even  an 
intelligent  impression  to  be  formed  as  to  the  real  character  of  the  work. 
If  the  grades  and  work  be  light,  it  may  be  because  the  line  was  well  laid 
out,  or  it  may  be  simply  because  there  were  no  serious  natural  obstacles 
in  the  way.  On  the  other  hand,  if  the  grades  and  work  be  heavy,  it  may 
be  due  to  bad  engineering,  and  so  discreditable ;  or  it  may  be  due  to  the 
existence  of  gigantic  difficulties,  and  so  an  evidence  of  skill.  It  is  but 
natural,  however,  that  the  magnitude  of  the  natural  difficulties  to  be 
overcome  should  in  general  be  regarded  as  bearing  some  nearly  constant 
ratio  to  the  magnitude  of  the  works  constructed  to  overcome  them  ;  and 
hence,  that,  even  when  the  construction  of  a  very  costly  line  may  have 
been,  as  a  matter  of  fact,  an  avoidable  extravagance,  due  to  lack  of  skill 
or  foresight,  the  very  magnitude  of  the  works  gives  more  instead  of  less 
reputation  to  the  line  as  an  engineering  work. 

Only  in  the  comparatively  rare  cases  when  two  independent  alternate 


927 

lines  exist  between  the  same  termini,  is  it  possible  for  the  engineer  to 
tind  m  prmted  descriptions  of  located  lines,  however  perfectly  mapped 
any  rational  basis  for  intelligent  judgment.  The  present  happens  to  be 
one  of  the  cases  in  which  this  is  possible,  owing  to  the  existence  of  the 
parallel  Ime  before  mentioned,  but  in  order  to  avail  of  it,  it  becomes 
necessary  to  enter  somewhat  into  what  would  otherwise  be  an  invidious 
—because  unnecessary-comparison  with  the  parallel  and  previously 
constructed  line.  The  writer  feels  the  less  embarrassed  in  doing  this 
•  as  owing  to  the  checkered  history  of  the  line,  no  one  engineer  can  be 
held  responsible  for  its  character,  and  there  were  certain  circumstances 
tending  to  impede  entire  freedom  of  choice  and  proper  investigation. 

The  whole  mterior  of  Mexico  is  a  vast  plateau,  at  an  elevation  of  5000 
to  9000  feet  above  the  sea,  bounded  by  an  abrupt  escarpment  from  which 
the  descent  to  sea-level  is  almost  immediate.     The  edge  of  the  plateau  is 
higher  and  sharper  on  the  Atlantic  than  on  the  Pacific  Coast,  and  at  no 
point  on  either  the  Atlantic  or  Gulf  Coast  is  it  higher  or  sharper  than 
directly  in  line  between  the  capital  of  the  country.  Mexico,  and  its  chief 
port.  Vera  Cruz.     Here  two  stupendous  natural  obstacles,  the  Pico  of 
•Orizaba  on  the  south  {i-j^Zn  feet  high),  and  the  Cofre,  or  ••  Box  "  of 
Perote  (12,500  feet  high),  both  of  them  described  in  physical  geographies 
as  volcanoes,  although  both  are  temporarily  extinct,  and  the  two  con- 
nected by  a  ridge  over  10,000  feet  high  at  its  lowest  saddle-combine  to 
forbid  a  direct  line  inward. 

Orizaba  is  one  of  the  three  mountains  in  Mexico  covered  with  per- 
petual snow,  the  other  two  being  Popocatepetl  (17.884  feet)  and   Ixtac 
cihuatl  (15.705  feet),  overlooking  the  valley  of  Mexico.     These   however 
start  from  a  plain  8000  feet  high,  whereas  Orizaba  starts  practically  from' 
sea-level  on  the  coast  side,  making  it  in  that  sense  by  much  the  hi-hest 
mountain  on  the  North  American  Continent,*  and  among  the  highest  in 
the  world.     Its  snow-clad  peak  is  visible  60  miles  out  at  sea.  long  before 
there  is  any  other  evidence  of  land,  and  with  the  morning  sun  shinin-on 
■It  IS  a  very  striking  sight.     Its  last  violent  eruption  was  in   1546  soon 
after  the  Spanish  conquest,   although  it  now  occasionally  throws  out 
smoke.     Only  one  or  two  men  have  ever  ascended  to  its  crater,  the  first 
one  having  been  Lieutenant  Reynolds.  U.S.A..  in  1848.     The  line  of  the 
Mexican  Railway  passes  to  the  south  of  this  mountain,  as  shown  in  Ficr 
308.  *• 


\ 


*  Mount  St.  Elias,  in  Alaska,  in  a  possible  exception,  being  only  about  30 
miles  mland  and  its  height  variously  given  as  14.970.  16.900,  17,850,  "oyer 
.10,000    (U.  S.  Census  Report),  and  19  500. 


928 


APPEiYDIX  C. 


The  Cofre,  or  "  Box,"  of  Perote  (so  named  from  a  cylindrical  basaltic 
needle  about  300  feet  in  diameter  and  300  feet  high  which  caps  the 
mountain,  like  a  box  laid  on  its  peak),  although  formerly  one  of  the  most 
active  volcanoes  in  the  world,  and  classed  as  still  active,  is  perhaps  per- 
manently extinct,  its  last,  and  probably  also  its  greatest,  eruption  having 
been  to  form  what  looks  to  be,  and  is  in  fact,  a  frozen  river  of  lava,  shown 
in  Fig.  309,  extending  to  and  running  into  the  sea  50  miles  distant,  filling 
up  an  enormous  barranca  or  deep  gulch  in  the  process,  in  a  manner 
which  was  very  convenient  for  subsequently  carrying  the  line  over  it,  as; 
may  be  seen  in  Fig.  309.  The  natural  variations  in  the  width  of  this 
gulch  have  caused  lakes  and  frozen  "  water-falls"  of  lava,  which  makes 
it  difficult  to  believe,  as  one  looks  up  the  slope  upon  it  from  some  com- 
manding point,  that  the  mass  is  not  still  flowing,  making  it  a  unique  and 
impressive  bit  of  natural  scenery.  Vessels  have  been  frequently  wrecked 
in  the  toe  of  this  flow  where  it  enters  the  sea.  It  has  still  hardly  any 
deposit  of  sand,  soil,  or  vegetation  on  it,  that  and  other  facts  evidencing 
that  the  flow  is  geologically  very  recent,  not  antedating  much  the 
historic  era. 

,  Around  the  north  side  of  this  mountain,  and  directly  over  this  lava 
flow,  the  line  here  described  passes,  as  shown  in  Figs.  308  and  309,  being 
about  sixty  miles  north  of  the  Mexican  Railway  line  at  its  greatest  diver- 
gence, the  two  beginning  to  come  together  again  very  soon  thereafter. 
The  summit  of  Perote  is  just  below  the  limit  of  vegetation  and  of 
perpetual  snow,  and  it  is  very  easily  ascended  on  horseback  to  the  foot 
of  the  "  cofre,"  or  box,  that  fact  alone  being  an  evidence  to  the  engineer 
of  how  different  the  topography  of  its  slopes  must  be  from  those  of  its 
southerly  companion.  Evidences  abound  of  tremendous  flows  of  lava  in. 
remote  geologic  times,  which  are  now  covered  to  a  considerable  depth 
with  soil,  and  in  the  kind  of  pocket  formed  between  the  foot-hills  of  the 
two  great  mountains,  in  which  lie  Jalapa  and  Coatepec,  the  detritus  of 
ages  has  accumulated,  including  probably  great  amounts  of  volcanic  ash,, 
so  that  no  rock  exists  over  large  areas,  as  was  afterwards  discovered,  ex- 
cept in  isolated  points. 

Cortez  followed  this  route  on  his  first  invasion,  as  did  General  Scott 
328  years  later ;  but  from  an  early  date  after  the  conquest  of  Cortez  two 
leading  routes  have  existed  between  the  interior  and  Vera  Cruz,  follow- 
ing substantially  the  two  railway  lines  here  described,  one  through  Jalapa, 
rounding  Perote  to  the  north,  and  the  other  via  Orizaba,  rounding  the 
mountain  of  that  name  to  the  south.  The  northerly  line  was  first  con- 
structed, and  over  it,  for   300  years  (between   1521  and  1812-20)  passed 


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[The  route  shown  for  the  Jalapa  line  after  reaching  the  summit  was  selected  (i)  to  reach  Puebia,  the  second 
dty  of  Mexico ;  (a)  and  chiefly,  to  nin  throu^!i  the  heart  of  the  pulque  district  between  Puebia  and  Mexico ; 

M    tj)  'o  connect  with  the  Mexican  National  system  at  a  favorable  point ; 

and  (4)  with  the  idea  that  a  line  might  be  run  southwardly  from  Puebia 

at  some  future  day.     Had  the  purpose  been  merely  to  reach  Mexico  in 

the  most  direct  way,  as  with  the  Mexican  Railway,  the  dotted  line 

marked   "  Natural  Route  to  Mexico"  would  have  been  followed,  or 

possibly  one  farther  to  the  North.     It  was  an  error  of  judg:ment  that 

the  main  line  of  the  Mexican  Railway  was 

not  carried  through   Puebia,  as  might  have 

been  done  with  perfect  ease,  with  equally 

favorable  grades  and  moderate  sacrifice  of 

distance,  with  less  total  line  to  construct.] 


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[The  route  shown  for  the  Jalapa  line  after  reaching  the  summit  was  selected  (i)  to  reach  Puebla,  the  second 
dty  of  Mexico ;  (2)  and  chiefly,  to  run  through  the  heart  of  the  pulque  district  between  Puebla  and  Mexico ; 

(3)  to  connect  with  the  Mexican  National  system  at  a  favorable  point ; 
and  (4)  with  the  idea  that  a  line  might  be  run  southwardly  from  Puebla 
at  some  future  day.  Had  the  purpose  been  merely  to  reach  Mexico  in 
the  most  direct  way,  as  with  the  Mexican  Railway,  the  dotted  line 
marked  "Natural  Route  to  Mexico"  would  have  been  followed,  or 
possibly  one  farther  to  the  North.     It  was  an  error  of  judgment  that 

the  main  line  of  the  Mexican  Railway  was 

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liiefly,  to  run  through  the  heart  of  the  pulque  district  between  Puebla  and  Mexico ; 
(3)  to  connect  with  the  Mexican  National  system  at  a  favorable  point; 
and  (4)  with  the  idea  that  a  line  might  be  run  southwardly  from  Puebla 
at.  some  future  day.  Had  the  purpose  been  merely  to  reach  Mexico  in 
the  most  direct  way,  as  with  the  Mexican  Railway,  the  dotted  line 
marked  "Natural  Route  to  Mexico"  would  have  been  followed,  or 
possibly  one  farther  to  the  North.     It  was  an  error  of  judgment  that 

the  main  line  of  the  Mexican  Railway  was 
not  carried  through  Puebla,  as  might  have 
been  done  with  perfect  ease,  with  equally 
favorable  grades  and  moderate  sacrifice  of 
distance,  with  less  total  line  to  construct.] 


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Mexico,  showing  the  Line  of  the  Mexican  Rail. 

WAY  AND  THE  JaLAPA  LINE  AS  ORIGINALLY  SKETCHED, 
AND  IN  SUBSTANCE  AFTERWARDS  LOCATED,  BELOW  Pe. 
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APPENDIX  C. 


929 

vj^t  sums  of  silver  and  gold,  practically  the  entire  product  of  the  Mexican 
mines    amountmg  ,n  the  aggregate  to  $3.ooo,oo<rooo,  or  nearly  half  of 

*velv  Ihtle      nr         n  f-  ''*""  '^'^'"'^  "^^"'^  '5^°'  ^^"'^h  «as  rela- 
canttra     hut       7^     ^     "  '""'  '*''  southerly  route  was  an  insignifi- 
r^n/h     ;  ^      ^^^^  '"  *""  '^^'""'■y  "'^  southerly  route  took  prominence 
and  the  Jalapa  camino  real,  or  "  King's  highwav"  ra,  th.  I.L  ?' 

ar<>  still  ,-oiia^  •  I-.-        ..  °     "iguvvay     ^as  the  leading  roads 

are  still  called  in  republican  Mexico),  was  suffered  to  fall  into  deL     It 
had  onginally  been  paved,  guttered,  and  curbed  for  the  entire  dTsLi 
from  Jalapa  to  Vera  Cruz,  some  73  miles,  and  from  Jalapa  upThemoun 
tarn  a  fine  macadamized  road,  likewise  curbed  and  guttered  existed  a.^d" 
still  exists  in  fine  order,  having  been  recently  repaired.*  ™^'  """ 

Witliin  fifteen  or  twenty  years  after  the  abandonment  of  the  north 
eriy  highway,  as  early  as  ,837,  the  movement  for  a  railwaj  between  vta" 
Cruz  and  Mexico  was  begun  by  Don  Francisco  Arrillaga  and  ve^  nat 
urally.  but  very  unfortunately,  the  route  which  had  byXttte  become 

^e^y-lfolt^al-^airra:^^^^^^^^^^^ 

from  which  the  ascent  was  abrupt  and  sham  to  ihT  .  '"0"nta,ns. 

u.uit.  for  a  railway  line,  but  Ls  cVu^dTT^e^'^^^^^^^^^ 

.unrnii^:„rrnrn,:^^ry\TeSa:i::f™\^^''  "T  '^■ 

instrumental  in  pushing  the  project  through  tr.i-  "'^'"''""y 

tat,>n  l„^M  „f  .1,  .      project  tnrough  to  completion,  having  then 

"bl^^dti:'     oVe: STnt^^^^^^^^  ^  --  --  -efr  r 

cott'  atrer-  "'"--  ^^  "^^    --  Cre^rrHVat 
cott.  an  American  engineer,  arrived  with  a  staff  of  assistants    ,7'      , 

member  of  which  now  living,  the  writer  beli:^  is  Mr  awrmr  m" 

Unzaba  line,  that  v,a  Jalapa  being  intrusted  to  a  Mexican  engi- 

nl,  or\f „;':7esrr:re;Vhe VS?r^ 

ahly  Claimed  to  he  "^Xl!^:^::'^^^  ^^^  .^^  ^"x  -  --on- 

order,  and  as  showing  .he  fine  quality  of  ,he  Mexican  L'h  "'   '" 

59 


930 


APPENDIX  C. 


I 


^^P^ 


neer,  Don  Pascual  Almazon.  According  to  other  accounts,  a  commis- 
sion of  engineers  examined  both  lines.  If  the  first  was  the  case,  it  is  less 
surprising  that  "  on  comparing  the  separate  surveys,"  as  the  history  of 
the  road  states,  that  by  Orizaba  was  finally  adopted,  on  the  grounds,  first, 
that  there  was  more  traffic  to  be  secured  on  it  (which  is  rather  more 
than  doubtful,  although  the  local  traffic  at  best  is  an  insignificant  ele- 
ment), and  secondly,  that  "  notwithstanding  it  requires  great  and  costly 
works,  the  line  presents  greater  facilities  than  that  by  Jalapa,  la/iere  the 
larger  number  of  ravines  and  the  harder  nature  of  the  soil  would  have  re- 
quired much  heavier  outlay"  A  greater  mistake  than  is  contained  in  the 
italicized  part  of  the  quotation  could  not  well  be. 

Colonel  Talcott's  estimate  of  the  line  was  $15,000,000,  but  nothing 
more  was  done  than  to  build  about  ten  miles  of  surface  line  out  of  Vera 
Cruz,  until  August,  1864,  when  the  militaiy  necessities  of  the  Emperor 
Maximilian  led  to  a  real  beginning  and  prompt  pushing  of  the  work 
under  English  engineers,  and  by  an  English  company,  which  still  con- 
trols it.  Beyond  a  statement  that  the  resumption  was  "after  rectifying 
the  plans  of  Colonel  Talcott,"  the  official  history  contains  no  record  of 
the  second  examination  of  the  whole  question  of  route,  which  was  in 
fact  made,  although  how  thoroughly  the  writer  cannot  state. 

By  1867  the  line  was  opened  from  Vera  Cruz  to  Paso  del  Macho,  47^ 
miles,  and  from  Mexico  to  Apizaco,  86|^  miles,  the  rails  for  the  latter 
being  hauled  by  wagons  an  average  of  200  miles  inland,  at  enormous 
cost — a  hard  condition  imposed  by  the  Mexican  Government.  A  third 
change  of  engineers  took  place  about  this  time,  while  the  heavier  parts 
of  the  work  were  still  unexecuted.  In  1868,  the  Puebla  branch,  29  miles, 
was  opened,  the  rails  for  it  having  been  hauled  in  the  same  manner.  In 
1870  the  line  was  opened  to  Atoyac,  54  miles  from  Vera  Cruz ;  in  187 1  to 
Fortin  ;  in  1872  to  Orizaba,  and  on  the  last  day  of  that  year  the  entire 
line  was  opened  with  great  ceremony. 

Shortly  thereafter,  in  1874,  Don  Ramon  Zangronez,  of  Vera  Cruz, 
succeeded  in  getting  a  branch  line  to  Jalapa  well  under  way,  and  in 
having  it  assumed  by  the  Mexican  Railway,  which  completed  it,  as  shown 
in  Fig.  308,  in  May,  1875.  It  is  operated  solely  by  animal  power,  being 
probably  by  far  the  longest  horse  railway  in  the  world.  Its  grades  are 
very  severe  (10  per  cent),  and  its  curves  of  ordinary  horse-car  radii. 
It  is  laid  for  a  great  part  of  its  length  along  the  old  camino  real, 
and  exhibits  the  same  trait  as  the  main  line  of  the  Mexican  Railway  to 
the  foot  of  the  mountains — that  is,  it  runs  obliquely  across  the  drainage 
lines,  thus  materially  increasing  the  difficulties  of  both  lines,  but  making 


I 


APPENDIX  C.  Q^j 

the  lower  pan  of  U,e  o^sce^rhLtlr  h^cldT^^rn'oTr^"  °' 
^  It  seems  impossible  that  an  ascent  frnn,  "7°"'^^'""«ion  of  the  route. 

The  main  line  thus  constructed  is  still  one  nl  ,h^ 
costly  in  the  world.     Its  cost  wa,  ■;,LT   ^  "'°''  ""^^"'^^  *"<' 

First,  the  political  cond,Uo„  o  th'cou  UvJir""''  '^  '"^  ^^"^^^  = 
that  it  no  doubt  added  much  to  the  cos7'  Id  "'"'.?  """^  '""'*^'' 
quiremeut  that  construction,  includin7trLck  1  ^  '^  "'^"''•^  ^^- 

both  ends  at  once   necessitatinc,  Vh  ^  faclc-laymg,  should  begin  from 

hauling  rails  over  ;;e  a  rroalsf:^^^^^^^^  expense  referred  to  for 
In  all  some  15,000  tons  of  ^^1—  J     u   T '°  *^''''"°  ^"-^  ^"ebla. 

believes,  of  soL  S80  Per  to^rorti  ^to  s^otf  sn:,r-'''ir'A" 
the  other  hand,  there  was  I.ffl^  a-      .  ^^  ^  55i,2oo,ooo  in  all.     On 

n^ost  Of  the  sha.  ^^^^tX^Z:^  'plidTn^r""^' 
nommal  cost  of  the  line  was  as  neprWac  ^      u     1^  ^  ^^^  S^^oss 

this  by  one  half,  we  shall  n^;.^  aTan  ;  eX^frr  ,^''T' 
abnormal  causes  tending  to  increase  cL,  Tf?  If         ^"^"  °'  "" 

Jalapa  horse  railway  and  the  smTamour/  ^f"''  n  '°''  '"^  '^°^'  °'  "^« 
8iO  cars),  leaving  $20,000,0^  to  represent  tjTfT""''  ^''  ^"^'"^• 
of  n,ain  line  and  29  miles  of  branch  Of ,,  ."'\^""^'  ~«  «'  ^64  miles 
del  Macho  and  Boca  del  Monte  alone  som:  t  T""  '""""'  ''''^ 
dimcult  or  costly  work.  The  remaining  rLSsTsh^h't'  '"  I"'  T" 
per  cent  grades,  which  latter  are  quite  L^^^^^^S'  "°^'''  """  '* 

nom'lnV^lt'LfolC: '"'"''""  '''  ^""^'  <^°^'  ^^'^  «  ''a.f  the 

223  miles  light  work,  at  $40,000  per  mile «» 

_6o  miles  very  heavy  work,  at  $.84,667  per  mii;.  '.'.'. [,'lTr,'°°° 

•*  *. 000, 000 

283  miles  in  all,  at  $70,670  per  mile. . .  ^ 

$20,000,0CX> 

out  oT  Ve';:  %:t:Tstrz:T:  ""t  "^  ^-^  =^^^^^-  ^-^  -  -"«« 

are  increased  tH pe  cent Tc  find",  ?^'"'  """'  ^''°"'>'  '""-f'- 
is  entirely  unbroke^for  the  ^^^  3  m Ues  0"^:° a^nd'^  T\  "'"^"  '"*^^ 
o.,er  points  on  the  ascent.  Curves  as  sl^s  335  "  'tTet"  d  "' 
(16  degrees  30  minutes  and  17  detrree,  .r,  ™-     »     .  ^'     '•""  '^"^'"^ 

eight  reversed  curves  of  these^adfof  et  succeed'tTa  T^'u'""  "^  °^ 
any  tangent  between  them,  and  ^i^^o.^:^^^::^^^^^ 


I' 


932 


APPENDIX  C. 


\ 


I 


the  virtual  gradient  fully  6  per  cent.  Fairlie  engines  are  used  to  operate 
this  grade  between  the  summit  at  Boca  del  Monte  (107  miles  from  Vera 
Cruz)  and  Cordova.  The  remaming  157  miles  to  the  city  of  Mexico,  as 
well  as  the  lower  and  easier  part  of  the  mountain  grade  (which,  however^ 
has  i\  to  3  per  cent  grades,  mcreased  by  unreduced  curvature),  is 
operated  by  American  engines.  Very  naturally  both  the  freight  rates 
and  the  expenses  are  fabulously  high,  receipts  ranging  from  10  to  12 
cents  per  ton-mile  and  as  high  as  $8  per  train-mile,  expenses  being  from 
50  to  60  per  cent  of  receipts.  To  show  how  radically  the  cost  and 
revenue  from  the  operation  of  this  line  differs  from  anything  with  which 
we  are  familiar,  it  was  calculated  in  1883  that  with  the  Mexican  rates  the- 
New  York  Central  would  earn  $27.25  and  the  Erie  $28.50  per  freight 
train-mile,  and  their  total  freight  earnings  would  have  been  in  one  vear 
$297,025,000  and  $244,300,000  respectively— $168,000,000  more  than  the 
Central's  whole  capital  account,  and  $93,000,000  more  than  the  Erie's. 

There  are  fourteen  tunnels  in  all  on  the  line,  none  of  them,  however^ 
very  long,  and  about  as  many  viaducts.  The  grading  is,  for  miles  to- 
gether, almost  wholly  rock,  and  the  work,  as  a  whole,  can  only  be  de- 
scribed as  Titanic,  so  that  it  is  small  matter  of  surprise  that  almost  every 
one  who  writes  about  the  line  describes  it  in  much  the  same  terms  as. 
does  Mr.  George  William  Curtis  in  a  late  number  of  Harper  s  Magazine 
(February,  1886),  who  chances  to  be  the  last  writer  whose  remarks  in. 
respect  to  it  have  come  to  the  writer's  knowledge. 

"  If  it  is  magnificent  scenery  that  you  seek,  here  at  hand,  with  no  inter- 
vening ocean,  is  the  railway  from  Vera  Cruz,  260  miles,  to  the  city  of  Mexico 
—a  marvellous  feat  of  scientific  skill,  crossing  the  mountains  at  a  height  of  8500 
ft.,  and  bearing  you  through  every  climate,  amid  unimaginable  luxuriance  and 
brilliancy  of  vegetation,  changing  into  temperate  hues  of  hardier  growths,  with 
awful  mountain  abysses  between  and  snow-clad  peaks  beyond  against  the  deep 
blue  sky." 

The  line  located  by  the  writer  rises  to  almost  precisely  the  same 
height  of  summit  as  the  Mexican  Railway,  and  is  as  nearly  as  may  be  of 
the  same  length,  but  in  almost  every  other  detail  stands  in  broad  con- 
trast with  it,  thus : 

Grade. — Continuous  2  per  cent  (uncompensated)  against  a  broken  4  per  cent 
(uncompensated) ;  including  the  effect  of  curvature  or  of  compensation  there- 
for, 2.6  per  cent  against  6  per  cent. 

Curves.— Curves  of  2S9  ft.  radius  (19'  50 )  connected  by  minimum  tangents 
of  40  metres  (131  ft.),  against  16°  30'  to  17°  40'  curves  (325  to  350  ft.  radius)  con- 
nected by  no  tangents  at  all  for  many  successive  reversions.     The  writer  con^ 


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[The  degrees  of  curve  given  are  for  ao-metre  chain  (chord  of  65.6 
somewhat  more  than  two  thirds  of  the  degree  of  the  curves  by  the 
(100-foot  chords).     Profile  of  this  line  is  shown  in  t  ig.  310.J 


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tion. 

LoCATluN   OF  SbCTIONS. 

Lr.s'gth. 

Increase 

by 
Develop- 
ment. 

By  Air-Line 

from 
Beginninf; 

to  End 
of  Section. 

8.5  kilos. 

7.5     " 

7.9     " 

»3  9      " 
.at  S      " 

By 
Located 

Line. 

19. u  kilos. 
15.0     '• 
20.5      •• 

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54.5      " 

9 
8 

7 

7-8-9 

Summit  to  end  of  ra^ged-clifT 
work 

End-section  0  to  middle  of  third 
horseshoe  curve 

luo  to  324 
too  to  300 
100  to  260 

Middle  of  third    horscsho?   to 
middle  of  flat,  opix>site  Jalapa 

Air-line  from  summit  to  Jalapa 

loo  tn  238 
100  to  354 

s:^ 


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Fio.   309. 


MEUMUmr  LOCATED  l/AE    ^ 

LAS  Visas SuMimr TO  JAlaj¥<. 

Scale  t-t»0OO-i>eauced  from Fiela  Sheats  to 
Sca/e  oFt-ioooo-aaHafeefperlncfi. 

AM.WaUmglon,  Ctiief  engineer . 
JalK  SBIiott,  atiefof/^rtf. 


vSa^i^ 


L^js(V4=AS. 


Section  9. 


Sections. 


Section  7. 


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[The  degrees  of  curve  given  are  for  20-metre  chain  (chord  of  65.6  ft.),  and  are 
somewhat  more  than  two  thirds  of  the  degree  of  the  curves  by  the  foot  system 
(loo-foot  chords).     Profile  of  this  line  is  shown  in  Fig.  310.] 


Section  8. 


jfor  ao-metre  chain  (chord  of  65.6  ft.),  and  are 
If  the  degree  of  the  curves  by  the  foot  system 
[ne  is  shown  in  Fig.  310.] 


nxm  here  to  below  JkLAPm^  Material  aepearr  to  be  £arm 
10  s  great  Depth  _  l^as/tecf  down  frotn  Mountain  SJofios. 


Fio.  309. 


^  J'MJMIJmr  LOCATED  UAE 


SH££r  N9i, 

LAS  ViGAS Suhmtrro  JAlapa.* 

Scale  i-toOOO- Reduced  From  Field  Sheets  ta 
Scale  oF/-ioooo>iaa*/aFeetperI/Tch . 

AM.Wellinaton,  Chief  Engineer , 
JOltnSa/ion^  Chief  of /^rfy. 


^ 


5 


rjiii^s 


□□DDL 

□□□at 

vrnKM 


APPENDIX 


933 


.he  Jalapa  ,i„e,  shown  on  pTg^.  3^    nd  3.0      tLT  '"^  "P""  "  '''■°'""-  <" 
be  seen  in  Ki,.  30,  .0  have  V^^t  L";  J^/a'Sr  "^  "'  '"^  ""^  ""' 

.anje^n:::Thr47"::.r:r::;  M^L^rn::;:  •"'  r  '^  ^-^-- 

upper  third  of  the  line,  shown  on  fL  3^  aL  ,!o  ''/"'"'  """'^''^  °"  "»- 
■tangent  (the  average  tangent  being  96  3  metres  oI'm'"  T  "'  '"^  ""^  '^ 

kilometres  which  have  been  engraved  48  per  cen    of  the  >"  ""=  """'^  ^* 

comparative  degrees  of  curvature  cannot  be  given  "  "'"^'"'-     ^""^ 

W,:  the  jalapa  line,'^,i.:;ra  IT  ;r;iiretr  ""Srh'"*  ■""">  '°"«" 
been  the  same,  however,  mereTy  ,0  get  to  mTxLo  .hifH^  '"'"'''  '"  "*=" 
been  more  than  eliminated  as  will  te  H  r  '  v  <''f"<^"«  "ight  have 
Marcos  on  Fig.  308.  ^"  ''''""  *=  ''°"^''  ""=  above  San 

Gauge.— The  Jalapa  line  was  intended  to  be  laid  to  ■x  ft   »= 

.ng  to  the  gauge  of  the  Mexican  National  Railway  whereasr'M"'''"'r'" 
way  was  4.ft.  Si-in.  gauge.  No  difference  was  ZL  n  theTodtL  ho  ""  •""'■ 
account  of  the  gauge,  the  road-beds  having  been  T21T  .'         ""'  °" 

r  to  .  in  cuts  and  .,  to  x  in  hlls.  and  rli  f  est  :    ed  ^t  sb'^:     T    ";'  ^'""^ 

:r,r  trroV-iVauV"-  --  -^  -  -'^  -  ^.i^edTa:; 
bia„?::e;a!:dr: :-;:  'i-ti^ttfi^io^-ofr'  t-  --  -•'■»- 

Table  No.  2  Is  an  abstract  clo.in/.         '^^^^^^^  of  the  entire  mountain  grade, 
^e  materia,  on  the  ^:Z:^:^Zt:::^^^^^^t^ 

wth'eTerr: rx-ed  e?'"'"^'^  t"'"^  — "p™«.:rsr  eX 

point,  any  engineer  can    orm  H      ^'"^'  f  °™  '"=  ^^"'"'"^'^  ""^"'"i"  at  each 

Table  No   .  (omi  fed  to    avT  sna  T"  '"h^™'"'  '''  "^  """"='  '"^  -™-'=  ■" 
still  I,   ,h=,  \  """*". '°  ^*^<^  space)  IS  adequate.     The  writer's  belief  was  and 

less  than  $.o'l'  permile     gaini:  ttTr,"""  ""f  r"""^'"^'"'  """"""^  "^ 
n,ou„tain-grade  of  the  Me.r  HliK.'r  irthTlltfoV  f  ToT  7  ral'^o; 

.e;Le::  t^'Sir^tr  unir- r-  --  - 1™  •-  ^^^-^ 

-ntrc^ir-e^r-r^ 


■The  general  route  of  both  l^^^^Th^^T^ibed  is  showT^n  Fig.  jos! 


In 


934 


APPENDIX  C. 


I 


>Iake  what  allowances  one  will,  there  is  a  great  contrast  in  these  two- 
lines,  and  it  therefore  becomes  of  interest  to  consider  how  this  latter  line 
was  obtained. 

In  March,  1881,  the  writer  was  engaged  by  the  Mexican  National  Rail- 
way Company  to  act  as  engineer  in  charge  of  location  and  surveys  on  the 
various  lines  for  which  they  had  concessions,  extending  from  the  city  of 
Mexico  to  the  United  States  and  to  the  Pacific  coast.  On  landing  at 
Vera  Cruz,  with  a  large  staff,  under  orders  to  report  in  Mexico,  he  was 
surprised  at  the  receipt  of  a  letter  of  instruction  to  the  effect  that  a  corps 
were  engaged  in  examining  a  line  from  Vera  Cruz  to  Mexico  v/a  Jalapa. 
and  that  he  should  detach  another  corps  for  service  on  this  line,  sending- 
forward  the  remaining  parties  by  rail;  that  he  should  then  make  a  re- 
connaissance "  sufficient  to  determine  the  general  possibilities  of  the 
route,  taking  such  escort  as  might  seem  necessary;"  set  the  new  and  old 
parties  at  work ;  and  not  delay  date  of  report  in  Mexico  "  more  than  six 
days." 


Fig.  309  IS  given  a  reduction  to  one.fifth  scale,  or  ^r^^j^  (i^  inches  per  mile, 
wiihm  I  per  cent),  of  the  large  topographical  map  on  a  scale  of  y^ig^  of  the 
upper  54  of  the  117  kilometres  of  the  mountain  grade.  This  in  turn  was  re- 
duced from  the  original  field-sheets  on  the  large  scale  of  t^\j^  or  83J  feet  per 
inch,  which  the  difficult  character  of  the  work  made  necessary.  The  topog- 
raphy was  very  accurately  taken  by  a  skilled  topographer.  Mr.  Max  Chapman 
M.  Am.  Inst.  M.  E. 

In  Fig.  310  is  given  a  photographic  reduction  of  the  original  profile,  which 
was  called  off,  station  by  station,  in  the  usual  way  from  a  paper  location  on  the 
original  field-sheets,  and  estimated,  station  by  station,  from  tables,  with  allow- 
ance  for  surface  slope,  which  often  more  than  doubled  the  level-section  quanti 
lies.  The  estimated  quantities  for  each  cut  and  fill  are  given  on  the  profile  and 
nature  of  material  indicated.  Retaining-walls  were  estimated  for  at  every  point 
where  a  fill  would  not  catch,  and  are  indicated  by  a  thick  line  on  the  profile. 
The  small  amount  of  masonry  is  due  to  the  almost  entire  absence  of  surf/ic? 
drainage  and  running  water,  as  elsewhere  noted. 

The  line,  profile,  and  estimate  here  shown  were  not  finalities,  but  prepared 
for  a  special  purpose.  Compensation  for  curvature  had  not  yet  been  introduced. 
It  was  fully  expected  to  do  still  better  at  points,  and  in  fact  the  location  shown 
was  greatly  improved  in  the  upper  section  {9)  by  a  new  line,  run  just  before  the 
suspension  of  work  which  threw  the  line  back  from  the  ragged  cliff  work  near 
the  summit.  As  maps  and  profiles  of  this  improvement  cannot  be  given,  no 
claim  in  respect  to  it  is  made,  but  only  for  what  had  been  actually  secured  and 
recorded  in  black  and  white. 


REDUCTION 


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Fig.  310. 

FERRO  CARRIL  NACIONAL  INTEROCEaIiICO. 

VCRACRU2viaJAtAPAfofheCirv  OF  MEXICO   and  »he  PAc.tc  COAST. 

ProRie  oPthePREUMINARY  LOCATED  LINEon  1 
UPPER  HALF  OF  the    MOUNTAIN  GRADE 

From  JALA  PA  to  LAS  VEGAS  * 

Sections  7, Sand  9. 

AM. WOLINGTON..  Chief  Enyine^r. 
John  S.  ELLIOTT.      Chief  of  ft»rt>iSfc«.7-9. 

Iflvers  «r«  ary  Old  Datum  reading  about  SO.ooo  metres  below  m,^        ,,fe.T. 

Scare  oF  Original  ProfUe  reduced  3/5. 

giving  the  foUoviivg  comparison  : 

ORIGINAL  scALcf  "r:;":;*'  '/^;°  *"'  ••'*!!/^  p^^Jrw*. 


PftOntC  o>  PA'^T  or  FIRST  MILE  after  reath? ng  fht  SUMMtT« 
(Une  continues  of  tHi«  general  character  For  the  entire  disfanca  to  the 
CITY   OF  MEXICO   some  160  Miles.) 

I  1 1  Tl  1  I  I         Cp|ntral|    PlgrHP.aii  |oF    f^extct^ 

F3 


Btainninq  oTZVz  iMreentGraai  *  94fS.O  MMrw. 
ai)oveTidf*  "^923  ft- ElevaHon. 
ef  Boca  del  MomeSummit  on  Mexican  R.RexacHv. 
rSfa.U-1190.    is»  Pretiw.) 


Vertical      V400      "....aai/j, 

Izontal  V12.SOO  ••  i,o««  -.»„ 
ical        4/4,000   » SaVSi. 


PRESENT  SCALE /"°"""^'  *''^-^°°  "  *«o*» 
I  Vert 


Pic.  310.— Profilk  of  Line  in  Fig.  309. 
[The  fine  horizontal  lines  are  a  meters  (6  56  ft.)  apart  on  this  profile.    The  total  width  of  the  plate  is  5  kilos.,  =  311 
miles.    Rock  is  shaded.     Retaining  walls  indicated  by  heavy  line  and  letters  R  W.    Many  of  the  minor  culverts  hare  been 
omitted  ft-om  the  reproduction,  but  the  effective  drainage  area  on  the  entire  line  was  iu  general  very  smaU] 


Lost  by  bfeatu  of  Grade,! n  the  entire  distance  t06  metres 
(4.7S  percent  ol  Fall)  of  which  ther«  was  _ 

On  the  portion  shown  36  metres  (3 .43  per  cent) 
•     •        •  n»t     .       TO      •        (ijbo  •     •   I 
All  Of  wich  ana  sontefhinor  more, it  was  expected  to 
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APPENDIX  C. 


935 


To  one  landing  in  Mexico  entirely  ignorant  of  the  language  and  the 
country;  provided  with  no  map  or  profile  of  the  existing  line,  and  know- 
ing nothing  more  of  its  character  than  the  general  fact  that  it  was  one  of 
the  heaviest  and  most  costly  railways  in  the  world;  unaware  that  its 
engineers  had  even  given  a  thought  to  a  route  via  Jalapa,  or  even  that 
there  was  such  a  place,  until  he  finally  learned  that  the  route  had  been 
examined  only  to  be  abandoned,  and  that  the  branch  which  had  been 
built  to  Jalapa,  at  the  foot  of  the  mountain  proper,  had  lo  per  cent  grades, 
and  was  practicable  only  by  horse-power;  unaccustomed  to  a  tropical 
climate  and  to  the  saddle ;  provided  with  no  map  of  the  region  better  or 
much  larger  than  Fig.  308  which  accompanies  this  paper;  and  innocent 
of  all  knowledge  as  to  how  large  an  escort  would  insure  safety,  if  indeed 
any  could— these  were  sufficiently  formidable  instructions,  and  could 
never  have  been  successfully  carried  out,  as  fortunately  they  were  to  the 
letter  (barring  two  days'  delay  from  an  unseasonable  rain),  had  recon- 
noitring such  lines  been  in  fact  so  entirely  lawless  a  matter  that  there 
was  nothing  for  it  but  to  look  over  the  whole  country  and  then  decide 
what  to  do,  or  at  least  to  try  for. 

The  line  which  was  found  to  be  under  examination  is  indicated  by 
dotted  lines  on  the  general  map  herewith,  and  was  at  once  rejected  as  im- 
practicable and  absurd.  It  ran  from  the  coast  north-easterly  to  Jalapa,  4500 
ft.;  then  descended  southerly,  850  ft.  in  about  10  miles,  to  an  elevation  of 
about  3650  ft.  at  Coatepec  ;  then  was  expected  to  ascend  somehow,  some 
7000  ft.  to  the  "  pass"  between  the  volcanoes  of  Orizaba  and  Perote,  at  an 
unknown  elevation,  estimated  at  10,700  ft.  in  an  air-line  distance  of  some 
15  miles;  and  then  to  descend  some  2000  or  3000  ft.  on  the  back  slope  of 
the  mountain,  to  the  general  level  of  the  plateau.  Very  naturally  the 
best  grades  which  it  was  even  hoped  to  obtain  were  those  of  the  Mexican 
Railway,  or  4  per  cent  uncompensated. 

It  was  at  once  clear  that  either  something  considerably  better  than 
this  must  be  obtained,  or  the  line  should  be  reported  as  impracticable  and 
the  whole  staff  withdrawn.  And  it  seemed  equally  clear  to  the  writer  that 
either  a  considerably  better  gradient  than  on  the  existing  line  must  be 
obtained,  and  lighter  work  as  well,  or  the  project  reported  as  unde- 
serving of  any  consideration  financially.  A  reasonable  hope  for  a  maxi- 
mum grade  of  not  over  2i  per  cent  at  most  was  therefore  fixed  upon  as 
the  highest  one  justifying  setting  parties  at  work  on  it,  and  hence  to  be 
considered  at  all ;  and  this,  to  make  the  project  a  meritorious  one,  re- 
quired that  2  per  cent  should  be  sought  for.  This  made  it  indispensable  to 
gain  considerable  development  forthe  ascent,  and  this  in  turn  made  it  out 


mil  n 


93<5 


APPENDIX  C. 


APPENDIX  C. 


937 


I 


of  the  question  to  ascend  between  the  two  volcanoes,  even  had  the  saddle 
between  them  been  cleft  down  to  the  level  of  the  main  plateau,  which 
was  known  not  to  be  the  case.  The  whole  problem,  therefore,  turned 
upon  the  question  of  whether  or  not  it  would  be  possible  to  turn  north- 
ward at  Jalapa  (assuming  that  point  to  have  been  successfully  reached  by 
the  required  grade,  which  seemed  a  minor  question)  and  run  parallel 
with  the  coast  line  and  the  coast  range,  gradually  ascending  with  all 
possible  development,  and  turn  the  mountain  of  Perote  to  the  north. 

This  possibility  the  writer  was  satisfied  would  turn,  negatively  at  least, 
upon  the  simple  question  of  whether  or  not  there  was  some  kind  of  an 
established  highway  ascending  from  Jalapa  to  the  plateau,  following  in  a 
general  way  the  same  course,  and  turning  the  mountain  to  the  north. 
That  is  to  say.  the  existence  of  a  highway  would  not  prove  the  line  was 
practicable,  but  the  absence  of  it  would  go  far  to  prove  that  it  was  im- 
practicable. In  respect  to  highways,  the  writer  had  even  then  learned 
by  sad  experience,  and  had  repeated  occasions  in  the  next  three  years 
to  realize  still  more  fully,  that  the  route  of  a  highway  is  ordinarily  the 
worst  possible  guide  for  a  locating  engineer,  except  as  it  may  serve  the 
negative  purpose  of  a  danger  sign  to  warn  him  away.  He  now  recalls  no 
less  than  twenty-three  instances  on  the  lines  in  Mexico  under  his  charge 
where  the  existence  of  a  travelled  road  proved  merely  a  snare  to  deceive. 
Some  of  these  instances  were  of  a  very  curious  character  and  of  much 
technical  interest,  but  description  must  be  forborne. 

But  in  regions  of  real  difficulty,  where  the  elevations  to  be  surmounted 
become  serious  even  for  animal  power,  and  even  after  all  avoidable  rise 
and  fall  has  been  eliminated,  the  case  is  different.  The  writers  experi- 
ence and  conviction  is  that  in  such  cases  the  aggregate  intelligence  of 
the  cows  and  the  natives  thereabout  may  safely  be  trusted  to  discover  and 
utilize  the  very  best  route  there  is  for  surmounting  the  elevation  with  the 
least  amount  of  work.  Even  what  would  be  regarded  in  Mexico  or 
Colorado  as  so  simple  a  problem  as  that  of  making  the  900  ft.  rise  over 
the  Allegheny  Mountains  in  Pennsylvania,  is  a  case  in  point.  The  pass 
above  Akoona  and  Hollidaysburg  was  discovered  and  utilized  in  the  very 
earliest  days  of  the  settlement  of  the  country,  and  four  generations  of 
engineers  on  four  successive  public  works  have  been  able  to  do  no  bet- 
ter. . 

The  first  question  asked  by  the  writer,  therefore,  after  learnmg  tne 
details  of  what  was  doing,  was  whether  there  was  a  travelled  highway 
turning  the  mountain  to  the  north,  the  map  before  him  not  extending 
far  enough  north  to  show  that  region  distinctly  at  all.     He  was  informed 


»at  once  that  there  was,  and  a  very  old  and  good  one.  Had  the  response 
been  otherwise,  he  should  have  regarded  the  result  of  the  reconnaissance 
as  practically  decided  then  and  there.  The  statement  was  coupled  with 
another,  however,  that  this  route  had  been  examined  by  the  engineers 
of  tlie  Mexican  Railway,  and  reported  far  less  practicable  than  the  line 
afterwards  adopted  and  built,  so  that  the  middle  line  described  was  under 
examination  as  the  only  hope  left. 

Tliis  was  discouraging  enough;  but  on  further  learning  that  the  high- 
way had  been  for  three  centuries  preceding  the  railway  era  the  leading 
•one  between  the  interior  and  the  coast ;  that  there  was  no  succeeding 
descent,  but  rather  a  gentle  rise  in  it  for  many  miles  after  the  mountain- 
grade  proper  was  surmounted  ;  that  the  summit  was  (this  afterwards 
proved  an  error)  several  hundred  feet  lower  than  that  of  the  Mexican 
Railway  ;  and  some  other  facts  which  seemed  hopeful,— there  appeared  to 
be  a  fighting  chance,  which  was  at  least  the  only  chance  that  the  line 
/might  be  developed  to  give  the  requisite  grade. 

.  The  more  immediate  question  became  then  to  make  the  ascent  of  4500 
ft.  to  Jalapa,  and  it  was  at  once  apparent  that  to  have  any  hope  of  doing 
this  on  such  favorable  grades  as  were  alone  worthy  of  consideration  under 
the  circumstances,  the  line  must  be  carried  down  to  as  low  an  elevation 
as  possible,  parallel  with  the  coast  and  the  mountain  slope,  by  running 
south  from  Jalapa  toward  Coatepec  before  beginning  to  lose  distance  by 
turning  eastward  to  the  sea.  It  appeared  probable  that  the  850  ft.  of  fall 
between  these  two  points,  as  to  which  some  definite  knowledge  was 
available,  could  not  be  made  on  a  steeper  grade  than  2  per  cent,  and  it 
was  this  fortunate  fact  (as  it  proved)  which  first  led  to  conducting  the 
reconnaissance  from  the  beginning  on  the  fighting  chance  of  obtaining  a 
2.  per  cent  grade. 

It  was  now  determined,  therefore,  that  the  line,  if  there  was  to  be 
any,  must  pass  from  Vera  Cruz  to  Coatepec,  and  thence  to  Jalapa,  instead 
of  to  Jalapa  direct.  Coatepec  lies  at  the  head  of  a  river  of  considerable 
size,  the  Rio  Antigua,  which  runs  from  it  directly  east  to  the  coast;  and 
the  map  and  known  elevation  of  the  town  made  it  at  once  clear  that  there 
was  no  physical  impossibility  in  descending  this  valley  directly  on  a  2^ 
per  cent  grade,  or  perhaps  less,  if  the  valley  had  a  tolerably  uniform  de- 
scent. It  needed  but  the  most  moderate  knowledge  of  the  general  laws 
of  topography,  however,  to  make  it  practically  certain  that  no  even 
approximately  uniform  descent  could  be  hoped  for  in  a  river  flowing  in  a 
deep  gorge,  cut  through  what  was  practically  only  a  narrow  footing  to 
xhe  most  tremendous  mountain  slope  on  this  continent.     The  foot-hills 


^g^ssssssz 


938 


APPENDIX  C. 


APPENDIX  C. 


939 


r 


of  a  slope  which  reached  a  height  of  17.873  ft.  and  started  practically 
from  the  level  of  the  sea,  was  certain  to  have,  like  all  such  slopes,  a  de- 
cidedly concave  profile. 

Nothing  less  than  5  per  cent  could  be  rationally  hoped  for  in  follow- 
ing the  bed  or  immediate  slopes  of  the  valley,  and  it  therefore  became 
quite  certain  that  the  line  descending  from  Coatepec  must  start  from  the 
lowest  point  at  the  head-waters  of  the  Rio  Antigua  which  it  was  possible 
to  obtain,  but  speedily  rise  up  on  the  higher  slopes  of  the  valley  and  out 
of  the  influence  of  the  stream,  until  at  last— and  probably  within  a  short 
distance— it  would  rise  above  all  supporting  ground.  No  resource  would 
then  remain  but  to  turn  across  northwardly,  at  some  favorable  point  on 
the  dividing  ridge,  into  the  valley  of  the  next  river  to  the  north,  the  Rio 
Chachalacas,  with  the  view  of  gaining  only  such  limited  development  as 
might  be  necessary  to  catch  upon  some  high  point  on  what  were  known 
to  be  the  gentle  slopes  of  the  lower  valley  of  that  river,  from  which  the 
line  could  descend  eastwardly  on  the  required  grade  to  sea-level  at  a 
point  as  near  to  the  coast  as  possible.  The  only  fear  in  this  process,  be- 
sides the  danger  of  heavy  work,  was  that  it  might  be  unavoidable  to  make 
a  long  horseshoe  development  up  the  valley  of  the  Chachalacas,  bring- 
ing the  foot  of  the  grade  far  inland  from  the  sea,  and  causing  just  so 
much  unnecessary  loss  of  distance  on  a  level  before  reaching  the  foot  of 
the  mountain  grade.  The  existence  of  these  two  parallel  and  deep-lying 
streams  made  it  certain  that  the  general  scheme  below  Coatepec  would 
be  practicable,  if  not  too  costly  ;  and  the  immense  depth  of  the  southerly 
valley,  which  varied  from  1000  to  2000  ft.,  together  with  the  absence  of 
all  supporting  ground  to  the  south  of  it,  made  it  certain  that  the  line 
could  at  no  point  turn  south  between  Coatepec  and  the  coast. 

Thus,  by  a  process  of  exclusion,  the  entire  line  was  projected  and 
sketched  upon  the  map,  with  most  dismal  apprehensions  of  the  charac- 
ter of  the  work  which  would  be  encountered,  but  with  absolute  confi- 
dence, expressed  at  the  time  to  the  gentlemen  who  accompanied  the 
writer  on  reconnaissance,  in  the  face  of  some  opposition,  that  if  this  line 
was  not  practicable,  there  was  nothing  in  the  region  which  was  suffi- 
ciently defensible,  from  an  economic  point  of  view,  to  make  it  even  worth 
examination.  The  line  shown  on  the  general  map  (Fig.  308)  which  the 
writer  now  has  the  honor  to  lay  before  the  Society,  does  not  differ  by 
its  own  width  at  any  point  in  the  entire  ascent  of  nearly  8000  feet  to  the 
plateau  from  that  which  the  writer  thus  sketched  upon  the  map  in  the 
city  of  Vera  Cruz,  and  showed  to  several  gentlemen,  on  the  evening  of 
the  day  when  he  first  landed  in    Mexico ;  within  two  hours  after  first 


learning  that  there  was  such  a  place  as  Jalapa,  or  that  there  was,  or  ever 
had  been,  such  a  project  as  an  ascent  to  the  plateau  through  that  region,. 
and  with  the  elevation  of  only  two  points  on  the  line,  Jalapa  and  Coate- 
pec, approximately  given.  Neither  does  the  line  on  Fig.  308  differ  by 
much  more  than  its  own  width  at  any  point  from  the  position  of  the  line 
as  finally  surveyed,  as  shown  on  the  detailed  maps  and  profiles  which  are 
herewith  laid  before  the  Society  complete,  the  more  diflftcult  upper  half 
of  the  mountain  grade  only  having  been  engraved  on  Figs.  309  and  310. 

The  writer  would  not  be  understood  to  assert  or  imply  that  equal 
positiveness  in  defining  in  advance  the  limitations  of  reconnaissance  is- 
often  possible.  On  the  contrary,  he  has  never  known  another  instance 
just  like  it,  although  it  became  his  duty  later  to  consider  projects  for 
several  other  lines  of  a  similar  but  less  exacting  character.  But  the 
j>eculiar  conditions,  it  will  be  seen,  left  no  escape  at  any  point  from  the 
chain  of  reasoning.  Had  there  been  no  existing  parallel  line,  one  might 
have  justifiably  taken  the  region  for  better  for  worse,  and  borne  with 
equanimity  finding  it  a  great  deal  worse  than  he  took  it  for.  As  it  was, 
the  fighting  chance  for  a  low  grade  was  the  only  one  economically  worthy 
of  attention,  and  this  primary  fact  given,  the  conditions  left  no  escape 
at  any  point  from  the  train  of  reasoning  that  it  was  that  one  route  or 
nothing. 

The  next  morning  at  daybreak  the  reconnaissance  began,  and  was 
pushed  through  with  increasing  confidence  as  fast  as  the  animals 
could  stand  it,  or  at  the  rate  of  some  40  miles  per  day,  the  entire  ex- 
amination of  the  mountain  grade  occupying  three  days — such  haste 
being  merely  in  fulfilment  of  the  writer's  positive  instructions,  and  nat- 
urally against  his  inclination.  Less  time  was  required,  however,  be- 
cause the  only  real  purpose  of  the  reconnaissance  was  not  to  find  a  route, 
but  to  examine  on  the  ground  the  features  of  what  was  already  known 
to  be  the  only  route  affording  a  rational  chance  of  success.  The  first 
1500  feet  of  rise  was  seen  to  be  on  slopes  smooth  in  detail,  but  suflS- 
ciently  steep  for  laying  down  a  surface  line  on  almost  any  grade,  and 
were  not  examined  critically.  The  dividing  ridge  was  then  followed  up, 
to  judge  of  what  was  really  the  only  critical  point  of  the  lower  descent 
(from  the  point  of  view  of  possibility  and  not  of  cost),  the  passage  from 
one  water-shed  to  the  other.  A  long  and  sharp  spur  ridge  running 
eastwardly  from  Coatepec  about  half  way  to  the  coast,  having  a  crest- 
5000  or  6000  feet  high,  and  standmg  at  right  angles  to  the  main  slope^ 
was  found  to  define  the  point  where  this  passage  must  occur  pretty  defi- 
nitely, and  the  material  and  topography  was  seen,  with  much  relief,  to- 


,1 


940 


APPENDIX   C. 


be  favorable  for  making  this  passage  with  as  much  or  as  little  develop- 
nient  as  might  be  necessary,  with  considerable  latitude  in  elevation  and 
easy  work.  The  south  slope  of  this  mountain,  where  the  line  would  lie, 
was  found  to  be  almost  impracticable  for  passage  on  horseback  without 
camp  equipage  and  time ;  but  observing  tlie  north  side  to  be  fairly  favor- 
able, and  taking  it  to  be  very  unlikely  that,  in  a  ridge  of  this  chanicier, 
tlie  topography  would  differ  widely  on  the  two  slopes,  it  was  passed  bv 
with  a  confidence  that  the  result  fully  justified,  as  well  as  such  verv  lim- 
ited information  as  was  available  at  the  time.  It  will  be  seen  from  the 
maps  and  profiles  of  this  section  (not  engraved)  that  on  the  surveys  now 
submitted,  a  few  of  the  most  costly  single  works  on  the  line  are  here,  and 
not  on  the  engraved  section  above  Jalapa,  which  was  really  the  critical 
section.  This,  however,  the  writer  is,  and  was  then,  satisfied  was  due 
chiefly  to  the  fact  that  the  lower  section,  not  being  a  source  of  much 
anxiety,  was  left  in  less  competent  hands.  In  part  it  was  radically  im- 
proved almost  at  the  conclusion  of  surveys,  and  the  writer  feels  no  doubt 
that  it  all  might  have  been  more  or  less,  although  he  makes  no  claim  in 
that  respect.  Owing  to  the  falling  away  of  the  country  to  the  south, 
before  referred  to,  and  the  existence  of  the  deep  barranca,  or  gorge,  in 
which  the  river  lay,  which  cut  down  almost  to  sea-level,  or  some  3000 
leet  below  the  line,  some  of  the  most  sublime  views  of  the  line  were  on 
this  section;  but  its  difficulty  was  not  in  proportion,  in  part  because  of 
the  very  fact  that  the  line  lay  so  high  as  to  be  above  the  immediate  influ- 
ence of  the  barranca.  The  material  on  all  this  section  was  exceedingly 
favorable. 

The  region  between  Coatepec  and  Jalapa  was  known  to  be  not  very 
rugged,  and  to  oppose  no  difficulty  as  to  elevation,  so  that  it  also  was 
passed  by  with  a  confidence  which  the  result  justified,  and  the  project 
was  complete  to  Jalapa,  as  a  basis  for  surveys,  with  a  reasonably  favor- 
able 2  per  cent  grade-line  all  but  assured. 

For  the  critical  section  above,  the  distance  by  highway  was  found  to 
be  almost  one  half  too  short,  and  all  hung  upon  the  possibilities  of  ('C- 
velopment.  The  material  and  topography  on  the  lower  half  was  found 
to  be  favorable  for  this  purpose,  being  earth  to  a  great  depth,  as  noted, 
and  sufficiently  broken  up  by  ridges  and  hills.  A  long  stretch  at  about 
the  middle  of  the  slope,  near  the  village  of  San  Marcos,  was  of  an  equally 
favorable  character,  being  literally  an  inclined  plane  on  a  slope  of  about 
I  in  10, — an  old  lava  flow  overlaid  with  soil, — and  not  much  broken  up 
in  detail.  The  upper  section  was  rugged,  but  short,  with  considerable 
opportunities  for  rather  expensive  development. 


APPENDIX  C. 


941 


The  whole  of  this  region  was  examined  on  the  third  day  of  a  verj- 
heavy  rain-storm,  the  end  of  which  could  no  longer  be  waited  for,  and 
the  examination  was  necessarily  restricted  to  salient  features  only.  On 
a  long  grade-line  of  this  character,  how^ever,  the  possibilities  of  develop- 
ing on  practicable  ground  to  reach  certain  elevations  at  certain  frac- 
tional portions  of  the  available  distance,  can  be  judged  of  with  some 
certainty,  the  general  character  of  the  slope  being  the  main  feature;  and 
the  writer  felt  no  real  doubt  then,  or  at  any  later  time,  that  a  grade  in 
the  neighborhood  of  2  to  2^  per  cent  was  easily  practicable,  there  being 
a  certain  considerable  belt  of  favorable  territory  on  which  to  place  it, 
although  above  and  below  that  the  topography  was  much  more  forbid- 
ding. A  leading  factor  in  reaching  this  apparently  hasty  conclusion 
was  the  splendid  and  ancient  highway  already  referred  to,  by  far  the 
best  in  Mexico,  if  not  on  this  continent.  It  is  a  broad  macadamized 
road  with  paved  gutters,  and  a  stone  curb  or  masonry  wall  at  the  side,, 
and  the  writer  desires  to  pay  a  tribute  of  admiration  and  respect  to  the 
unknown  engineer,  whoever  he  was, — very  possibly  one  of  the  soldiers  of 
Cortez,  or  one  of  his  immediate  successors,— who  laid  it  out.  From  a 
point  near  Jalapa  to  the  summit,  near  Las  Vegas,  there  is  not  a  break  in 
the  steady  ascent,  and  there  are  few  points  on  it  where  a  fresh  team  of 
horses  would  not  readily  break  into  a  trot.  The  conclusion  was  natural, 
that  if  a  Spanish  soldier  in  1530  could  put  something  like  a  6  per  cent 
highway  down  that  mountain  slope,  an  American  engineer  in  1881  ought 
to  get  a  2  per  cent  railroad  line  down  it,  or  take  off  his  hat  to  his  prede- 
cessor. 

After  reaching  the  summit,  the  continuation  of  the  line  to  Mexico,, 
or  any  other  point  on  the  plateau,  was  a  detail  offering  no  difficulties 
and  needing  no  immediate  stud\\  The  line  was  therefore  reported 
on  in  writing  to  Mr.  W,  C.  Wetherill,  chief  engineer,  three  days  later 
(March  28),  as  follows  : 

"The  line  under  examination  was  too  forbidding  to  be  worth  further  at- 
tention. ...  I  feel  no  doubt  that  the  proper  place  for  the  line  is  to  the  north 
of  Peroie,  and  that  something  like  a  2|  per  cent  grade,  or  possibly  a  2  per  cent 
grade,  is  practicable  above  Jalapa.  Whatever  grade  is  there  obtained  can  cer- 
tainly be  continued  down  to  sea-level  and  slope  without  excessive  work.  I 
have  instructed  surveys  to  be  conducted  above  and  below  Jalapa  on  a  2  per 
cent  basis  for  the  present,  and  consider  the  prospects  for  a  fairly  favorable  line 
good." 

It  should  be  mentioned  further,  that  the  writer's  examination  had 
been  merely  in  a  consulting  capacity  (the  line  not  being  formally  a  part 


/ 


•942 


APPENDIX  C. 


APPENDIX  C. 


943 


♦ 


of  the  Mexican  National  projects),  and  for  some  months  later  he  had  no 
permanent  connection  with  or  knowledge  of  the  progress  of  the  work, 
being  absent  on  the  Pacific  slope.  On  being  again  asked  to  examine 
the  line,  August  ist,  1881,  he  found  that  his  conclusions  had  been  re- 
ported on  as  impracticable,  and  that  a  3  per  cent  compensated  grade  had 
been  adopted,  located  in  part,  and  was  under  construction.*  Fortu- 
nately, however,  a  most  intelligent  assistant  engineer,  of  great  natural 
capacity  for  location,  Mr,  John  S.  Elliott,  was  in  charge  of  the  upper 
locating  party.  To  his  admirable  conduct  of  surveys  the  success  of  this 
line  was  very  largely  due.  Aided  by  information  he  had  acquired,  it 
was  soon  discovered  that  the  abandonment  of  the  2  per  cent  grade  had 
been  an  over-hasty  conclusion,  from  data  which  in  fact  assured  its  suc- 
cess. The  work  in  progress  was  therefore  stopped  by  the  writer's  advice ; 
some  $30,000  of  completed  work  abandoned,  chiefly  in  the  approaches 
to  a  costly  tunnel  in  earth  ;  and  the  writer  appointed  chief  engineer,  con- 
tinuing in  charge  until  some  time  after  the  completion  of  the  surveys 
now  laid  before  the  Society,  when  the  abandonment  of  all  furtherance  of 
the  project  by  the  Mexican  National  Railway  compelled  his  resignation, 
and  shortly  afterward  led  to  the  stoppage  of  all  work.  But  for  the  fact 
that  he  was  favored  with  an  unusually  competent  assistant  in  immediate 
charge  of  surveys  on  the  more  difficult  section,  the  writer  fears  that  he 
should  never  have  been  able  to  carry  through  the  line  with  the  limited 
time  at  his  command. 

Two  features  on  the  upper  ascent  are  worthy  of  special  note :  One,  the 
great  lava  flow  shown  in  Fig.  309,  and  before  referred  to;  and  the  other, 
a  still  grander  feature,  the  barranca  of  Zimilahuacan,  a  vast  sink-hole  in 
the  earth  some  2  or  3  miles  in  diameter,  and  some  3000  feet  deep  by  the 
barometer,  about  half  of  it  sheer,  with  no  transition  or  "  ragged  edge" 
whatever  from  the  surrounding  surface  of  the  plateau,  which  was  as 
smooth  and  treeless  as  an  Illinois  rolling  prairie,  but  sloping  about  i  m 
12  or  15  in  the  chasm.  This  feature  was  encountered  some  miles  beyond, 
where  all  difficulties  had  ceased  at  the  summit;  and  so  smooth  was  the 
edge  that  the  line  skirted  it  with  a  mere  surface  line,  so  near  to  it  that 
a  stone  thrown  from  the  car-window  would  fall  sheer  full  1000  feet  before 
touching.  On  the  plateau  the  locality  was  so  cold  and  so  much  exposed 
that  it  was  stated  that  wheat  would  hardly  head,  while  immediately  be- 
neath one's  feet  bananas,  coffee,  oranges,  and  every  form  of  tropical 
vegetation  could  be  seen  growing  luxuriantly.     A  few  miles  beyond  was 


*  The  concession  permitted  of  no  delay  in  beginning  construction. 


a  large  and  very  ancient  fortress  still  in  good  repair,  but  unoccupied, 
which  would  cost  perhaps  $5,000,000  or  $6,000,000  to  duplicate,  in  which 
for  two  centuries  the  great  bulk  of  the  silver  product  of  Mexico  was 
stored  pending  the  arrival  of  transports  at  Vera  Cruz.  Several  of  the 
old  line  of  visual  telegraph  towers  which  were  used  to  communicate 
between  the  two  points  are  still  pointed  out,  although  out  of  use  more 
than  a  century.  From  several  points  on  the  upper  ascent  the  city  of 
Vera  Cruz.  80  miles  off  in  an  air-line  and  6000  to  8000  feet  below,  is 
visible  in  clear  weather.  These  and  other  features  make  the  region  one 
of  the  highest  interest  to  the  tourist. 

In  view  of  what  has  preceded,  the  writer  hopes  that  he  may  not  be  sus- 
pected of  over-estimating  the  difficulties  of  securing  such  lines,  or  of  per- 
sonal inability  to  cope  with  them,  when  he  declares  his  conviction  that 
this  whole  method  of  taking  railway  lines  up  difficult  ascents  by  a  con- 
tinuous succession  of  curves  and  tangents  on  a  rising  grade,  over  which 
the  locomotive  keeps  up  a  steady  march,  is  fundamentally  wrong  and 
bad,  and  one  which  might  profitably  be  modifipd  in  nearly  all  cases  when 
an  elevation  of  over  1000  feet,  or  possibly  much  less,  is  to  be  surmounted. 
To  furnish  a  suitable  background  for  the  expression  of  these  conclusions, 
by  showing  that  they  are  formed  in  spite  of  fairly  successful  experience 
in  following  up  the  more  usually  approved  plan,  is  a  main  purpose  of 
this  paper. 

Three  general  methods  for  surmounting  such  elevations,  besides  the 
almost  universal  one,  are  more  or  less  in  use:  ^ 

First.   Rack  or  grip  railways. 

Second.  Inclined  planes  operated  by  stationary  engines. 

Third.  Switchbacks. 

The  first  of  these  was  proposed  in  a  practicable  form  over  thirty  years 
ago,  and  the  two  latter  antedate  the  locomotive  itself.  Either  one  of 
them  is  probably  deserving  of  more  use  than  is  given  it,  but  the  third 
(switchback)  the  writer  deems  worthy  of  adoption  by  engineers  as  the 
standard  plan  for  surmounting  considerable  elevations,  always  provided 
the  switchbacks  be  constructed  and  operated  in  quite  a  different  manner 
from  that  usual  in  the  few  which  exist,  which  have  for  the  most  part 
onlv  been  resorted  to  as  a  last  resource. 

One  feels  a  natural  hesitation  in  expressing  a  conclusion  which,  it 
must  be  admitted  at  once,  all  the  tendency  of  modern  practice  tends  to 
discredit.  The  accumulated  verdict  of  experience  is  rarely  wrong,  and 
it  is  undeniable  that  all  these  plans  have  been  in  many  cases  tried  and 
abandoned,  and  have  met  decreasing  favor.    Nevertheless,  causes  need- 


-ttSSftg^--:' 


944 


APPENDIX  C. 


APPENDIX  a 


945 


less  to  go  into,  other  than  lack  of  real  merit,  may  explain  in  part  at  least: 
this  result,  and  the  writer  sees  no  escape  from  believing  that  they  do  so 
wholly. 

The  capabilities  of  the  inclined  plane  or  cable  plan  have  been  greatly- 
extended  in  recent  years,  as  applied  to  street  and  local  passenger  service,, 
and  it  is  clearly  destined  in  the  near  future  to  still  wider  use.     Super- 
ficially, the  record   of  its   use  in  connection  with  ordinary  railways   is 
most  discouraging  to  any  hope  of  its  future  usefulness  in  that  direction. 
In  the  early  days  of  railways  it  was  constantly, considered,  and  often 
used.     A  complete  plant  of  the  kind  existed  over  the  Allegheny  summit 
of  the  Pennsylvania  Railroad  before  that  line  was  built,  and  was  aban- 
doned in  favor  of  locomotive  traction,  even  to  connect  two  lines  of  canals. 
Several  complete  railways  operated  by  successive  inclined  planes  and 
gravity  inclines  were  built  in  Pennsylvania  and  elsewhere — two  in  North- 
ern Pennsylvania  of  considerable  length,  one  of  which  is  still  in  use  and 
the  other  only  recently  abandoned,  but  not  chiefly,  if  at  all,  for  reasons- 
affecting  its  abstract  merit.     It  is  not  generally  known  that  the  existing 
main  line  of  the  Pennsylvania  Railroad  over  the  Alleghenies,  which  was- 
built  long  after  the  old  planes  had  been  abandoned,  was  laid  out  with 
the   distinct  view  of  afterwards  adding  a  new  and   enlarged  system  of 
planes  for  freight  traffic  when  the  volume  of  traffic  had   increased  tO' 
justify  it.     This  policy  was  favored  by  its  distinguished  chief  engineer, 
Mr.  J.  Edgar  Thompson,  and  some  elaborate  and  interesting  data  in  re- 
spect to  it  are  given  in  the  early  reports  of  that  road,  notably  in  a  report- 
by  the  then  Superintendent,  Gen.  Herman  Haupt,  in  which  the  ground 
is  distinctly  taken  that  it  is  a  mere  question  of  volume  of  traffic  whether 
inclined  planes  are  economical  or  not. 

That  view  the  writer  apprehends  to  be  the  true  one.  The  fixed  trac- 
tive plant  is  costly  to  construct,  maintain,  and  operate,  and  expenses  are 
not  greatly  affected  by  whether  the  tonnage  moved  by  it  be  large  or 
small.  It  by  no  means  follows  that,  because  the  system  was  wisely 
abandoned  in  favor  of  locomotive  power,  for  the  thin  traffic  of  those 
early  days,  that  it  is  wise  to  continue  to  neglect  it  at  points  where  almost 
a  steady  stream  of  laden  cars  is  to  be  carried,  first  up  and  then  down  a 
dividing  ridge,  day  and  night,  the  year  round,  as  on  the  Pennsylvania 
summit,  and  at  many  similar  localities.  At  such  points  it  is  demonstra- 
ble that  not  only  may  the  great  amount  of  power  used  in  lifting  locomo- 
tives be  saved,  but  that  the  descending  and  ascending  cars  may  be  bal- 
anced against  each  other,  thus  largely  eliminating  the  effect  of  the  rise; 
while  the  superior  economy  of  stationary  engines  will  largely  reduce  the: 


cost  per  horse-power,  after  allowmg  for  the  friction  of  cables,  which,  on  a 
short,  steep  incline  is  a  minor  element.  Especially  now  that  the  making 
of  long  continuous  cables  is  so  well  understood,  so  that  as  long  an  in- 
cline as  the  topography  permits  may  be  readily  worked,  it  is  worthy  of 
the  most  serious  study  whether  a  very  large  economy  is  not  readily  pos- 
sible at  such  special  localities,  a  considerable  number  of  which  may  be 

counted  up. 

A  proper  switchback  system,  however,  seems  to  the  writer  the  most 
generally  useful  and,  meritorious  for  lines  of  probably  thin  traffic,  as  well 
as  the  most  unquestionably  practicable  for  use  in  all  such  localities.  The 
germ  of  the  proper  system  was  contained  in  the  first  switchback  laid 
out  in  America,  if  not  in  the  world, — that  at  Mauch  Chunk, — which  was 
used  for  dropping  empty  coal-cars  down  into  the  Nesquehoning  Valley, 
before  the  tunnel  of  that  name  was  completed.  That  track  was  used  only 
for  cars  passing  in  one  direction  (descending),  and  was  operated  as  fol- 
lows: 

The  cars  were  started  from  A,  Fig.  311,  on  a  down  grade  of  about  i 
per  cent,  calculated  to  give  a  considerable  velocity.  At  B  an  automatic 
switch,  whose  exact  mechanism  the 
writer  cannot  give,  was  run  through  and 
the  car  brought  to  a  rest  by  the  next  suc- 
ceeding up  grade  at  C,  from  which  it  im- 
mediately started  back  towards  I),  pass- 
ing through  the  switches  B  and  D  until 
again  stopped  at  E ;  and  so  on  indefinitely, 
the  cars  descending  several  hundred  feet 
in  all  without  the  slightest  attention, 
very  rapidly,  with  very  rare  accidents^ 
and  with  no  one  on  them  or  stationed 
along  the  track. 

Thus,  to  say  the  least,  every  advantage  was  gained  that  could  have 
been  gained  by  a  long  continuous  descent,  with  the  immense  advantage 
that,  owing  to  the  entire  liberty  of  choice  as  to  the  length  given  to  each 
plane,  the  best,alignment  and  lightest  work  available  on  any  part  of  the 
surrounding  country  may  be  chosen. 

But  more  than  this  was  gained.  Any  long  continuous  grade  which 
is  steep  enough  to  move  cars  with  journals  in  rather  bad  order,  must  be 
steep  enough  to  speedily  give  cars  in  good  order  a  dangerous  velocity. 
Thus  it  would  be  impossible  to  let  cars  run  of  themselves  down  a  con- 
tinuous grade  of  any  kind,  while,  on  the  switchback,  not  only  was  this 
50 


Fig.  311. 


946 


APPENDIX  C. 


APPENDIX  C. 


*i 


f 


t 


very  readily  done,  but  a  pretty  high  average  velocity  could  be  safely 
used,  from  the  fact  that  it  in  any  case  could  not  exceed  a  certain  maxi- 
mum. Again,  when  necessity  required,  it  was  easy  to  stop  cars  at  any 
point. 

Analogous  advantages  are  readily  obtainable,  mutatis  mutandis,  by 
switchbacks  operated  by  regular  trains  running  in  both  directions,  but 
not  under  the  conditions  of  ordinary  practice,  which  necessitates  the 
complete  loss  of  all  the  vis  viva  of  the  train  at  every  switch.  The  plan 
shown  in  Figs.  312  and  313  will  apparently  obviate  this  necessity  com- 
pletely, and  introduce  no  new  elements  liable  to  cause  difficulty,  but,  on 
the  contrary,  give  smooth,  easy,  and  rapid  motion.  The  details  of  this 
plan  are  as  follows  : 

As  Respects  the  Switches. — The  switches  should  be,  and  are  easily 
made,  entirely  automatic.  Their  normal  position  should  be  that  in  Fig. 
312,  in  position  for  running  up  hill,  and  not  down  hill.  A  runaway  train 
or  car  cannot  then  pass  a  switch  and  continue  down  grade.  As  respects 
a  train  going  up  grade,  this  arrangement  presents  no  difficulty.  It  may 
simply  run  through  the  switch  D,  springing  the  points  over  to  let  the 
wheels  pass.  Simple  devices  of  many  different  forms  may  be  used  to 
restrain  too  rapid  return  of  the  points  after  the  passage  of  each  single 
wheel,  but  this  is  not  essential,  as  the  wear  and  tear  would  be  small. 

The  mechanism  here  outlined  acts  as  follows: 

Down  Trains. —  A 
places  B  and  C  in  position 
to  act,  which  are  otherwise 
entirely  inop>erative. 

iff,  when  first  made  op- 
erative by  A^  opens  the 
switch  D  for  track  C,  and 
holds  it  open. 

C,  always  operative 
when  B  is,  returns  A^  B, 
and  D  to  their  original  positions. 

A,  By  and  C  are  supposed  to  be  located  with  reference  to  having  the  engine  always  at 
the  same  end  of  the  train.  If  the  engine  be  at  the  other  ends  the  switches  must  be  oper- 
ated by  hand. 

Up  Trains. — If,  by  carelessness,  the  engineer  of  an  up  train  should  leave  the  switch- 
actuating  lever  down,  nothing  will  happen  except  to  set  ^  as  if  for  a  down  train,  in  leav- 
ing the  switchback.  This  will  not  afiFect  following  trains,  either  down  or  up.  Should  a 
succeeding  up  train  be  equally  careless,  it  will  act  first  on  C  and  then  on  A^  thus  running 
through  the  switch  with  no  effect, 

A  train  descending  should  be  able  to  operate  the  switch,  so  as  to  con- 
tinue descent,  by  a  single  act  of  the  engineer,  but  only  by  intention  on 


947 


^P 


Fig.  3x8. — Mechanism  for  Automatically  Operating  the 
Switches  of  Switchbacks. 


■\ 


o 


his  part.     This  may  be  accomplished  by  a  very  simple  and  inexpensive 
apparatus,  such  as  that  outlined  in  Fig.  312.  operated  by  a  lever  or  idler 
wheel    on    the    locomotive    controlled    by   the    engineman,   and   with 
mechanism  somewhat  similar  to  that 
of  the  simpler  forms  of  interlocking 
apparatus,  which  it  would  be  super- 
fluous to  describe  in  detail,  as  it  can 
be  designed  in  a  few  hours  by  any 
signal  engineer.    The  general  meth- 
od of  operation  is  described  beside 
Fig.  312,  the  whole  insuring  that  (i) 
up    trains    shall     always    pass    the 
switches  freely  and  automatically;  (2) 
that    runaway    down     trains    shall 
never   pass  them,  but    be   caught ; 
<3)  that  regular  down  trains  shall  be 
enabled  to  pass  the  switches  auto- 
matically by  a  single  act  of  the  en- 
gineer; (4)  that  careless  neglect  of 
this  act  shall  do  no  other  harm  than 

to  cause  the  train  to  run  back  again 

on   the  up  track;    (5)   that  danger 

signals  shall  be  set  when  the  switches 

are  wrong,  or  any  part  of  the  appa- 
ratus broken;  (6)  that  the  switches 

can  at  all  times  be  operated  by  hand 

if  desired,  or  if  the  mechanism  is  out 

of  order. 

As  respects  the  Adjustment  of  the 

Crades.—F\g.   313    shows   in    detail 

what  the  writer  regards  as  the  proper 

adjustment  of  grades  for  a  2  percent 

switchback,  and  the  principle  of  the 

adjustment    for    any    grade.     With 

this  arrangement  it  is  unnecessary 

for  an  up  train  to  use  brakes,  or  even 

shut  off  steam  at  all,  for  making  the 

stop  and  then  starting  backwards. 

It  will  be  seen  that  the  up  grade  continues  unbroken  until  it  has 

passed  the  switch  and  then  rises  in  a  sharp  vertical  curve,  which  rises 


r 
I- 

5   J 


u»— 


. 


948 


APPENDIX  C. 


above  the  regular  grade,  slowly  at  first,  and  at  the  further  end— merely 
as  a  precaution  against  accidents— rises  very  rapidly  indeed.  This  is  to- 
bring  the  train  to  a  stop  slowly  and  gradually,  but  certainly,  without 
either  shutting  off  steam  or  using  brakes.  The  rise  necessary  to  do  this, 
for  any  given  train-speed  may  be  computed  exactly,  and  is  given  in  Table 
•.  i8  of  this  volume. 

Suppose  a  train  to  be  ascending  the  2  per  cent  grade  at  a  uniform 
Gpeed  of  15  miles  per  hour.  Then,  by  the  table,  a  lift  of  7.99  ft.  above 
the  regular  grade  will  bring  it  to  a  stop  even  with  the  engine  still  using 
steam.  If  the  velocity  be  only  10  miles  per  hour,  a  lift  of  3.55  ft.  only 
will  be  necessary,  and  this  will  or  can  readily  be  made  to  be  the  usual 
speed  of  approach.  In  that  case,  if  the  train  consist  of  10  cars  and  be 
400  ft.  long,  it  will  come  to  rest  with  the  steam  still  on,  unchanged,  when 
the  rear  of  the  train  has  passed  a  little  over  100  ft.  past  the  switch,  the 
centre  of  gravity  of  the  train  being  then  3.55  ft.  above  the  tangent  grade- 
line.  The  slack  of  the  train  will  be  taken  out,  under  these  conditions, 
very  gradually  indeed,  and  almost  at  the  instant  of  coming  to  rest. 

If,  then,  without  changing  the  throttle,  the  reverse  lever  be  thrown 
over  into  back  gear,  or  even  merely  into  mid-gear,  so  as  to  do  no  work 
at  all,  the  train  will  immediately  start  backward,  still  holding  all  tlie  slack 
out  of  the  train,  which  will  continue  out  until  forward  motion  is  resumed 
at  the  next  switchback.  If  the  lever  were  immediately  placed  in  the 
same  notch  of  back  gear  in  which  it  formerly  stood  in  forward  gear  (which 
would  be  unnecessary)  the  speed  which  the  train  would  have  acquired  on 
resuming  the  upper  straight  grade  at  T,  Fig.  313,  would  be  that  due  to 
the  height  c,  which  is  3.55  +(8x4)=  35.55  ft.,  or.  as  per  Table  118,  31^ 
miles  per  hour,  an  objectionably  high,  but  not  dangerous,  speed.  Had 
the  velocity  of  approach  from  below  been  15  miles,  this  speed  would  have 
been  that  due  to  37.99  ft.  or  only  32^  miles  per  hour,  and  had  the  velocity 
of  approach  (in  case  of  passenger  trains)  been  even  20  or  25  miles,  this 
speed  would  have  been  only  36  or  39  miles  per  hour.  Thus  the  switch, 
with  grades  arranged  as  shown,  can  be  run  through  at  any  speed,  making 
no  more  change  in  the  brakes,  steam  or  engine,  than  to  throw  over  the 
reverse  lever,  at  the  moment  the  train  comes  to  a  stop,  from  full  gear  for- 
ward to  full  gear  back. 

With  ordinarily  careful  and  safe  working,  the  speed  at  T,  Fig.  313, 
would  be  about  10  miles  per  hour  higher  than  the  speed  of  approach, 
a  gain  far  more  than  sufficient  to  obviate  all  loss  of  time  from  the  stop, 
and  equivalent  (for  speeds  of  10  miles  per  hour  approaching  and  10  miles 
leaving)  to  a  subtraction  of  10.65  vertical  feet  from  the  rise  in  the  next 


APPENDIX  C, 


949 


t?rade-a  gain  which  will  considerably  increase  the  average  speed  or  haul- 
ing  capacity,  or  both.* 

Fig  313  equally  well  represents  the  conditions  at  the  next  ensuing 
switchback,  where  the  train  approaches  rear-end  to  it,  if  we  simply  as- 
sun^e  the  engine  to  be  at  the  other  end  of  the  train.  It  reaches  the  po- 
sition shown,  backing  up  from  below,  with  all  slack  out  of  the  train  In 
starting  forward  on  the  up  grade,  the  rear  end  of  the  train,  being  on  a 
steeper  grade  than  the  engine,  will  tend  to  crowd  slightly  upon  it,  and  by 
setting  the  reverse  lever  in  the  second  or  third  notch  of  forward  gear 
the  slack  will  be  taken  out  in  the  gentlest  possible  way,  far  more  gently 
than  IS  ever  possible  in  starting  on  a  level. 

Thus  the  ordinary  and  great  objections  to  sharp  hollows  in  grade-lines 
do  not  apply  in  this  case.  On  the  contrary,  the  action  is  smoother  than 
It  would  be  without  the  curved  profile.  Similarly,  the  still  greater  ob- 
jections to  a  stop  on  the  grade-line  do  not  apply  at  all  in  this  case.  We 
rather  gain  by  it,  because  the  whole  train  stops  and  starts  again  with  the 
gentleness  and  economy  of  energy  of  a  pendulum,  for  identical  mechan- 
ical reasons. 

Tiiis  being  so,-there  being  no  loss  of  time,  no  loss  of  distance,  no  loss 
of  hauling  capacity,  and  no  measurable  loss  in  smoothness  of  motion  - 
we  have  left  as  a  net  gain  two  things:  First.  A  great  additional  safe- 
guard against  collisions  with  and  derailments  of  runaway  trains  or  parts 
of  trams.  Accidents  resembling  the  terrible  one  on  the  Southern  Pacific 
on  the  Tehachapi  grade,  some  years  ago,  in  which  nearly  all  of  a  train- 
Ivad  of  people  were  killed  or  injured,  are  not  likely  to  occur.  Before  a 
train  can  attain  a  velocity  of  60  or  70  miles  per  hour  it  must  fall  128  or 
174  feet  in  excess  of  the  fall  required  to  overcome  its  resistance.  If  we 
•estimate   its  average  resistance  in  acquiring  that  speed   at  20  lbs.  per 


*  If  the  train  were  running:  up  a  straight  grade  LOT  at  15  miles  per  hour 

•<say  22  feet  per  second)  in  ^  =  18.2  seconds. 

22 
J^ia  the  switchback  it  takes: 

O  to  stop,  800  feet  at  average  speed  of  about  ^±^  =  48.5  seconds. 


Stop  to  T,  1200         *« 


0+37 

91.8 


t€ 


Loss  of  time,  as  nearly  as  may  be,  i^  minutes. 
The  train  is  then  moving  10  miles  per  hour  faster,  so  that  it  will  save  this 
lost  time  almost  within  the  next  mile. 


!  " 


1  f: 


h:\ 


I  :'1 


950 


APPENDIX  C. 


I 


I 


ton,  equivalent  to  the  acceleration  on  a  i  per  cent  grade,  a  train  must  de- 
scend a  2  per  cent  grade  for  2i  to  3^  miles  before  it  will  acquire  those 
velocities.  A  single  car  would  take  much  longer  yet,  so  that  a  switch- 
back every  3  or  4  miles  would  go  far  to  insure  against  the  worst  results 
from  such  catastrophes,  which  no  care  can  wholly  avoid. 

Second.  A  great  reduction  in  cost  of  construction  and  amount  of 
curvature,  and  usually  in  rate  of  gradient  as  well,  is  assured  ;  in  some 
cases  more  than  others,  but  always  considerable.  In  the  line  described 
in  this  paper,  the  writer  estimates  that  half  the  curvature,  and  nearly  half 
the  cost  of  construction  to  sub-grade,  might  have  been  saved  by  usin^- 
not  more  than  eight  or  ten  switchbacks  on  the  whole  ascent  of  8000 
feet,  through  the  better  choice  of  ground  afforded.  An  entirely  different 
route  would  have  been  selected,  and  nearly  the  whole  line  might  have 
been  reduced  to  but  little  more  than  a  surface  line. 

On  the  other  hand,  there  is  the  unquestionable  disadvantage  in 
switchbacks,  that  engines  do  not  pass  curves  well  running  backward.  In 
part  this  is  remediaWe  in  the  design  of  engines,  and  by  leaving  the  rear 
drivers  blind,  but  the  only  proper  course  would  be  to  use  an  easier  maxi- 
mum curve  on  the  sections  on  which  the  engine  runs  backward,  which 
would  be  the  same  both  ascending  and  descending,  and  to  make  those 
sections  as  short  as  possible. 

Thus,  the  writer  believes,  this  objection,  while  it  cannot  be  entirely 
removed,  may  be  reduced  to  very  small  dimensions  ;  and  should  it  again 
fall  to  his  lot  to  locate  a  line  of  railway  upon  an  ascent  of  8000  vertical 
feet,  or  even  a  half  or  a  quarter — or,  possibly,  even  an  eighth — of  th^t 
amount,  he  will  in  no  case  willingly  attempt  to  locate  it  for  an  unbroken 
locomotive  run,  but  either  use  switchbacks  for  a  light  traffic,  or  study 
with  great  care  the  possibilities  of  the  locality  for  inclined  planes  with  a 
heavy  traffic. 


INDEX. 


INDEX. 


r 


References  to  tabular  matter  are  indicated  by  *  and  references  to  many  of  the  more 
important  conclusions  for  immediate  application  are  in  small  CAPITALS. 

To  save  space,  many  page  references  are  marked  thus- 
500 +.  meaning  ''Page  500,  and  following  pages  not  in  the  immediate  context." 
^1  I' Page  500.  and  preceding  pages  not  in  the  immediate  context." 

"  Page  500,  and  pages  both  preceding  and  following  not  in  the  imme- 
diate  context." 

"Page  500,  and  in  various  other  places  throughout  the  volume  to 
which  more  specific  reference  under  this  head  did  not  seem  con- 
venient or  expedient.     See  elsewhere." 

q.v.  (which  see)  has  been  used  in  many  cases  for  giving  cross-references,  as  most 
economical  of  space. 

Because  there  are  many  cross-references  it  must  not  be  assumed  that  they  always  exist. 


500 -, 
500  ±, 

500  &, 


il 


Aba— Agr 

Abandonment  of  old  work,  786 
of  schedule  trains,  102 

Abraswn,  rails,  q.v.,  as  affected 
theory  of,  562  [by  speed,  561 
rate,  iron  and  steel,  320 

Abt  rack  railway,  descr.,etc.,  6<)i, 

Abutments,  prelim,  ests.,  899  [932 
pile,  770 

Acceleration  of  gravity,laws,33r-3 

of  trains  on  grades,  342,  346-56 

{See  Virtual  Profile^  etc.) 

Accidents  as  affected  by  curv,,  245 

by  (Trades,  598,  949 

by  handling  locos,  359 

[900 
by  re-railing  bridge  g'ds, 
by  superelevation,  300 
marvellously  few,  257 

Adams,  C.  F.,  as  to,  252-7 
p.  c.  pass,  and  ft.  trains,  *248 
p.  c.  sum'r  and  winter,  *249-56 
train,  13  years,  *246 

east  and  west  of  Ohio.  252 
Accuracy  and  precision,  863  4- 

instrumental,  not  an  end,  865 
Adams,  C.  F.,  on  accidents,  252-7 
Adhesion,  ratio  of,  436,  532,  551, 
Adiabatic  curve,  469  [598  & 

Admission,  period  of,  def.,  458  -f- 
Advertising  and  agts,  cost,  full  de- 
by  easy  curves,276  [tails,*i72-6 
by  maint.  way,  124 
by  route,  charac.  of,  683 
Africa,  railways  of.  ♦43 

rolling  slopes  in,  844         [*203 

Age,  effect  on  car  and  eng.  repairs. 

Agents    &    station    service,  cost, 

[full  details,  *x-j2-6 

Agricultural  regions,  traffic  from, 

exception,  618  [618  1 


Ain— Ane 

Ainsworth,  D.  H..  on  location,  n 
Air-brakes,  q.v.,  effect  on  sp'd,  370 
Air  resistance,  amount,  911 
.,  .        knowledge  as  to,  513 
Alabama,  area,  populat'n,  sidings, 
per  cent  op'gexp.,  earnings  per 
mile  and  head,  *9o;  wealth  per 
cap.,  *26 
Albany  &  Susq.,  align.  statist.,*259 
Alignments,  comparing  minor  de- 
Itails  and  grades,  581 

WHEN  NEARLY  EQUAL,  583 

crooked,  and  safety,  252 

{See  Curvature.) 

indicating  on  profiles,  862 

States  and  rys.  U.  S..  *259 

{See  Curvature  Grades.) 

Alleghanies,  Altoona  pass.,  936. 

planes  on,  687,  699,  944 
Allegheny  river,  fall,  841 
Allegheny  Valley  Ry.,  p.  c.  switch 
Alliteration  of  6%  656  [miles,  *i8i 
A  mazon,  P.  &  Mex.  Ry.,  930 
Alsace-Lorraine,  cost  rys..  etc.,*45 
Altazimuth,  use  of,  847,  881-2 
Altoona,  car  movement  at,  609 
grades  at,  618 
pass  at,  936 
pusher  service  at.  595 
shops  opened,  141 
Amcca  River,  descent  into,  682 
America,  railways  of,  *42-3  & 
American  line,V.C.  to  Mexico,  925 
loco.,  gv.,  weights,  etc.,  V? 
American  C.  ry.,  align't  staUst., 

1*262 
Ames  car-coupler,  489 
Andes  and  rough  country,  840 

summits  in.  698-9 
Aneroid,  use  of,  838,  877 


Ang-Ass 

Angles,  eye  exdggerates,  84a  -f- 

plotting,  886 
Anthracite,  effect  on  fire-box, ♦419 

lump  of,  449 

N.Y.  supply  and  distance,  710 
traffic  west,  609,  615 
Apennine  railways,  profile,  698 
Apex  distance,  det'g  diffs.  in,  *644 
Arbitranes.'  nature  of,  156,  218 

examples,  219,  820 
Arbitration  and  interl'k'g,  812  4- 
Arc,  mental,  striking.  839 
Area,  miles  ry.  for.  world,  *43  & 
Arizona:  area,  pop'n,  sidings,  p. 
c.  op^g  exp.,  earnings  per  mile 
and  head,  *9o;  wealth  per  cap.. 
'26 

Arkansas:  area,  pop'n,  sidings,  p. 
c.  op  g  exp.,  earnings  per  mile 
and  head,  *9o;  wealth  per  cap., 

Arkansas  river,  fall,  841 
Art  and  science,  831 
Ash-pan,  loco.,  g.7>.,  wt.,  *axa 
Asia,  railways  of,  +43 

rolling  slopes  in,  844 
Asphalt,  H.  U.  in,  *45o 
Assistant  engines,  585 

and  low  grades,  590,  650 
cost  of,  601  ^^ 

and  train  wages,  671 
how  to  estimate,  604 
interest  charge,  604 
duty  of,  598 -f-  ^ 

and  lighi  traffic,  599 
separate  engs.  necessary, 

for  passenger  service,  5a« 

example,  607 
grades  for,  591 


.j,i 
^1^ 


95- 


INDEX. 


INDEX. 


95S 


i 


Ass— Bac 

Assistant  engines— C<7«//««r«/. 

GRADES,  BALANCE  OF,  593  — 

example,  604  + 
companng  with  uniform 
[grade,  604  + 
curve  comp'n  for,  598 
projecting,  high,  669 

low,  596,  666 
as  aff'd   by  length  gr., 
[618-9 
duplicate  tracks,  691 
temporary  grades,  766 
vrhen  wrong  to    reduce, 
<4d  lines,  introd^  on,  788  [671 

CONCLUSION  AS  TO,  8o8 

operating  at  yards  and  sta'ns, 
block  signals  for,  601  [599 
cutting  trains  in  two,  599 
power  of,  491 

best  wt.,  597 
tank  engines  as,  593 
without  stopping  t'ns,  792 
presumpt'ely  always  adv.,  586 
two  or  three  rarely  advisab., 
work  with  nature,  589    [669  & 
Assistants,  discred'g  rep's  of,  836 
Atchison,  T.  &  S.  F.  Ry.,  fluct. 
[in  stocks,  ^46 
jOco.  performance.  *439-4i 

.  "Uncle  Dick"  loco.,  421 
miles  and  earnings,  ♦719 
sharp  curves  on,  279 
Atkinson,  E.,  forecast  of  ry.  con- 
[struction,*4i 
Atlantic  &  Gt.    W    as  Erie  con- 

[nection,  730 
loc'n  at  Springfield,  O.,  56 
strategic  disadvantage  ot,  222. 
{See  New  York.  P.  &  O.) 
Atlantic,  M.  &  O.  Ry.,  alignm't 
[statist.,  ^264 
Atlanta  &  W.  Pt.  Ry.,  loc.  per- 
[formance,  *439 
Australia,  Am.  Iocs,  in,  423 

pop'n.  railways,  wealth,  etc., 
rolling  slopes  in,  844  [*27,  *43 
Austria,  bridges,  wt.  of,  767 

locos.,  no.  and  work  of,  *i6o 
pop'n,  r'ys,  wealth,  etc.,  ^27, 

[*43.  *45 

rolling-s  k  and  tiaflric,  etc..  ^43 

receipts  per  inhab't  pass,  and 

[frt.,  ♦105 

Austrian   N.  W.  Ry.,  lub'n  tests. 

Automatic  brakes,  q.7>.,  488      [516 

couplers,  q.v.,  488-9 
Axiom  as  to  location,  660 
Axles,  accidents  from,  *246 
car,  cost  and  deprec'n,  ^204 
maint.  of,  *i63 
w't  of.  ♦lej 
size  of  M.C.B.,  ^13 
effect,  on  fric,  513 
French,  521 
loco.,  life  of,  *43o 

w't  and  cost,  ♦412  -f- 
radiating,  possible  effect,  283 
Axle-boxes,    loc.    w't    and    cost, 

[♦413  + 
Axle-friction,  q.v.,  and  rolling,  515 
better  lub'n  needed,  509  -f- 
comp've  cocflE.,  512  ± 

Babbitt  metal  in  loc.,  *4i2-4 
Backing  locos,  q,7>.,  950 
Backing  up  in  loc'n,  865-6 


Bac-Bel 

Back  pressure,  locos.,  q.v.^  47a 
Baden,  cost  rys.,  etc.,  ♦45 
*'  Bad  times"  and  ry.  const.,  763  & 
Baggage  cars,  q.v.^  dimen's,  etc., 

1*491 
Balance  of  grades,  q.v.,  593.  608 
traffic,  q.v.^  flucts.  in,  lot 
slide-valve,  q.v.^  532 
Baldwin  Loco.  Wk's  and  Consol. 
catalogue,  422  [cn^M  ^78 

computing  cap'y  of  Iocs.,  442 
Decapod  loc..  det'ls,  *4io 
loco,  cost,  comp.  all  sires,*564 
narrow-gauge,  *564-5 
per  ton,  ^ii 
dimens.,  etc.,  •408 
fast  pass.,  421 
performance  table,  ♦438 
test  of,  •461  + 
wt.  of,  incr.  13  yrs.,  *466 
on  drivers  per  sq.  ft.. 
Ballast,  cost  of,  773      [grate,  •452 
various  roads,  ♦120 
economy  of,  772 
imp'i  in  practice,  114 
lining  with  string,  124,  277 
Ballast  trains,  handling  of,  773 
Baltimore  &  O.  rd.,  cars,  heaviest, 
wheels  on,  486,  513       [490 
curves,  sharpest,  278,  325 

Y  on, 279 
fastest  train,  *529 
flucts.  in  stock.  ^46 
history    and    causes  success, 
inundations  on,  783  [730 

location,    Allegheny    incline, 
balance  of  grds.,  618  [^699 
for  pushers,  585 
profile,  condensed,  698 
temp'y  lines,  '700 
loco,  boiler  pres.,  *4o8 

cost  and  miles  pr.  y.,  'isg 
mogul,  dimens.  etc.,  ♦408 
maint'ce  exps.,  34  yrs.,  *i29 
miles  and  earnings,  *7i9 
opg.  exp.  and  trains  per  day, 
p  c.  opg.  exp.,  ♦no  [*i72 

why  low.  no 
per  train-mile,  cost,  ♦n6 
train-load,  frt.  and  pass,  *2t7 
Bankrupt    lines,    pass    far  from 

[towns,  68  & 
never  from  curves.  655 
Bar-iron,  past  prices  of,  763 
Barranca,  def.,  928 
Blanca,  spiral,  678 
Zimilahuacan.  942 
Barometer,  use  of,  838,  847 
Basaltic  lava,  684 

river  of,  928 
Bath  lubrication,  q.v.,  eff'y,  509 
Bavaria,  cost  rys.,  etc.,  *4S 

fJange-fric.  tests,  516 
Beams,  comp've  strength,  742 
stiffness,  740 
Bearings,  compass, 

for  taking  off  paper  loc'n, 

for  transit  work,  888    [893 

use  always  for  map'g.  886 

loco.,  q.v.^  lire  of,  420      r*i6o 

Belgium  locos.,  no.  and  work  of, 

popu.,  rys.,  wealth,  etc.,  *27, 

l*43»  *45 
rolling-stock,  traffic,  etc..  ^43 
Bell,  loco.,  cost,  ^is  [♦262 

Belleville  &  E.  rd.,  align't  statist., 


Bho— Bra 

Bhore  Ghaut  incline,  *699 
Birmingham, Eng.,  stat'n  exp.  at, 
Bissell  truck,  q.v.,  430  &  [828 

Blackmail,  r'ys  built  to,  14 
Blast-nozzle,  sfze,  '409 
Block-signals,  interl'g,  q.v.^  and 
[assist,  engs.,  6ot 
Blue  Ridge  rd.,  60  ft.  &  6"  comb'n, 
'  Bogie'  truck,  q.v.,  421  [656 

Boiler,  loco.,  q.v.^  449 

cost  new,  details,  *i5o-s 
explosions,  ♦247 
life  of,  *4i9 

pres..  effect  increas'g,  401 
repairs,  details,  *i46 
English,  *i44 
.  p.  c.  due  to  various 
[causes,  *203 
and  minor  det'ls,  »i49 
water  in,  wt.,  *4oo  & 
marine,  efficiency,  *456-7 
Bonds  and  stock  per  mile,  sect'ns 
building  on,  30        [U.S.,  *xo^ 
nature  of.  29 
^  Boom'  and  inception  of  rys.,34  & 

and  prices,  763 
Boot,  on  Mex.  ry.,  *699 
Boreas  summit,  descent  from,  696 
Boring  tools,  868,  893 
Borrowed  money,  intox'g  eff't,  34 
Bosnia,  cost  r'ys,  etc.,  ^s 
Boston — N.  Y.  traf.,  loss  bydist., 
side  track  at,  823  [709 

train-speed  to,  650 
Boston  &  Albany  rd.,  alignment 
[statist.,  ♦259 
curve  comp'n  on,  621 


flucts.  in  stock,  ^46 


[•'59 


locos.,  cost  and  miles  i»er  yr,, 
fast  pass.,  wt..  etc.,  421 
slide-valve  tests,  532 
tubes  in,  *42o 
op'g  exp.  and  trains  per  day, 
rates,  fall  of,  ♦726  [*i72 

sidings  on,  ^825 
ton-mile  rect's,  etc.,  'ns 
train-load,  frt.  and  pass.,  *2i7 
growth  of,  •100 
Boston   &  Lowell,  Iocs,  cost  and 
[miles  per  year,  *iS9 
p.  c.  switching-miles,  *i8i 
Boston  &  Maine,  locos.,  cost  and 

[duty.  *i5» 

Boston  &  Prov.,  locos.,  cost  and 

washouts  on,  781     [duty,  *i59 

Bottom    lands  and    high   water, 

[850  & 
Bound  Brook  line,  fuel  tests,  528 
Box  cars,  q.v.,  dimensions,  etc., 
60,000  lb.  st'd.  ^490        [*486-7 
Box  culverts,  q.v.,  wooden,  755 
Brake-gear,  accidents  from,  '246 
Brakes,  automatic,  cost  new,  ♦is* 
effect  on  speed.  370 
gain  from,  804  & 
cost  of,  deprec'n,  *204 
destructive  to  wheels.  377 

extent  of  do.,^3i8 
efficiency  of,  average,  494 
coefr.  fric.  of,  290 
computing,  33^1  494 
maximum,  495 
on  caboose,  359 
waste  of  power  by,  691 

examples,  337-343  \yi}~^ 
when  needed  on  grades. 


Bra-Bui 

Brakes — Continued. 

hand,  and  low  speed,  268 
Branches,  rjr.,  731,  51 

av.  earnings,  732 

early  building  bad,  764 

for  defence,  718 

pass,  traff.  of,  734  [732 

reason  for  great  increase  of, 

PROJECTING,    UNIV'L   RULE    for, 

SECOND,  do.,  734         [733 
to  develop  territory,  735 
Brasses,  car,  maint.  of,  ♦162  & 
locos.,  q.v..   wt.,   etc..  ♦150, 

[♦412  & 
Breckenridge,  Col.,  loc'n  at,  695 -f- 
Brenner,  ry.  profile,  698-9 
British  ry.  dividends,  ^41 

operating  expenses,  *i78 
{See  Great  Britain,  etc.) 
Bridge-building,  cause  of  prog,  in. 
Bridges,  accidents  from,  ♦247     [3 
cost  new  per  lb..  905 

asaff.  by  rolling  Id.,  7674- 
draw,  weight  of,  905 
erecting,  cost,  905 

all  spans  but  one,  68 
floor  of,  900,  904 
heaviest  car-loads,  *49o 
maint.,  cost  of  U.S.,^i2o,  *i28, 
prelim,  esis.  of,  003       [♦172-6 
rerailingguard  tor,  900 
rolling  load,  767  -|-,  490 
types  of.  for  var.  spans,  904 
vibration  of,  447 
weight  of,  903 

as  aff.  by  depth,  ^904 

by  rolling  I'd,  ♦767-72 
by  span,  ♦767-71 
by  st'l  or  iron,  ♦767-71 
double  track,  765 
draw,  905 
formulae  for.  903 
light,  save  little,  765 
on  narrow-g.,  752 
width  of,  904 
Bridge  piers,  prelim,  ests.,  898 

pile,  770 
Bridge  spiral,  q.v.,  678-9,  681 
Bridging,  p.  c  cost  to  total.  ^757 
Broad  St.  station,  Phila.,traffic,  69 
'  Broken-back '  curves.  870 
Brooklyn,    B.   &   C.    L.  sharpest 

[curve,  325 
Brooks,  rate  of  fall  of,  840  & 
Brooks  Loc.  Works.,  loc.  dimen- 
[sions,  etc.,  ^407-8 
load  on  drivers  per  sq.  ft. 
[grate,  ^452 
Brunswick  &  Ch.  rd.,  alignment 
[statistics,  ^264 
Buffalo,  greatest  yd.  in  world,  822 
inundations  at,  783 
miles  of  sidings  in,  ^821 
Buffalo  Creek  rd.,  side  tracks,  ♦821 
Buffalo,  N.  Y.  &  Phila..  alignment 
[statistics,  ♦259 
sidings,  Buffalo  yd.,  ^821 

total,  ^825 
loco,  perf'ce,  ♦458 
Building,  const'n  of,  and  surveys, 
on  bonds.  30  [856 

what  is  built  well,  655 
Buildings  (houses),  U.  S 

ry.  cost  new,  p.  c.  tototal.^757 


Bul— Car 

Bulgaria,  cost  rys.,  etc.,  ^45 
Bunching,  curvature,  q.v..,  655 

grades,  q.v.,  587  & 
Burlington,  la.,  brake  tests,  496  & 

slack  tests,  489 

train-res.  tests,  496 
Burlington   &   S.  W.,  alignment 
[statist.,  ^262-4 
Burlington, C.  R.  &N.,  do.,  ♦262-4 
Burr,  J.  D.,  paper  by,  279 
Burnettizing  cross-ties,  q.v..,  124 

Cable  traction,  merits  of,  686,  944 
modern,  origin  of,  689 
passing  summits  by,  689 

Caboose  brakes  set,  359 
dimensions,  etc.,  ^486-7 

Caledonian  ry.  locos.,  cost    and 


&    [*25 
value. 


maint.  various 


rds.,  •120 
[♦170-6 


[duty,  ♦isg 

int'l  rad'n  tests,  4:72 

'California:  area,  pop'n,  sid'gs,  p.c. 

of  op'g  exp..  earn'gs  p.  mile  and 

head,  ♦90;  wealth  per  cap.,  ^26 

Calumet  mine  bch.  (8^  gr.),  ^700 

Camden  &  Atl.  rd.,  wheel-wear 

[on,  ♦287-8 
Camp  outfit  for  loc'n,  q.v.,  867 
Canada,  Am.  Iocs  in,  422 

bonds  and  stock  per  m.,  ^107 
earnings  per  m.,  ♦107 
growth  rys.,  ^424 
pop'n.  rys.,  wealth,  etc.,  ^27 
ry.  subsidies  by  govt.,  ^107 
Canada  Southern  ry.,  align't,  and 
[Huds.  R.,  328 
branches,  money  spent  on,  764 
earn'gs  and  length,  ^719 

per  mile,  ^107 

flucts.  in  stock,  ^46 

nature    of    traffic,  local    and 

[through,  214 

train-load  growth,  ♦loo 

{See  Michigan  Central.) 

Canadian  Pac.  ry.,  length  of  divs., 

rolling-stock  per  m.,  ^47    [169 

Canals,  U.  S.  value,  ^25  [^325 

Canarsie  &  Rock'y.  sharp' t  curve, 

Carbon,  H.  U.  in,  ^450  [dents,  254 

Carelessness,   as  cause    of    acci- 

Cant  (superelev..  q.v\  271 

Cape   Government,  roll'g-st'k  p. 

[mile,  ^47 
Capital,  floating,  U.  S.,  amt.,  ^25 
in  rys.  of  world,  ♦27,^43  & 
made  less  by  bad  loc'n,  60 
return  on  Am.  rys.,  ^41 
English  rys.,  ♦41,  ^79 
Capital  acct.,  danger  of  increas- 
[ing.  113,  654 
distrib'n  of,  ^71  & 
Car-Builders'  Dictionary,  491 
Car,  falling,  ex.  of  grav.,  342 
Car-couplers,  aut.,  and  speed,  804 
pass.,   why    easily   intro- 
[duced,489 
probabilities  as  to  frt..  488 
types,  two  distinct,  489 
bad,  impede  long  trains,  566 
Car  (^.r.)  mile,  fuel.  P.  R.  R.,^i4o 
Carpets  falling   over,   accidents, 
Carr's  Rock  disaster,  255         [258 
Cars  and  rail- wear,  122 

capacity  of,  increase,  485,  ii4i 

effect  on  exp.,  485     [135 

on    car     constr.     and 

[sp'd,  370 


Car-Car 

Cars — Continued. 

capacity  of.  effect  of  narrow 
[gauge  on.  485,  752 
transition  state  of,  487 
classes  of,  fr't,  486  -|- 
pass.,  491 
side-dump,  774 
cost  of  maintenance,  160-7 
as  affected  by  additions, 
age,  162  [»66 

M.  C.  B.  rule,  205 
curvature,  319 
radius  of,  641 
distance,  201-4 
growth  of  traffic,  i66 
high  mileage,  162 
local  service,  162 
rise  and  f.,  377 
train  length,  570 
average  cost  of,  160 
per  cent,  details,  full,  frt., 
pass.,  167  [♦161-4 

bodies  and  trucks  sepa- 
[rate,  ^164 
pass.,outsideand  inside, 
[204 
distrib'n  to  causes,  ^203 

TO  VARIOUS   PARTS,  167 

Chicago  rds.,  ♦174-6 
sections,  U.  S. ,♦170-6' 
trunk  lines,  ♦172-6 
34  years,  129 
English,  ♦mS  & 
per  car  per  year,  ♦148 
cost  new,  163-4 

box  and  stock.  details,^204 
flat  and  coal  details,  ^205 
per  mile  N.  Y.  C,  ^71 
depreciation    of  (see  above), 

[162,  205 
varying  causes  for.  202 
dimensions  of  frt.,  all  classes. 


pass.,  ^491 


[486-7 


irreg'iies  in,  487 
European,  520  -\- 

and  Am   cross-sec,  522 
elev'd  ry..  646 
friction    of,    q.v.     (&     train 
[kes.),  501 
European,  ^283,  ^502 
invention  of  Am.  car,  421 
load  of,  cannot  be  full,  6ix 
E.  &  W.,^6o9-f 
how  to  est.  prob'le,  99 
mileage  of.  cost,  all  parts  U. 
frt.  cars,  161-2   [S.,  ♦170-6 
average,  168 
why  low,  165 
pass.,  168 

sleeping,  168  [^47  & 

number  per  mile,  world,  *43, 

riding  of.  and  curves,  275 

ht.  cent  of  grav.,  271 

ton-miles  per,  U.S.  sects.,  '97 

weight  of  frt.,  486-99        [♦49> 

extra    large    and    heavy, 

mat'ls,  separately,  ♦163, 

pass.,  451  [567 

WHY    GROW  HEAVIER,  I39 

Car  q.v.  springs,  compres'n  of, 272 
Car-wheels,  accidents  from,  ^246 

and  rail.  307,  516  & 

cost  and  depreciation  of,  *204. 
failures  on  for'n  rds.,  166 

cracks  and  breaks,  loc'n,  319 

maint.  of,  ^164 


jl 


i 


r 


956 


Car-Cha 

Car-wheels,  maint.  oi— Continued. 
causes  of  failure,  ♦ji; 
p.  c.  due  to  van  causes, 
^mileage  life  of,  319    [*203,*377 
as  affected  by  quality, *3i7 
lead'g  and  trail'g  wh  Is, 
[*288 
loco,  and  tend'r  trucks, 
[*288 
comparative  pass,  and  ft., 
•on  curves.  q.7>.,  282  [167 

as  pulleys,  302 
flange  wear,  308 
rotation,  energy  of,  334 
size  and  wt.  of,  *i63,  av.,  335 
42-in.,  513,  912 
French, 521 
U.  S.  standard,  ^Sd 
eflf't  on  train  r.,  513     [335 
p.  c.  wt.  to  total  oftrains, 
skidded,  fric,  g.v.,  *29o 
tread,  proper  form,  308 
errors  as  to,  307 
•Carting,  amt.  of,  and  ry.  traffic,  52 

cost  of,  820 
■Castings  in  locos.,  ^.w.,  ♦150  & 

prices  Am.  and  Eng.,*4i6,*763 
Cattle,  accidents  from,  *245,  ^247 
Cattle-guard,  plan  for,  770 
Caucasus  ry.  profile,  698 
Cement,  co.  should  furnish,  903  & 
Census  U.  S.,  defects  in,  *26i 

(Otherwise,  the  many  abstracts 
tnot  indexed.) 

Centre  of  gravity  of  cars,  271 
of  exchange  traflfic,  227 
of  trains  in  sags,  357-60 
of  two  towns,  67  [629  & 

Central  angle  and  curve  comp'n, 
Central  la.,  align't  statist.,  *262 
Central  N.  J.,  fastest  train,  *529 
fluct.  in  stock,  +46 
loco,  perform.,  *44o 
Central-rail  rys..  404 

{See  Rack.) 
Central  Vt.,  alignm't  statist.,  ♦259 

p.  c.  switching-miles,  *i8i 
Central   Pacif.,  alignm't  statist., 
fluct.  in  stock,  *^6  [*265 

loco.  "El  Gubernador,"  de- 


[tails, 


^ ,  '410 

Mastodon    loco.,    details, 

,      .        .  .       1*4^0.  *433 
load  on  drivers  pr.  sq.  ft. 
Mogul,  421       [grate,  *452 
miles  and  earnings,  *7i9 
mountain  grade,  *7oo 
Centrif.  force  on  curves,  g.z>.,  269 
common  error  as  to,  301 
effect  on  curve  resist.,  298 
position  wheels.  300 
safety,  300      [eflf't,  ♦273 
limits    of     objectionable 
lbs.  per  ton  var.  curves, 
of  counterwts.,  446    [etc.,*27o 
Ceylon,  long  grades  in,  *6go 

rolling-stock  per  mile,  *47 
Chain,   with  wheels,  and    curve 
Chains,  metric,  266  [res.,  303 

radii  by,  *266 -f 
Chairs  for  cross-ties,  English,  125 
Chances,  theory  of,  864  & 
Chanute,  O.,  on    loco,  adhesion, 
loco,  rail  wear,  123  [44- 

train  resist'ce,  518,  525     f*264 
Charlotte,  C.  &  A,  align't  statist.. 


INDEX, 


Cha-Chi 

Charlotte,  C.  &  A —Continued. 

maint.  wayexp.,  128 
Chattahoochee  River  fall,  841 
Cheap  lines,  a  priori  preferable,  18 

when  to  prefer,  583 
Cheat  River,  fall,  841  ['264 

Chesapeake  &  O.,  align't  statist., 
curve  comp'n  on,  621 
60  ft.  and  6*  comb'n,  656 
Chicago,  distances  to,  240 
grain  rec'ts,  728 
train  speed  to,  650 
rates  to  and  through,  218  & 
terminals,  loc'n  of,  72 
relative  size,  827 
Chicago    roads,    op'g    ex  p.    and 
[trains  per  day,  *i74 
train-Id.  growth,  *ioi 
rates,  fall  in  20  yrs,  *726 
Chic.  &  Alt'n,  align't  statist.,  *26« 
fluct.  in  stock,  *^6 
op'g  exp.  and  trains  per  day, 
rates,  fall  of,  *726  [*i74 

train-Id.  growth,  *ior 
Chic.  &  E.  111.,  align't  statist.,  ♦262 
Chic.  &  G.  T.,  align't  statist.,  ♦262 
Chic.  &  N.  W.  flucts.  in  stock,  *45 
furniture  car,  *49o 
miles  and  earnings,  *7i9 
op'g  exp.  and  trains  per  day, 
chart,  of,  etc.,  35        [+174 
rates,  fall  of,  *726 
train-Id.  growth,  *ioi 
Chic,  R.  I.  &  P.,  fluct.  in  stock,*46 
miles  and  earn'gs.  ♦719 
op'g  exp.  and  trains  per  day, 
rates,  fall  of,  *ji6  [*i74 

train-Id.  growth.  *ioi 
Chic.  &  Spr'fd,  align't  statist.,*26a 
Chic,  B.  C.  &  W.,  align't  statist., 

_^.  „  [*262 

Chic,  B.  &  p.,  align't  sutist.,*262 
dining-car,  *49i 
dynamom.  tests,  501 
fluct.  in  stock,  *46 
locos,  cost  new,  det'ls,  *iso-7 
p.  c  labor  and  mat'ls,*i52, 

A-  ■  *      t%i6 

dimensions,  etc..  *407 
Id.  drivers,  per  sq.   ft. 
[grate,  ♦452 


INDEX. 


957 


performance  of,  *44o 

wt.  and  cost,  det'ls,  ♦416 

tender  capacity,  standard, 

1*378 
miles  and  earnings,  *7i9 

motive-power  expenses,  157 

op'g  exp.  and  trains  per  day, 

rates,  fall  of,  •726  [•174 

traffic,  growth  of,  157 

train  and  brake  tests,  497  -j- 

water-supply  on,  *378 

Chic,  M.  &  St.  Paul,  alignment 

[statistics,  *262-3 

fluctuations  in  stock,  *^6 

miles  and  earnings,  ♦719 

op'g  exp.  and  trains  per  day. 


rates,  fall  of.  ♦726 


t*»74 


timber  structures  on,  770 

train-load  growth,  loi 
Chief  engineer  should   make  re- 
[connaissance,  23,  83a  & 

of  party,  duties,  867 
Child,  sense  of  distance.  844 
Chili,  loco,  performance  in,  ^sS 

railway  grade  in,  *699 


Chu-Col 

Churches  and  schools,  U.  S.  value 

Cincinnati,  Erie  business  to,  222*^ 

Cine,  H.  &  D..  align't  statist'.  *26i 

distance,  value  of,  2^1 

curve  comp'n  on,  621   6i:fi 

Cinc.,N.O.&Tex*.P.,l^o{esS 

So.    Ry..   pedest.iis  and  'via^ 

[viaducts,  cost,  etc.,  got 

60  ft.  and  e*-  comb'n,  656 

Cine,  N   O.  &  Tex.  P.  (Cine.  So  ). 

,.l*"8f""'*"^  statistics,  ♦264 

Cmc,  W.  &  Mich.,  align't  stat.* 

[•261 
Cities,  great,  to  nowhere,  731 

,  and  small,  traffic  of,  70 

Cities  often  in  hollows,  859 
party-wall  laws,  814 
terminal,  q.v.,  655  <fe 
traffic  of,  a.v.,  heavy  into,  617 

growth,  *7i4 
train  speed  between.  648-50 
Clark,  D.   K.,   on  adhesion  and 
.     .  [speed, 435 

train  resistance,  518,  528 
radiation,  int'l,  472 
^,    wire-drawing,  etc.,  474 
Classification  of  material,  and  con- 
[tour  maps,  877 
Clearance  spaces,  loco..  q.7>.,  472 
Clearing,  illusive  eflfect  from,  850 

p.  c,  cost  to  total,  *757 
Cleaning  locos.,  g.i>.,  cost,  *i47 
Cleveland,  Erie  business  to,  222 
Cieve'd  &  Mar.,align't  statist.*26i 
Clev'd   &.   Pitts.,  p.  c  switching- 
^.  ^  [miles,  *i8r 

Clev'd. ,C.,  C.&  I.,  align't  statist., 
p.  c.  switching-m.,  *i8i    [*26i 
rates,  through  and  way,  con- 
fstaiit  ratio,  224-5 
growth,  traffic,  *2i6         [♦214 
p.  c  local  traffic  and  thro', 
p.  c  various  classes.  *2i5 
tons  and  ton-miles,  E.  and 
[W.,  etc.,  *2i6 
train-load  growth,  •loi 
Clev'd,T.V.  &  W.,  align't  statist., 

[*26l 

Clev'd,  Mt.V.&  D.,align't  statist., 

[*26l 

Cluster-bent  trestles.  900 
Coal,  cost  per  ton,  U.  S.,  132 

lbs.  per  car  and  eng.  m.,  139  & 

{See  Fuel.) 
ship'ts  west,  economy  of,  135 
used  at  N.  Y.  terminals,  *8i9 
car,  ^.7'.,  extra  heavy,  ♦490 
trains,  operating,  *i32  &. 
Coatepec,  line  at,  937 
Coasting  and  ry.  accidents,  257 
Cocks,  loco.,  cost.  412 
Col  burn,  Z.,  loc.  tests,  437 
Collins,  C,  on  ditching,  773 
Collisions,  causes  of,  245 
Colorado:   area,  pop'n,  sidings,  p. 
c.  op'g  exp.,  earnings  per  mile 
and  head,  '90 ;  wealth  jier  cap., 

[♦26 
ditches,  ocular  illusions,  847 
elevations,  696-8,  700 
rys.,  cost,  682.  696 
example,  694 
gauge  of,  694 
Colo.  Cenlr.,  align't  statist.,  *26^ 


Col-Con 

Columbus,  C.  &  I.  C,  p.  c.  switch- 
^  .  .  .  [ing-mile.s,  ♦i8i 
Combustion,  heal  in  gases,  *456 

loco.,  ^.7'..  capacity,  449  -+- 
Commerce,  triangular  course  of, 
*  Company,'  nature  of,  28-9  &  [615 

rent  their  line,  36 
Compass  lines.  863  - 

(of  transit)  graduating,  888 
Compensation  of  curv.,  g.v.,  620 
Competition,  eflfect  on  p.  c.  op'g 
f.  .  .  [exp.,  109 

Competitive  rates  and  non-comp., 
{Sie  Through  and  Local.)  [58 
are  from  door  to  door,  54 
on  very  long  haul,  218 
traffic,  true  classif'n.  212 
eflfect  distance  on,  215 
Compound  interest,  *8o-83,  *747 
eflfect  of,  80 
locomotives,  chances  for,  133 
Composition  of  vel.  ex.,  287 
Compression,  loco.,  g.v..  loss  and 
f,  .         [gain,  470 

concentrating    resistances,     gain 
r>  fby,  587 

Concord    &   Portsm.,    alignment 
[statistics,  *259 
Concrete  for  pedestals,  903 
Cond^,  Hacienda  del.  locn  at.  682 
Condensing  eng's,  cost  and  eflf'y. 


gain  by, *468 


[' 


& 


Coning,  eflfect  on  amt .  slipping, 

path  of  wheels,  312   [288 

probably  injurious,  289 

no  eflfect  on  position  of  wh'ls, 

soon  disappears,  284  [282 

Connecticut:  area,  pop'n,  sidings. 

p.  c  op'g  exp.,  earnings  per  m. 

and  head,  ♦90;  wealth  per  cap., 

♦26 

Connections,  short,  desirable,  21Q 
Connellsville  &  So.   Penn.,  map 

n         vj   .•         ,  [on,  888 

Consolidation    loco.,  q.v.,  origin 

[of,  278 
most  us*d   on  heavy  curves, 
on  136  ft.  radius,  279   [148,  281 
rel.  cost  reprs.,  *i46 
Construction,  abandoning,  787 
a  priori  basis  of,  18 
'cheap  and  nasty.'  768 
cost  of,  and  accidents,  252  [-f- 
and  cable  traction,  688 
curve  limit,  635        [694 
indep't    return     tracks, 
switchbacks,  684,  950  — 
washouts,   783 
bad  lines  cost  most,  926 

CONTRAST  BETWEEN  SHEND- 

[ING  TOO   MUCH  AND  TOO 
LITTLE.  87 

economizing,    safe  direc 
[lions  for,  655,  757 
effect  on  val.  of  distance, 

[211 

danger  of  increasing,  113 

estimating,  834 

by  eye,  833  [849 

ocular   g.7'.   illusions, 

in  Colorado.  682.  696 

Mexican  r'y.  931 1*757  & 
p.  c.  cost  various  items, 
to  S.  G.  a  minor  item,  8:53 
unevenly  distr'd  on  line. 

BCONOMV   OF,  76a  [750 


Con-Cul 

Construction— O// ;'/««<'</. 

fixed  sum  only  available,  762 
order  of  ti^ne  in,  763 
postponing,  86 
similar  st'd  for  all  lines,  737 
temporary,  q.?/.,  624  & 
Constructive  mileage,  218,  241 
Contour  lines,  nature  and  def.,  873 
errors  in  drawing,  884 
maps,  CONCLUSION  as  to,  880 
good  and  bad.  ex.,  888 
Contractors  and  cement,  903 

estimates  by,  834 
Convenience    of  buyer,    consult- 
Corliss  engine  tests,  553      [ing,  52 
Corn,  acres  per  mile  ry.,  *go 
Cornfield,  locating  through,  652-[- 
Corporation,  modern  ry.,  28 
and  grade-crossings,  815 
errors  of,  707  & 
Corpus  Christi,  error  at,  722 
Cortez,  route  in  Mexico,  928 
Cotton-bales,  per  mile  ry.,  *9o 
cloth  and  transp'n,  manuf're 

/-  .   .  [o^  48 

Counterweights,  loco,  wt.,  *4r3  -(- 
centrif.  force  of,  446 
eflfect  on  bridges,  447 
Coupler,  car,  g.?'.,  488 
Couplings,  car,  g.v.,  close,  need- 
forces  acting  at,  303     [ed,  365 
slack,  g.7>..  eflfect,  358 
strength  of,  and  grades,  328 
three  conditions  for,  362 
when  most  broken,  368 
Courtesy  of  employes,  649 
Country  farmer  ^nd  steep  hill,  656 

inspecting  grades,  662 
Credits,  scap,  l(x:o.,  *i46-9 
Crest  of  hill,  contours  of,  885 

eye  fixes  on,  842  -f- 
Creusot,  Corliss  eng.  tests  at,  533 
as  to  steam  pressure,  474 
Cricket  and  ry.  accidents,  258 
Crossings,  grade,  g.?'.,  accidents 

r  •  ,       .  r^^-  *246 

Cross-sections  plotting,  898,  897 

rods  ffir,  882 
Cross-ties,  burnettizing,  114,  125 
creosoting,  320 

cost  of,  AVERAGE,    124 

putting  in  track,  125 

cost  of  maint.  U,  S.  sections. 

[*i28,  *i7o-6 

various  roads,  120,  170-6 

as  aflfected  by  ballast,  774 

by  rad.  of  curves,  640 

cutting.  125 

economy  and  form  of,  775 
length,  780 
no.  7's.  wi.  rails,  776 
thickness,  778 
life  of,  and  curvature,  320 
seasoning. 124 
preserving,  114 
practice  as  to.  777-81 
size,  U.  S.,  777 
Gr.   Brit,   and  Europe, 
Croton  water,  purity.  *378        [124 
Crown-bars,   loco.,    g.v.,    weight 

r     K-ii  •     ,        f^"*^  <^°s^  *4" 

Cuchillo,  spirals  on.  684 

Cul-de-sacs,  def'n,  851 

examples,  852,  855 
Culverts  and  floods   781 

loc'g  in  deep  fills,  851 


Cul-Cur 

Culverts— Co»e  in  ui'd. 
prelim,  esls.,  898 
wooden.  755  [statist..  *26a 

Cumberland     Valley,     alignment 

loc.  performance.  *438-4i 
Current  of  water,  judging,  840 
Curtis,  G.  W.,  on  Mex.  ry.,  932 
Curvature,  242 

accidents  from,  245 

Adams,  C.  F.,  on,  254 
danger  of,  real,  257 
Monte  Carlo  disaster,  252 
on  elevated  rys.,  646 
p.  c.  accidents  due  to,  249 
possible  pay'ts  for,  250 
a  minor  detail.  185 
amount  of.     (See  a /so  Sharp.) 
as  aflfected    by  care  and 
[skill,  635  & 
inexperience,  654  & 
radius,  641-2 
smooth  slopes,  843    [656 
time  given  to  surveys, 
limits  of  choice,  narrow. 
No.  of,  U.S.,  249.  259  [188 
on  high  line  to  Leadville, 

[697 

on  Rocky  Ml.  rys.,  *265  & 

per  mile,  av.,  628        [*259. 

States  &  rys.,  U.S.,  full, 

possible  change  in  loc'n 

[not  great,  251 

use  to  reduce  grades,  ex., 

and  heavy  engines,  278  [661  -f- 

loco.,  reprs.,  small  eflfect  on, 

,.        .  [-^188 

making  lime,  268 
smooth  riding  of  cars,  275 
bad  practice  as  to,  *263 

English,  242 
'broken  back,'  870 

COMPENSATION    FOR,  620 

as  aflfected  by  speed,  622 
by  length  train, 634 
by  radius,  633 
at  stopping-point's,  633 
computing  from  cent,  an- 
[gle,  629 

CONCLUSIONS  AS  TO,  632 

eflfect  diflf.  rates,  *63o 
on  pusher  grades,  598 
origin  of,  621 
proper  rate  not  fixed,  627 

EXAMPLE.    628 

virtual  profile  given    by, 

COST  OF.  312  [621 

as  aflf.  by  radius,  323 
by  repairs  engs  ,  315 
by  rate  grades,  581 

causesof.  two  distinct,  312 

CONCLUSIONS  AS  TO.  321 

eflfect  on  cross-ties.  320 
p.  c  on  loc.  and  car  re- 
( pairs,  *203 
per  train-mile,  *:!22 

DEGREE  OF.   MEANING,  258 

distinct  objections  to,  636 
eye  exaggerates,  842-!- 
max.  and  min.  of  limiting, 
max.  limits  for.  635      [652 
disadvantages  vi.-sible,  743 
distribution  irregular,  622  & 
ends  of.  trackmen  flatten,  276 
transition.  ^.7'., curves,  276 
entering  and  leaving  worst, 

I275 


958 


INDEX. 


INDEX. 


959 


l| 


Cur— Cur 

Curvature— OwZ/wKf-t/. 
forces  acting  on,  281 
loss  of  power  small,  316 
loco.  q.v.  safety  on,  148,  433 
loss  traffic  from,  375 
lost  time  on,  648  & 
moral  effect  of,  B76 
prevailing  error  as  to,  344 

LIMITING,  620 

TABLE  OF,  652 

limit  of,  and  bankruptcy,  655 

CONCLUSIONS  AS  TO,  653 

effect  on  construction,  635 
fixing  in  advance  wrong, 
on  light  rys.,  749  [654 

60  ft.  and  e"  comb'n,  656 

TOPOGRAPHICAL    LIMIT,  655 

wrong  mode  of  det'g,  244 
limits  of  objecl'able  spd.,*273 
metric,  degrees  of,  684 
Tadius  of,  bankruptcy  never 
[comes  from,  655 
effect  on  compar've  rail 
[wear,  296 
curve  com  pens' n,  633 
curve  resistance,  con- 
[cLusiONS,  305 
distance,  64a 
speed, 645 

train-load,  650        [292 
flange,  q  z/.,press.  unaff'd, 
in  ft.,  ch.,  and  m.,  •267 
inherent  cost,  638 
length  between  same  T. 

,.    .  .        „  [Ps.,  *644 

limiting  effect,  645 

loss  of  time  by,  647 

cost  of,  648 
various  modes  of  design- 
[ing,  358-66 
rail  wear  on,  ex.,  293 
rel.  importance,  ex.,  395 
sharp  and  zigzag  devei'ts,  678 
examples,    elevated   rys., 

[NY.,  645-7 
high  line  to  Leadville, 
Mexican  ry.,  931       [697 
Peruvian,  679 
sharpest  in  regular  use 
[U.  S.,  ♦325 
U.  S.  Mil.  R.  R.,  326 
flange,  q.-i<.,  wear  on,  29a 
gives  choice  more  routes, 
[656.  698 
lengthens  tangts.,  641 
may  save  dist.,642 
on  pusher  grades,  667 
radii  for,  *266  [266-7 

running  with  short    ch., 
taking  out  on  old  lines,  787 

on  Penna.  rd.,  277 
*  train-degree '  of,  58a 
Curve  protractor,  892 

CURVB  RESISTANCE,  MECHANICS  OF, 

[281 

ami.  due  to  surf.  fric.  only, 

[291 
as  affected  by  age  of  rails,  295 
form  do.,  295 
centrifu.  force  and  super- 
[elevaiion,  298 
greasing  flange,  516 
obliquity  of  traction.  301 
six    and    four   wheel 

[truck,   288 
various  types  loc.,*279—    I 


Cur-Den 

Curve  resistance—  Continued. 
as  affected  by  velocity,  911 

CONCLUSIONS   AS  TO,  304 

distinction  force  and   power, 
600"  =  I  mile  dist ,  315        [293 
Curves,  broken  rails  on,  356 

centrif.  force,  q.v.,  on,  269  -f- 
functions  of,  det'g  diffs.,  *644 
inside  and  outs,  rail,  differ, 
[length,  284 
loco.  q.v.  truck,  why  needed, 
offsets  to,  det'g,  872  [426  -f 
projecting,  892  — 

to  fit  topog'y,  668 
transition  curves  for.  869 
radii  of,  determ'g  diffs.,  644 
sharp,  short    chords    prefer- 
[able,  267 
slipping  of  wheel  on,  cause, 
error  as  to.  287       [284-6 
velocity  of,  289 
transition,  q.v..  why  needed, 
vertical,  q.v.,  869  [276 

Gushing,  G.  W.,  loc.  tests  by,  553 
Cut-off,  loco.,  q.v.,  av.,  *463  -f- 
and  speed,  47T 
theoret.  gain  by,  •467-8 
Cuts(excav.,  q.v.\  shallow,  snow 

[in,  126 
generally  last  work  done,  893 
Cutting  of  cross-ties,  cause,  125 

trains  in  two,  599 
Cylinders,  non-conducV  theoret. 

loco.,  q.v.,  life  of,  420 

Dakota,  align't  statistics,  ♦363; 
area,  pop.,  sidings,  p.  c.  op. 
exp.,  earnings  per  mile  and 
head,  ^90;  wealth  per  capita,  *26 

Danville  &  S.  W.,  align't  statis- 

[tics,  *263 

Days  per  year,  uken  at  365,  97 
Dayton  &  Mich.,  align't  statistics, 
Dazio,  spirals  at,  673  [♦261 

Dead  weight  and  fuelconsump'n, 
freight  cars,  av.,  610  &      [139 
mineral,  present  ratio.  614 
of  loco.,  alt  grades,  ♦688 
pass,  trains,  491 
why  little  injurious,  139 

WHY  TENDS  TO  INCR.,  567 

Decapod  loco.,  q.v.,  details,  ^lo 
Defaults,  railway,  ^o  [258 

Degree  of  curve,  q.v.,  measur'g, 
Depreciation,  fr't  cars,  rate,  *204 

M.  C.  B.  rule,  ^205 

Delaford,  M.  F.,  expts.  as  to  st'm 

^  ,  [press,  474 

Delaware,    area,  pop'n,  sidings, 

p.  c.  opg.  exp.,  earning  per  mile 

and  head,  *9o;  wealth  per  cap., 

[*26 

Delaware,  Lac.  &  West.,  align't 
[statistics,  ♦260 
loco,  performance,  ♦438 
sidings,  total,  *82s 
p.  c.  switching-miles.  ♦181 
terminal  exp.,  etc.,  N.  Y.,  *8i9 
track.  Buffalo  yd.,  ♦821 
train-load,  growth.  ♦100 
Delaware  &   H.  C.  Co.,  gravity 

[r'v,  692 
Denmark,  rail'ys,  cost,  etc.,  '^s 
Denver  &  Rio  G.,  Calumet  Mine 

[bch.,  *7oo 


Den— Dis 

Denver  &  Rio  G.—Continutd. 

Consolid'n  engs.  on,  281 

curve  comp'n  on,  6ai 

effect  n.  gauge,  753 

financial  status,  41 

fluct.  in  stocks,  ♦46 

long  grades  on,  699 

profile  condensed,  698 
Denver,  So.  P.  &  P., location  map. 
Depots.    {See  Stations.)  [696 

Derailing  switches,  def.,  811 
Derailment  accidents,  q.v.,  245 

and  caboose  brakes,  359 
Desdoint,  M.,loco.  tests,  521 
Detroit  grain  receipts,  728 
Detroit,  G.H.  &  M.,  align't  statis- 
tics, •362  [700,  932  & 
Development,  examples  of,  679  -(-, 

in  flat  country,  661  •\- 

RULE  AS  TO,  694 

spiral,  extreme  ex.,  684 
wrong  practice  as  to,  671 
Diagrams  lor  ests.  of  structures, 

[898 

geometric,  exagg'n  in,  387 

Differences  in  receipts  and  exp. 

[to  govern,  17,  63 

of  rev.  make  corps,  rich,  50 

Dining  cars,  competition  witli,  73 

dimensions,  etc.,  *49i 
"  Discounting"  the  future,  34 
Dispatching,  train,  and  improve- 
[ments,  old  lines,  791,  803 
and  ballast  trains,  774 
Disproportion  of  traffic,  q.v.,  608 
effect  on  train-Id  ,  100 
coal  movement  west,  135 
Distance  (Chap.  VII.),  195 
a  minor  detail,  185 
and  breaking  tangts.,  334 
light  railways,  756 
reducing  low  grades,  660-}- 
radius  of  curves,  641  4- 
between    towns,     effect    on 
[earnings,  700 
compar.  value,  great  and  small 
[diffs.,  208,  240,  709,  721 
construction    cost,    allowing 

[for,  3IX 
contradictory  law  as  to,  219 

example  of,  728 
cost  of,  198,  207-8 

as  affected  by  amt.  of  ex- 
[tra  dist.,  198 
by  rate  grades,  581  ^ 

by  way  rects.,  234 
credit  side  to,  211 

nature  of,  197  [*63i 

developing,  q.v.,  to  gain,  ex., 

to     red.    pusher    grades 

[wrong,  671 

diff.  via  any  curve,  *644 

effect  of,  on  competitive  rects, 

[*229 

on  loco,  and  cars  rep'rs, 

[*203 
ON  OPG.  BXP.,  198,  207-8 

great  diffs.,  309 
on  receipts, 
on  through  rects,,  228 

LAW  AS  TO,  228 

do.  GREAT  diffs.,  709 

errors  in  values  of,  211 

estimating  by  eye,  845 
across  water.  845 
eye  foreshortens,  843  -f- 


Dis— Ear 

Distance— Cow/Z/iMt-^/, 

esumating  by  tim/^  illusions, 
less  often  exagf?.,  237  [850 
OE  reconna*sf»i»*ce,  838 

GREAT  diffs.  of,  effect,  240,  709, 

increasing,  discourages  traffic, 

[238 
to  secure  way  bus.,  237 
rule  as  to,  238,  720 
LAW  AS   to    THROUGH   CONNEC- 

example,  728        [tioks.  219 
moral  effect  of,  239  [195 

mistaken  views  as  to,  cause, 
passing  towns  to  save,  58 
rel.  importance,  ex..  395 
why  made  basis  of  rates,  196 
Distributing  side  tracks,  *82i 
Ditching,  importance  of,  773 

oc.  illusions  as  to,  847 
Dividends,  L.  S.  &  M.  S.,  *99 
p.  c.  of  rev.  sections  U.  S., 

[*io8 
rates  of  U.  S.  &  Brit.,  *4i 
sections,  U.  S.,  *89,  *92-94 
Division,  length  of,  effect  on  cost 

[grades,  573 
tendency  to  incr.,  169 
Dome,  loco.,  wt.  and  cost,  *4i4 
Dom  Pedro  II.,  ry.,  loco,  perfce., 
Dorsey,  E.  B.,  paper  by,  529  [*44o 
Double-ender  loco.,  def.,  433 
Double-tracking,  764 
and  jfravity  rys.,  693 
obtaining,  by  imp'ts  grade,8o6 
Drainage,  mental  map  of,  836 
Draw-bars,  elev'd  r'y,  646 
tension  on,  in  sags,  356 

as  mod.  by  speed,  347,  349 

when  most  broken,  368    [*346 

Drawbridges,     accidents     from, 

weight  of,  905. 
Draw-gear,    frt.,    cost    and    de- 
[prec'n,  ♦204 
repairs  of,  161 

p.  c.  due  to  various  causes, 

-.  [*203 

Dredge,  J.,  "  Penna  R.,"  error  in, 

^  .    .  [*4»6 

Dnving-wheels,  centres,  life,  420 
Id.  on  persq.  ft.  grate,  ^452 
weight  {see  also  Loco.),  414 
*  Drop  test '  for  tr'n  resist.,  909 
Drummers,  and  minor  details,  192 
Dubuque  &  S.C,  align't  stat.,  *262 
Dudley,  P.  H.,  expts.  on  ft.  speed, 
on  train  resistance,  518      [370 
Dudley.  P.  H.,  fuel  tests,  529 
Dudley,  C.  B.,  exp'ts  on  rail-wear, 
Duluth,  grain  rec'ts,  738  [320 

Dump-cars,  774  [222 

Dunkirk,  constructive  mileage  to. 
Duplicate     tracks     for      pusher 

r*       wv.     u      •        •  [grades,  691 
Durability,  buying,  in  rails,  739  + 
Durango,  location  at,  723 
Dynamics  of  train  move't,  331 
Dynamometer  tests  and  vel.,  346, 
and  zero  temp's,  508  (349 

deceptive  effect  of,  435 

Earnings  as  affected  by  dist.,  229 
by  dist.  between  towns, 

[709 

per  mile,  sections  U.S.,*73-8i, 

[*89-94.  '107 


Ear~Eco 

Earnings,  per  mi\&— Continued. 
distribution  of  do..  *io8 
elevated  r'ys,  646 
Iowa,  77 
L.  S.  &  M.  S.,  99 
Mass..  78 
per  head,  pass,  and   fr't,   by 
[sections  U.  S.,  ♦73-81,  ♦92-94 
do.    whole  U.  S.,  ♦73-85, 
Iowa,  77  [•g^ 

Mass.,  78 
per  engine.  Am.  &  English. 


sections  U.  S.  *89      [♦ 


159 


{See  Revenue,  Europe,  etc.) 
Earthwork,  computing,  895 

cost  of,  on  narrow  g.,  753 

exec'g  by  train,  773,  806. 

prismoidal  form 'a,  895       [511 
Eastern  ry.,  France,  journal-box, 

loc.  tests  on,  466,  533        [*i8i 
Eastern  Rd.,p.c.  switching-miles. 
Eastern  States,  fall  rivers  in,  841 
East  Kent'y.  loco.perf'ce.  *438 
East  Tenn.,  V.  &  G.  loco,  perfce, 

loco,  tests  on,  701  [^438 

Easy  country,  errrors  in,  584  & 
Eating  station,  and  compet.  traf- 

y>  [fic.  73 

isconomy    in    construction,  q.v., 

[why  generally  safe,  87 

Engravings,  Index  by  Numbers:  '         ' 


Edg-Eng 

Edgehill,  sidings  at,  827 
Elasticity,  modulus  of,  def.,  345 
Electricity     as     motor,    possible 
_,  [effect,  328 

Electric  interlocking,  q.v.,  811 
Elevated  r'ys,  cost  per  lb.,  905 
curves,  resist,  on,  297 
sharpest,  ^325 
speed  on, 273,  325 
earnings  and  exp.,  646 
growth  traffic  on,  ^714 

Eer  inhab't,  ♦714 
andling  of  trains,  ^559 
length,  stops,  etc.,  ^559 
Elevations,  oc.    q.v.  illusions   as 

[to,  844-f 
Elizabeth,  L.  &  B.  S.,  align't  stat- 
ist., ^264 
Elliott,  T.  S.,  &  Jalapa  line,  943 
Ely,  T.  W.,  on  Consolidation  eng., 
Emery,  C.  E.,  paper  by,  *53i  [*i4a 
Employes  and  break  in  twos,  359 
and  heavy  engines,  360 
at  N.  Y.  terminals,  ^819 
courtesy  in,  649 
no.  on  XJ.  S.  r'ys,  249     [in,  896 
End-areas,  earthwork,  q.  v.,  error 
End  platforms,  frt.  cars.  ♦486 
Energy  and  press.,  confusion  as 
how  used  up,  333  [to,  473 


Fig, 

Jo 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0 

— 

33 

34 

35 

157 

189 

189 

230 

230 

230 

10 

20 
30 

230 

282 
292 

230 
283 
294 

230 
283 
293 

237 
284 

293 

242 
28s 
293 

251 
286 

293 

253 
287 

293 

256 
287 
293 

271 
291 
293 

271 
293 

293 

40 
50 
60 

293 
302 

3" 

293 
303 
3" 

294 

305 
339 

298 
306 

339 

298 
307 
343 

299 
308 
344 

299 
308 

345 

299 
310 
345 

300 
310 

347 

301 

13 

70 
80 
90 

350 
363 
387 

351 
366 

387 

352 
366 

387 

355 
369 
389 

356 
371 
389 
430 

360 

377 

S:»0 

361 
38s 
391 

362 
386 
403 

362 
386 
426 

363 
386 

427 

lUO 

427 

429 

429 

430 

430 

431 

433 

449 
476 
481 

1  447 

447 

110 
120 

130 

447 
455 
477 

448 
459 
478 

448 
461 
478 

448 

462 

478 

448 
467 
480 

448 
467 
480 

448 
476 
480 

455 
476 
481 

455 
477 
481 

140 
160 

482 
489 
514 

482 
489 

515 

482 
493 
516 

482 
494 
518 

483 
497 
521 

483 
504 
521 

483 
5»i 

483 
5" 
536 

484 
5«i 
537 

489 
511 
552 

170 
180 
190 

561 
621 
647 

561 
623 

647 

562 
624 
652 

562 
624 
660 

625 
661 

587 
629 
661 

588 
636 
664. 

588 
636 
664 

588 
642 

668  1 

604 

642-6 

666 

'l\ni 

668 

671 

672 

672 

673 

673 

673 

676 

678  I 

679 

210 

220 
230 

679 
686 
696 

679 
686 
697 

680 
689 
698 

681 
68q 
708 

682 
680 
708+ 

684 
691 
710 

684 

693 
711 

684 
694 
711 

685 

695 
712 

685 
696 

723 

240 
250 
260 

727 

775 
802 

728^ 

775 
803 

735 
783 
805 

735 
8^5 

736 
791 
806 

739 
796 

807 

763 
799 
838 

767 
801 

843 

769 
801 
843 

770 
802 
844 

270 
280 
390 

845 
859 
882 

846 
862 
882 

846 
863 
883 

847 
869 

884 

848 
870 
88s 

849 
870 
885 

853 
871 
887 

853 
872 
888 

859 
874 
889 

859 
874 
889 

3U0I 

897 

902 

9»4 

917 

918' 

918 

918 

919 

928 

933 

ilU| 

934 

945 

946 

947 

234',  P 

.708;  ' 

241',  p. 

734- 

i 


960 


Engravings 

Engravings,  Inukx  by  Subject: 
Abutments,  pile.  770 
Alignment,  possible  devia'ns 
[small,  189 
Ameca  River  spirals,  etc.,  684 
Ames  car  coupler,  489 
American    line    to   Mexico, 
[maps,  etc.,  93a  -f 
Arc,  mental,  strikinjf,  838 
Areas,  ft.  lbs.  and  H.  U.,  455 
Ball  on  plank,  308 
Belter  country  than  it  looks. 
Bissell  truck,  426.  429-31     [848 
Boiler  power,  adaptingf,  403 
Brakes,  computing  eflf'y,  494 
brancli  lines,  examps.,  734-6 
Breckenridge,  Col.,  loc^n  at. 
Bridges,  comp.  wt.,  767     [696 
diff .  rolling  I'ds.  769 
vibration  of,  447-8 
Broken-back  curves,  ex.,  870 
Burlington  train-r.    tests.  497 
Cable  system, planes  for,689-93 
Cars,  centre  grav.  of.  271 
Car-wheels,  compression    of, 
usual  Am.,  514  [562 

Cattle  guard,  C,  M.  &  St.  P., 

Centre  of  gravity  in  sags,  360 
of  rolling-stock,  271 
Chicago,  M.  &  St.  P.  timber 
[strucs.,  770 
N.  W.  grain  receipts,  728 
Cine,   N.  O.  &  Tex.  P.  loco. 
^     ,   ,  ,       [tests,  482 -(- 

Coal,  lump  of  unbiirnt,  449 
Cochituatc,  L.,  rainfall,  783 
Cone,  contour  map  of.  874 
Coning,  model  for  testing,  311 
radius  of  path  wheels.  319 
Contour  lines,  errors  in.  884-5 
maps,  Hnishing,  888 
nature  of,  874 
Counterweights,  loc,  447 
Couplers,  automatic,  489 
Couplings,  forces  at.  301,  303 
Crossings,  stops  at.  grades,8oa 
Cross-section  rods.  882 
Cross-ties,  theory  of  form,  775 
Curvature  and  accidents,  253 
and  tunnels,  242  [629 

compensating,  effect,  621, 

on  low  grades,  652 
radius    of,     5°    and    io», 
_  [636-40 

Curves  and  wheel-bases,  283-!- 
checking  speed  on,  647 
comp.  safety  locos,  on,  433 
offsets  to,  determ'g,  872 
position  truck  on,  256,  aSaJ 
radius  of,  and  speed,  647 
rail-wear  on,  293  [646 

Curves,  sharp,  elevated  rys., 
may  save  dist.,  642 
variat'ns  dist.  via,  643 
Denver,  So.   P,  &   p.,    map, 
[etc.,  695-7 
Development,  effect,  588 
examples,  668-686'& 
Distance  and  rate  grade,  671 
and  sharp  curves,  642 
effect  on  receipts,  230 
oc.  illusions  as  to.  859 
slight  effect  lateral  dev'ns, 
total  &  rategrades,67i[237 
via  various  curves,  642 


INDEX. 


Engravings 

Engravings,  I.nukx  By  Subject: 
Double  track,  uses  of,  693-4' 
Eastern    ry.,    France,    jour.- 

Klevated  ry.  curves,  646-8 
English  tunnel,  242 
Estimating,  from  profiles.  897 
Falling  bodies,  paths,  339 

vel.of,624  [887 

Field-sheets  for  mapping,  ex., 
Flange-prcs.,  loc.,  on  curves, 

[433 
resultant,  292,  294,  299 
-wear,  actual.  308 
alleged,  307 
Foot-lbs.,  areas  and  H.  U.,455 
Forces,  triangle  of.  closg,  s^? 
Forney,  M.  N  .  modd.  3I1 
Friction,  apparatus  for  test- 

[ing,  914 
coef.  of,  light  press.,  504 
experiments   as    to,    504, 
Gauge,  effect  of,  305      [917-19 
ueometric  diagrams,  exagger- 
[aiions,  387 
Georgetown  spiral,  681 
Grade-lines,  possible  devia'ns 
n     A  .  [small,  189 

(trades  and  uncomp'd  curv., 
.      ,  [625,  629 

broken,  sags  and  up'd,  624 
forces  on,  339,  536 
heavy,  of  world,  698 
long,  broken  vs.  cont's, 
momentum,  344-5  &  [^85 
of  repose  iucreas'g  speed, 
last  car,  362  [369 

rate  of,  and  asst.  eng.,  587 

St.  Gothard  r'y,  672-3 
reduc'g  by  devel  t.  588,668 

saves  no  dist.,  671 
resistance  of,  5:56 
sags  and  summits,  623-4 
switchback  grades,  947 
train-load  on,  552 
unif.  and  pusher,  604 
virtual,  ^r.?..,  348-^,703 
long,  353 
Grain  rec'is,  N.  W.,  728 
Gravity,  action  on  grades,  536 
on  diff.  paths  of  desc't,  634 
r'ys.  typ.  profile,  691 
Great  inclines  of  world,  698 
Grooved  wheel,  294 
Gyration,  radius  of,  739      [455 
Heat-units  and  temp.,distinc.. 
Hemisphere,  contour  map  of. 
Hill,  J.  W.,  loc.  test.,  461  [S74 
Hut,  ocul.  illusion  as  to,  846 
Impact  at  ioints.  561 
Inclined  planes,  forces  on,  339 
vel.  down,  624 
types.  689-93 
Indicator  diagrams,  actual  ex- 
.  [amps..  476-84 

typical,  simplest,  456 
with  expan.,  467 
Interlocking  app's  for  switch- 
[backs.  946 
Interpolating  dist.,  effect  on 
[reel's,  230 
Iron,  pnce  of,  past,  763 
Jalapa  line,  maps,  etc.,  932  -f 

profile,  698 
Janney  car-coupler.  489 
Journal-box.E.  r'y,France,5ix  I 


INDEX. 


g6i 


Engravings 

Engravings.  Index  bv  Subject- 
Jour'l-box,  usual  Am.,  514  [0,^ 
Jour'l  fric,  app'ius  for  lesiV 
diagrams  of,  5,5,  917  +    ' 
Lake    Shore    &    .Vl.   s.   train 
.  [resist,  tests,  518 

Latitudes  and  departures,  dia- 
fgram  for  comp'g,  880 
Leadville,  high  line  to.  695-7 
Lehigh  Valley  rail  sec'n,  310 
Located  and  prelim,  line.  863 
Location  around  ridge,  668 

in  fiat  country,  661 
Locomotives, asst.  and  grades 
profile  for,  666        [587 
vs.  through  engs.,  604 
use  o  ve  r  su  m  in  i  I  s,  689- 
boiler-power  of,  403       [04 
Bissell  truck,  426,  429-31 
coal,  unburnt,  lump,  449 
centre  grav.  of,  271 
comp.  safety  on  curv's,433 
counterweights,  447 
indicator  diags.,  476-84  — 

power  of,ongrades,552. 587 
resist,  of,  prop'nal,  521 
trucks,  429  ± 
tests,  461-81 

wheel-base  diags.,  426 -f- 
wts.,  769         [test,  463 
London.  Br.  &   So.   C.   loco. 
Lubrication,   effect  on    fric. 

[917-n 
Manhat'n  elev.  ry  c'rves,646-7 
Mapping,  field-sheets  for,  ex., 

[887 
good  and  bad  ex.,  888 
Mexican   Central,    Ameca    r. 
[spirals,  684 
Tepic  to  coast,  676-7 
spiral  on,  678 
National,  Pacific  b'ch,  723 
Mexico- Vera  Cruz,  map,  932 
Momentum     grades,     344-5, 
[623-5.  703 
Monte  Carlo  disaster,  253 
Mounuin  grade,  Jalapa  line, 

KT-  ..  .  .     r9.34  + 

Niagara  cantilev'r  brdg.,  wt., 
[etc.,  902 
Norihwestern  gram  rects.,  728 
Obliquity  of  traction,  301 
Ocular  illusions,  84^  -f-,  665 
Offsets  appear  too  large,  665 

to  curves.  872 
Oroya    ry.   developm'ts.  679. 
Overlap,  views  of,  846-7  [684-6 
Parabola,  principle  of,  387 
Parallelogram  ol  forces.  302 
Pass,  oc.  illusion  as  to.  845 
Peruvian  r'ys,  profile,  698 
Prelim,  and  located  line,  863 
Prices,  fiuct'ns  in,  763 
Profile  condensed,  ex.  of,  862 
estimating  from,  897 
Jalapa  line.  938  [853 

of  badly  reconnoit'd  line, 
virtual,  pass.,  348  -f- 
frt.,  352  -f 
long  grade,  355 
saR''.  356  -f- 
Pulley  and  rope,  302 
Radiation,  effect  on  cyls.,  476 
Rails,  alleged  corner  wear,  307 
and      wheels,     positions, 
[292-4 


Engravings 

Engravings,  Index  bv  Subject- 
Kails,  bending  of,  493,  775 
compression  of,  516,  562 
price  of,  past,  763 
section,  L.  V.,  310 
sections,  worn,  293 
strength  of,  739 
yielding  of,  493 
.     at  joints,  561 
Kainlall,  past  20  yrs.,  78^ 
Rates,  dec.  in   U.S.,  727   ^^-c 
Reconnaissance,  ex.  of' bad, 

I853 
manner  of  making,  838 
Resultant,  flange  press.,  292 
Ridge,  low.  loc'g  over,  661-4 
Rise  and  fall,  on  grades  and 
[level,  366 
worstclassof,  37,,  377 
Rolling-load,  comp.  effect,  767 

diags.  of,  769 
bags  and  summits,  363,  623-4 


centre  ot  grav.  in,  360 

motion  through,  356  -(- 

filling  up,  806 
<!t    ^" 'o^fi^/rade,  62s     [672-3 
bt,  Gothard  r'y  prohles,  etc.. 
blopes,  oc.  illusions,  843-9 
Speed,  check'g,  on  curves,  647 

increas'g.  virt'l  protile,:,6Q 
bphere  rolling  on  plank,  308 
bpirals,  Ameca  river,  684 

bridge  &  tunnel,  typ'l,  679 
bridge,  Mex.  C.  ry.,  678 
Un.  P.,  G'town,  680-2 
St.  Gothard  ry.,  672-3 
Stations,  grade    ^t,  801  -f 
grades  bek   i.  791 
on  grades,  801,  803 
Stops  on  switchback.  947 
Stop-watches,  mounting,  796 
Stroudley,  Wm.,  loc.  test,  462 
Summits,  stations  at,  805 

types  of,  689,  693 
Superelevation,  effect,  298 
Surveys,  when  to  make,  exs.,  j 

Switchbacks,  grades  for,  94/''  j 
Peruvian,  685-6  I 

sketch  of  principle,  945 

switches  for,  946  [455 

Temperature  and  H.U.,  dist'n, 
Tepic.  descent  from,  676-7 

spiral,  678    [map,  ex.,  888 
Topography,  good   and    bad 

law  of  dif.  in  slopes,  588 

taking,  883 

errors  in  do.,  884-5  1 
Towns,  loss  dist.  going  to,  859  1 
Track,  yielding  of.  493  ; 

Train-load  on  grades,  552  ' 

Train-resistance  tests,  497,518, 

[521 

Traffic,  gr'th  of.  U.  S.. 727.33-5 

law  of  growth  of.  712  — 
Traffic  points,  effect  of  multi- 

T«.     .,.  [plying,  708  -I- 

Iransttion  curves,  nature  of, 

use  of,  exs.,  870-2  [869 
Trestles,  iron,  effect  ht.,  902 

wood,  C,  M.  &  St.  P.,  770 
Trunk  lines.  Mexican,  72^  [306 
Trucks,  Igth.  of,  effect,28'3,287, 

position  on  curve,  256,  282 

rotation  on  curves,  286 

swing-motion,  429 

61 


Eng-Eur 

Engravings,  Index  by  Subject: 
Tunnels  and  curvature,  242  ' 
ex.  of  avoiding,  668 
.spiral,  672-84 
Union  Pacific  spiral,  68i 
Valley  lines,  oc.  illus'ns,  848 
Vertical  curves,  theory,  386  4- 
examples,  389 -f  [703 

Virtual  grades  and  actual  ex 
descend'ggrade,  369.  799' 
level,  pass'r.  348  -f ,  352 1 
stations,  801-2-5  + 
theory  of,  348  4- 
Way  trafhc,  effect  inc'g,  708  -f 
Wellington,  fric.  diags.,  9,7^ 
„„  train-resist,  diag.,  518 
Wheel-base,  length,  effect,  306 
117     .^^'  ""curves,  283,  287 
Woodbury,C.J.H.,  fric  tests. 

Work  and  stress,  distinct.,  45^ 
Worse  country  than  it  looks, 

]  Entrained  water,  loss  by,  470+'^^ 
J^ngineer,  The,  on  great  inclines 
j  .  [of  world,  *6qq 

on  tram  resist.,  pass..  527 
iingineering,  cost  per  mile,  N   Y 
I  -   _   .  .         ^    [C.&H.  R.,*7t" 

definition  of.  i  [two,  359 

;  Engineers  and  am'tof  curvature 
errors  among,  880  [6si 

\  needless  as  to  grades,  659 

have  first  chance  at  co.  funds, 
locating,  av.  work  of,  583-4  [J 

province  of  the.  17 
untrained    and     half-trained, 
u      •  [^sts.  by,  83i 

lingineman  controls  breaking  m 

A  1-        .  [two,  359 

do.  slipping  drivers,  q.v.. 
Engine-mile  and  train-mile,  rati? 

r*    ' 

Engine   wages     g.v.,    per    traiS^ 

(-Vf*- Loco.,  Steam.)    [mile,  *r47 

U-nglish  practice  as  to  curvature, 

J     •  ,  [242 

designation  of  curves,  266 
r'ys.  growth  of,  *79 

loco,  and  car  exp's,  *i48 
motive-power    exp.      de 


[tails,  *J47 
pass,  trains,  on.  96 
ratio  eng.  and  train  miles, 
statistics  of.  *79  [*,  .- 

{See  Great  Britain.)       [42c 
Equalizing  lever,  loco.,  q.v..  4*1 
Equanimity  essen'l  to  .success,  840 
Equilibrium,  theory  of,  536 

.       stable,  282  fR.  *7i 

Equipment  cost,  N.  Y.  C.  «&  P.  R. 
per    mile  sections    U.  S 
.        (-S"^*?  elsewhere.)  [*8g 

Equivalent.   (.V?^  Virtual  Grades  ) 
Erection,  bridges,  cost,  905 
Erie.    (See  New  York,  L.  E  &  W  ) 
Erosion,  water,  effect  of,  684 
Escandon,  A.  &  Mex.  Ry.,  929  [♦41 
Kstimate  of  future  r'y  construe 
of  future  traffic,  method,  24, 76 
preliminary  895 

precision  not  imp't,  895 
two  opposite  errors  in,  834 
Europe,  cheapest  r'ys  in,  ♦4<: 
growth  r'ys,  ♦42 


Eur-Exp 

Europe — Continued. 

pass,  trains  in,  96  [+45 

pop'n,  r'ys,  wealth,  etc.,  *27, 
rolling-stock,  traffic,  etc.,  *43 
terminals  in,  827 

European  car  resistance.  '•=502 
rolling-stock  on  curves!!'  283 

Evans,  W.  W..  paper  by.  691  [*26i 

Evansville&T.H.,align't  statist., 
Evaporation,  loco.,  q.v.,  av.  rate. 

as  an  d  by  rate  com  bus., 
sources  of  loss,  *456     [450 
per  lb.  coal,  av.,  156  & 
per    sq.    ft.    grate,    rate, 

H      TT     f  ..  f*'f^4+ 

H.    U.    from   and    to   various 

[temp.,  *45o 
stationary  g.v.  engines,  *53i 
Excavations,  earth.  893-5 

shallow  rock,  868 
Exhaust,  work  of  piston  on,  473 
Expansion,  period  of,  def.  458 

theoretical  gain  by,  467 
Expenditure  on  const  c'n,  g.v.,  15 
Experience  and   am't   curvature, 
and  grades.  583-4,  659        [654 
Experiments  as  to  adhesion,  443 
air-brakes.  290 
bridge  vibration,  447 
brake  efficiency,  434 

max..  405 
coal  per  K    P. ,  ♦460  & 
coning,  efi  ci  on  pos'n  wheels, 
Corliss  engine  fric.,  533      [283 
curve  resistance,  306  & 
sharp  curves,  297  & 
entrained  water,  470 
falling  bodies,  laws,  332 
friction,  brake,  290 
friction,  laws,  503  -f-,  913  & 
luel  consump.,  light  Iocs.,  137 
grate-area  efficiency,  484 
greasing  flange,  516 
kindling  fires,  200 
locos,  fuel  combustion,  464 
head  resist.,  *52o 
high  speed,  473 
horse-power,  451,  466  -4- 
p'rf'nre,*46i-f-,*476-84& 
relative  resist.,  521,  279  & 
running  light,  137 

loose  wheels,  306 
narrow-gauge,  306 
path-coned  wheels,  309 
radiation,  313 

internal.  472 
rail-wear,  1,9,  294,  320,  380 
.   slide-valve  fric,  532 
slip,  imperceptible,  445 
slipping  wheels  on  curve<;  28? 
speed  of  freight  trains,  370 
steam  press.,  economy  of,  474 
tram  resist'n'e,  497  -f,  909,  9,3 
elements  of,  517  -|- 
high  speed,  526  -}- 
trucks  on  curves,  28a 
wheel  pressure,  122 
Experiments  by  Abbey,  H..  a,a,% 
Baldwin,  O.  H.,  445  ** 

Boston  &  Albany,  553 
Chanute,  O.,  122,  526  - 
Clark,  D.  K.,  472,  474 
Cloud,  J.  W.,  285^^* 
Coltoum,  Z.,  437 


\ 


wm 


962 


INDEX. 


INDEX. 


Exp-FII 

Experiments  \y^ — Continued. 
Gushing,  G.  W.,552 
Delatield,  M.  F.,  533 
Desdoint,  M.,  521,  528,  535 
Dieudonn^,  etc.,  443,  533 
Dripps,  I.,*279 
Dudley,  C.  B.,  320,  380 
Dudley,  P.  H.,  370,  518 
Emery,  C.  E.,  297 
Forney,  M,  N  ,  309  + 
Gallon,  D.,  290,  434-5,  495 
Hill,  J.  W.,  *445,  *46i  +,  *526 
Hudson,  C.  H.,701 
Galileo,  332 

Guebhard.  etc.,  443,  533 
Latrobe,  B.  H.,  297,  443 
Mari^,  G.,  464,  470 
Morin,  A..  503 
Rabeauf,  M.,  445 
Regray,  M,,  466 
Rhodes,  G.  W.,  497  -f 
Ricour,  M..  527 
Robinson.  S.  W.,  447 


Sedgeley,  J.  H.,  313 
Smith,  C.  A..  445,  4' 


47a 

Sprague,  F.  J.,  559 

Stroudley,  W.,  137,  200,  451, 

[460,  526 
Thurston,  R.  H.,  504  -f-,  917  + 
Tower,  B.,  504+,  917  + 
Vuillemin,  etc.,  443,  ^33,  535 
Wellington,   A.    M.,  282,  293, 
«r    1^97;  320,  380,  504.  904,  913 
Wells,  R.,  137,  306        [435,  495 
Westinghouse,    G.,   290,   434, 
Woodbury,  C.  J.  H.,  504  -f- 
Exploration  line,  860 
Export  traffic,  relative  imp'rt'n'e, 
grows  less.  615  [*io5 

Southern    States,    triangular 
[course,  615 
Exposure,  effect  on  car  and  eng. 

[reps.,*203 
Extra  haul  not  a  burden  on  traffic. 
Extra  freight  trains,  102  [61 

Eye  for  country,  acquiring,  23, 

[834.  876  & 
ocular  illusions,  842 

Fairlie,  R.  F.,  inv.  narrow-gauge, 

locos.,  def.  and  use,  424      [424 
ex.  of  heavy,  410 
in  Mexico,  932 
Falling  bodies,  laws,  338-9  & 
Falling  down-stairs,  deaths  from, 
False  summits,  836  [257 

False  works,  cost  of.  905 
Farmer,  and  steep  hill,  656 

inspecting  grades,  662 
Farms,  U.  S.,  value,  ♦25 

machinery  on  do.,  value,  *25 
Far  West  States,  area,  pop.,  earn- 
ings per  mile  and  head,  etc.,  *9i 

gen.  r'y  statistics,  *88,  ^90 

maint.  way  exp.  details,  ♦128 
Feat,  sci.  skill,  marvellous,  933 
Fell  system,  fric.  r'y,  690 
Fences,  cost  U.  S.  sections,  ♦128 

maint.  Chicago  lines,  *i74-6 
sections,  U.  S.,  ♦170-6 
trunk  lines,  *i72-6 

p.  c,  cost  to  total,  *757 
Field-sheets,  mapping,  ^.i;.,  886 
Field-work  of  surveys,  q.v.^  860 
Fills,  and  cuts,  balanc'g.  895 

locat'g  culverts  in,  851 


Fil-Fra 

Fills  and  culs— Continued. 

min.  height  tor,  893 

nature  makes  in  valleys,  850 

prove  deeper  than  expected, 

should  exceed  cuts,  893      [851 
Finland,  cheap  r'ys  in,  %5 

Iocs.,  no.  and  work  of,  ♦160 
Fire,  accidents  from,  *247 

and  r'y  accidents,  258 
Fire-box,  loco.,  f.v.,  life,  *4i9-2o 

radiation  q.v.  from,  313 

sheets,  fractures,  *4ao 

size,  *407-4io 
Fisher  rail-joint,  123     [miles,  *i8i 
Fitchburg    r'd,   p.  c.    switching- 
Fittings,   loco.,  cost   new,  det'b, 
[* I 50-1-2-4-5 

wt.  and  cost.  *4i3  + 
Fixed  charges,  def'n,  33 

nature  of,  106 

rel.  amt.  of.  13-4-5  & 
Flag  for  trains,  how  carried,  102 
Flange,  best  form  of,  307  -f- 

FRICTION,  291 

greasing,  effect,  516 
independent  of  rad.,  391 
pressure,  291 

and  centrif.  force,  269 

CONCLf  SIONS  AS  TO,  304 

effect  of,  294 
independent  of  rad.,  392 
resultant  of,  292 
sharp,  proportion  of,  ♦317 
wear,  erron.  views  as  to,  307 
Flat  cars,  dimens.,  etc.,  *486-7 
Flint  &  P.  M.,  loco,  perfce,  •438 
Floating  capital,  U.  S.,  value,  ^25 
Floods,  accidents  from,  *247 

in  valleys,  q.v.,  783  [*304 

Floor,  frt.  car.  cost  and  deprec  n, 
Florida  :  area,  popu.,  sidings,  p.  c. 
opg.  exp.,  earnings  per  mile  and 
head,  ♦go;  wealth  per  cap.,  ^26 
Fly-wheel,  energy  of,  334 
Fog,  as  cause  of  accidents,  254 
Foot-pounds,  expl'n  of,  338 
of  work,  and  grades,  329 
Foot  travel,  illusions  from,  850  -}- 
Forces,  triangle  of,  536 
Foreclosed   lines    pass  far    from 
Foreclosures,  r'y,  39       [towns,  68 
Foreign  countries,  pay'ts  per  head 
[to  r'ys,  ♦105  & 
Foreign  haul,  effect  on  value  of 

[dist.,  339 

rys.,  gen.  stat.,  ^27,  ^42-4 

Foreshortening,  oc.  ^.tk  ill'n, 842-f- 

Forgings,  prices.  Am.  &  Eng.,^4i6 

Forney  loco.,  ^.7/., def.  and  meritii, 

[423 
Forney,  M.N., Catechism  of  Loco,, 

on  rail-sections,  307  [423 

record  wt.  loco,  parts,  ^414 

Fortress,ancient.in  Mex.,9^3  [♦261 

Fort  W'ne,  M.  &  C,  align\  stat., 

Fractional  sta'ns  and  prelim,  ests.. 

Frames,  loco.,  ^.f .,  cost  new,  etc., 
weight,  414   [♦150-1-2-4-5 
France,  exp'ts  on  adhesion,  443 
journal-boxes  in,  510,  515     [45 

f)opu.,  r'ys,  wealth,  etc.,  27.  43, 
oco.  drivers,  size,  535        [445 
imp>erceptib1e  slip  exp'ts, 
no.  and  work  of,  ^160 
repr.  details,  *i45 


963 


Fra— Fue 

France — Continued. 

loco.drivers, tests  of,  521,533  -|- 
railway  manage't  in,  ^575 
safety  in,  258 
system,  growth  of,  44 
rec'ts  per  inhabt.   pass,   and 
[frt.,  ♦los 
rolling-stock,  traffic,  etc.,  43 

details,  521 
train-loads  in,  and  Am.,  575 
train-resist,  tests,  521,  528 
Francis.  Chas.,  diagram  by,  889 
Free    omnibuses    and    errors    of 

[location,  54 

Freight   and    pass,    locos.,    q.v., 

[tire  reps.  *i49 

Freight  cars  a.v.  per  mile,  sects. 

[U.  S.  *89 
world,  43 
earnings,  ^.7/.,  thro'  and  local, 
[sect'ns  U.  S.,  ♦231 
per  head,  do.,  92-4 
tons  of,  world,  ^43   [U.S., ♦181 
traffic,  f.T.,  p.  c.  of,  sections, 
trains,  q.v.,  no.,  load  and  haul, 
[U.  S.  sections,  ^97 
growth  of  load,  98-100 
Fremont  pass.,  ♦700 
Freshets  and  structures,  781 
Freycinet,  est.  by,  loco,  rail-wear, 

[122 
Friction  and  heat,  journals,  314 
app's  for  test'g  in  lathe,  914 
as  affected  bv  area,  295 
by  lub'n,  509,  917-9 
by  press.,  504-5,  917-9 
by  temp're,  ^505 
by  coei.  fric,  time,  ^290 
by  velocity.  289,  913 
bath  lub'n,  509, 918 
brakes,  y.7'.,  av.,  494 
brake-shoes  and  wheels,  ♦290 
car-wheels.  289 
driving-wheels,  435 
loco..  O.V.,  *529  -j-  & 
Morin  s  exp'ts,  503 
of  rest,  920 

rotative,  wheel  on  rail,  291 
skidded  wheels,  ^290 
slide-valve.  532 
starting,  y  v.,  919 
stationary  eng..  ♦ssi 
Friction-grip  r'y,  origin,  etc.,  691 
Frogs,  accidents  from,  ^246 

and    switches,   cost,    various 

[roads.  *i2o 

Frost  and  broken  rails,  256     [♦409 

Fry,  Howard,  and  W.  S.  enRines, 

on  English  coal  consump.,  133 

Fuel,  consumption  of,  132 

as    affected     by   comp  d 
[eng.,  133 
train-length,  *i36 
due  to  head  resist.,  53°  — 

English    and  Am...   ^^^^ 
^  [diff.,  134 

per  mile,  ♦sig 
cost  of,  132 

as  affected  by  curv.,  3*3 
distance,  199 
radius  of  curve,  639 

rise  and  fall,  375 

temperature,  3'4 

wt.  of  engine.  563 

wt.  trains,  568 

work  done  by  eng.,  376 


Fue-Gra 

Fuel,  cost  ol— Continued. 

causes  of  variation,  158 
C,  B.  &  Q.,  tendency  on, 
per  ton-mile,  ^147         [157 
Chicago  rds.,  *i74-6 
sections,  U.  S.,  *i7o-6 
trunk  lines,  ♦172-6 
ejected  from  smoke-stack,  449 
heat  units  in,  ^450 
high  and  low  speeds,  529 
per  car-mile,  P.  R.  R..  *i4o 
H.  P.,  actual,  ^460 
stationary  engines,  531 
theoretical,  ^460 
train-mile    P.  R.  R.  lbs., 
cost,  ^140  [♦ho 

rate  of  combustion,  449 
terminal  wastage  of,  2cx) 
wastage  of,  by  blast,  449 
wood  as,  139 

amt.  burned  P.  &  R.,  ♦200 
furniture,  U.  S.  value,  ^25 
Furniture  car,  C.  &  N.  W.,  ^490 
Future    growth,  f.v.,  of    traffic, 

[est'g,  24 
not  to  be  est'd  far  ahead,79 

■fl,  value  of,  332 

■Gallon,  D..  exp'ts  on  brakes,  290, 
•Gauge,  def'n.  284  [434-5,  495 

and  curve  resist,  305 

[751 
narrow,  q.7'.,  pros  and  cons, 
tight,  effeci,on  wheels,  283 
'General  and  sia'n  expenses,  118, 

[178 
as  affected  by  distance,  206 

considerable  diff 's,  210 
no.  trains,  568 
of  car  repairs,  j6o 
of  loc.  repairs,  ♦145-7 
Oeneral  officers  and  clerks,  cost, 
[Chicago  r'ds,  ♦174-C 
sections,  U.  S.,  ♦170-6 
trunk  lines,  ^172-6   [lence,  832 
Geometric  and   commerc'l  excel- 

diagrams,  exagg'd,  387 
■Georgetown,  spiral  at,  680  -[- 
■Georgia,     align't     statist.,    ^264; 
area,    pop'n,  sidings,  p.c.   opg. 
exp.,    earnings    per    mile     and 
head,  ♦go;  wealth  per  cap,  ^26 
Georgia  r'y,  align't  statist.,  ^264 
miles  and  earnings,  ^719 
pile-driver  car,  ^490 
Germany,  align't  statist.,  ^265 
axle-boxes  in,  515 
coal  consumption  per  m.,  135 
growth  r'y  system,  44 
locos.,  life  of,  *4ig 

no.  and  work  of,  ♦160 
high  steam-press.,  ^519 
popul'n    r'ys,     wealth,    etc., 

^27,  '43.  *45 
rolling-stock,  traffic,  etc.,  ^43 
Giovi  r'y  grade,  ^699 
Gondola  cars,  dimens.,  etc.,  ♦486-7 
■*  Good  times  '   and    r'y   constr., 

[763  & 
Gothard  r'y,  condensed    profile, 

[698-9 
Governing  points  for  grade-lines, 

[675 
Grading,  p.  c.  cost  to  total,  ♦757, 
filling  by  train,  773,  806    [^833 
cost  of,  vs.  rail-sections,  749 


790. 
(809 


Grades 

Grade-contour,  def.,  874 

examples,  678,  684,  888 
horiz'l  approx.  to,  error, 

.      .  [877 

use  in  projecting,  890 

Grade  crossings  and  curve  limits, 

[655 

AND      INTERLOCKING, 

old  lines,  802-3 
laws  as  to,  812 
Grades,  accidents  on,  949 
and  ductuating  vel.,  346 
and  rise  and  f.,  distinct.,  327-9 
asst.   eng.,  g.v.,    laying  out, 

[596,  600 
bad  not  always  cheapest,  583 
balance  of,  for  assi.  engs.,  591 
for  unequal  traffic,  608 
diff.  for  each  class  traff., 
example,  617  [617 

errors  in  computing,  61 1 
practical  consid'ns,  611 
table    for     all    con- 
[ditions,  612 
breaks  of,  measure  cost  rise 
[and  f.,  384 
bunched,  585  -|-.  618 

{See  As&t.  Engines.) 
changes  in,  comp.  effect  with 
[diff.  locos.,  555 
choice  of,  659 

GENERAL  RULE  FOR,  66o 

comparison    of    pusher    and 

[uniform,  604  -j- 

cost  of,  560 

asaff'd  by  Tgth  division.  573 

cheap  pass,  traffic,  580 

conclusions  as  to,  573 

diff.  for  through  and  pusher 

[gr.,  ex.,  674- 

due  to  work  not  done,  589 

interest  charge  on  new  Iocs  , 

[570 
per  daily  train  and  ton-m., 
[compar'n,  ^574 
French  est.,  ^576 
German  est.,  576 

VALUE  OF  AVOIDING  IN- 
[CREASE, 574 
de  facto,  def'n,  543.  515 
descending,  when  brakes 
[needed,  371 
disadvantages  not  visible,  242 
effect  on  loc.  and  car  repairs, 

[♦203 
on  net  train-Id.,  diag., 

.     ,       ,  ^552 

on  train-load,  536 

estimating  by  eye,  844  -|- 

fixing  rates  of,  893 

and  inundations,  783 

high,  causes  favoring,  671 
expedients  for  red'g,  675 
great  inclines  of  world, 
[♦698-9,  ♦700 
handling  trains  on,  diff'y, 
p.  c.  wt.  eng.  on,  669 
rel.  train-l'ds  on,  ♦669 
speed  on,  369 

how  expressed,  537 
in  England,  538 

humps  in,  dangerous,  367 

hydraulic  grade  line,  625 

improving,  and  more  traffic, 
[comp.  value,  112 
double  track,  806 


Grades 

Grades —  Com  in  u  ed. 

improving,  loco.   q.v.   design 
[an  obstacle,  478  — 
on  old  lines,  788 
inherent  objections  to,  328 
irregular,  effect  on  pass,  ir'ns, 

length  of,  effect  on  virt.  pro- 

[file,  704 
per  sta.,  boriz.  and  along 

,       ,   u     ^,         •     [slope.  *34i 
level,  hardly  exist,  551 

limit'g  eff't,  and  rail-wear,  379 

locating,  field-work  for,  865  -f- 

selecting  rate,  675 

long,  errors  as  to,  329 

longest  in  the  world,  925 

switchbacks  for,  943 

loss  of  wt.  on,  539 

low,  adapting  to  topog'y,  665 

compens'g  for  curves,  620, 

projecting,  660  [652 

reducing,  665 

wrong  use  of,  671 

moinenlum,  def.  and  ex.,  344 

motion  of  trains  on.  342  -f 

objections  to.  two  distinct,  327 

of  repose,  def.,  341 

table,  ^358 

French,  ^522 

pass.,  all  speeds,  ^579 

last  car  in  sags,  362 

one  p.c,  effect,  changes  in.  on 

[loco,  mileage,  ^557 

pass,  locos,  aff'd  little,  479 

PER    CENT    CHANGE    NET    LOAD 
[due  TO  CHANGES,  554-7 

projecting,  890 

descent  ag'st  valley  slope, 

[682 

GENERAL  RULE  FOR,  66o 

lifting  bodily,  892 
long  g's  dangerous,  893 
ovtr  streams.  893 
selecting  rate,  675 
shallow  cuts  bad,  126,  893 
prop'n  traffic  affected  by,  576 
rale  of,  as  aff'd  by  care,  659 
and  light  rys.,  758 
effect  on  cost,  minor  de- 
[lails,  581 
fitting  to  ground,  ex.,  670 
improving  old  lines,  785 
order  of  importance,  768 
projecting,  893 
p.  c  wt.  eng.  to  train,  all 
[grades,  66g 

PER    MILE    AND    P.     C, 

small  imp  ce  with 

[pushers,  ^587 

REDUCING,  BY  LOWER  PASS. 
[speed,  579 
by  more  care,  ex.,  667  & 
relative  imp'ce,  ex.,  395 
net  load  on,  ^574 
train-load  for  all,  ^669 
resistance  of,  536-40 

effect  on  gross  load,  540 

on  net  load, 541 
formulae  for,  540 
gain  by  concentrat'g,  ^587 
how  determined,  339 
rolling  frict.  adds  to,  34^ 
rising  above  and  below,  diff.. 

[367 


I 


964 


INDEX, 


INDEX. 


965 


Grades 

Grades — Continued. 

ruling,  AND  LIMITS  OP  cunvA- 

[tuke,  652 
eflfect  on  pass,  trains,  577 
devices  lor  reducing,  659 

NATUKE  OF  EXPENSK  FROM, 
u  ,1587  + 

pusher  vs.  throuf^h,  667 
rule  for  reducing,  665 
60  ft.  and  6°  comb'n.  656 
speqd,  slow,  effect,  622 
stations  on,  788  -|- 
starting,  TO  ELiM.  f.xtra  fric, 
station,  ^.7'.,  788-4-  [512 

and  pass,  trains,  4Q1 
statistics  of,  U.  S.,  Stales,  etc., 

stops,  q.v.,  on,  ♦512 

importance  of  (elev.  rys.), 

switchback,  947  -f- 

TRAIN-LOAU    ON    ALL,    FOR   ALL 
[logs..  *543  -f 

(small  table),  •593 
undulating,    q.  v.,    and    im- 
[proving  old  roads,  799 

eliminated  by  speed,  348 

error  as  to,  329 

little  eff't  on  pass,  I'ns,  592 

on  light  railways,  755 

safe  limits,  356 
uniform,  hard  to  secute,  586 & 
virtual,  q.v.^  and  actual,  diflf., 

length  makes  no  diff.,  799 

starting,    ex.   of    compu- 

[tation,  *S59 

Grading,  abandoning  old,  cost,  787 

Grain,  bushels  of,  per  mile  r'y,  +90 

Northwest  receipts,  728 
Grand  Central  sta.,  N.  Y.,cost,  70 
Grand  Trunk,  capM  and  earnings. 

L*io7 
competitive  disadv's,  240 
Grate  area,  loco.,y.7/.,  act'l,*407-io 
H.  P.  p.  sq.  ft.,  expt.,  484 

limits  for,  451-3 
wt.  on  drivers,  p.  sq.  ft.,  452 
Gravity,  acceleration  of,  333 

action  on  incl'd  planes,  339,  536 
railways,  nature  of,  and  ex., 
rail-wear  on,  122  [691 

tests  of  train  res.,  497  [124 

Great  Britain,  cross-tie  practice, 
curves,  mode  of  design'g,  266 
curves  not  compens'd,  621 
fastest  trains,  and  Am.,  *529 
fuel    g.v.    consump.   in,  and 
lU.  S.,  131-3 
cause  of  dm.,  134 
expenses  per  mile  road,  116 
grades,  modes  of  expr'g,  538 
growth  traffic,  q.z'.,  131-2 
locos.,  f.v.f  comp.  safety  on 
[curves,  434 
duty  of,  comp.  with  Am., 
life  of  parts,  *4i9   [*i59  & 
maint.  per  year  per  eng., 
[and  Am.,  ♦159 
p.  c.  labor  and  mater'l. 

[*I52  & 

no.  and  work  of,  ♦159-60 
scrap  value,  ^20 
type  of  wheel-base,  428 
wt.  and    cost,  and  Am., 
error  as  to,  *4i6  [*4ii-i- 


Gre-Hau 

Great  Britain— r<)«//««^a'. 
no  grade  crossings,  8ro 
op'g  exp..  cts.  and  p.  c,  ♦178 
pass,  speed,  why  higher,  ♦530 
p.  c.  op'g  exn.,  *iio,  *i78 

recent  tendency,  116  [*io5 
rects.  p.  inhab.  pass,  and  fgt., 
switching-mileage  prop'n,  135 
terminals,  y.r.,and  term,  exp  , 

[827  & 
train-mile  cost,  etc.,  *ii6 

Vignoleson,  187 
wages  in  and  Am.,  *isi 
Great  Eastern  r'y.  locos.,  cost  and 
[miles  per  yr.,  ♦159 
traffic  and  fuel  consump..  ♦131 
Great  inclines  of  world.  *698-9 
Great  North,  ry.,  fastest  trains, 

1*529 
locos.,  cost  and  miles  per  yr, 
repr.  details,  *i45       [•iso 
Great  So.  &  W.  ry.  ^ 

locos.,  cost  new  details,  155 
per  ton.  details,  ^ii 
repairs  in  detail,  •144-5 
and  renewals,  146 
many  small  details.  149 
p.c.  labor  and  mat'ls,  *i52 
wt.  and  cost  in  det'l,  *4i6 
motive-power  exp.,  ♦133 

details.  *i47 
wages  in  shop,  *isi 
Great  system  of  r'y.  U.  S.,  *7i9 
Great  VVestern  r'y,  fastest  trains, 

[*5*9 
locos.,  cost  and  miles  per  yr.. 

_,     „    [*»55,  *iS9 
p.  ton,  det  Is,  *i55,  *4ii 

repr.  details,  ♦145 

motive -power   exp..'  details, 

trarncand  fuel  consump.,  *i3i 
Green  river,  fall,  841  [533 

Grossman.  J.,  on  lubrication,  516, 
Growth  of  r'y  system,  world,  *43 
traffic,  q.v.,  irregular,  85 
how  to  estimate,  87 
ratio  to  rate  interest,  85 

TO     BK     CONSIDERED    ONLY 

[for  3  to  5  VRs.,  80,  85 
in  no.  engs.,  Engl.,  *i45 
of  train-load,  q.v.,  •97-101 
Guadalajara.  Mex.  Nat.  loc'n  to. 
Guessing,  effect  of,  658  &         [723 
Gulf  States :  area,  pop'n,  earn  gs, 
[p.  m.  and  head,  etc.,  *9i 
fall  rivers  in.  8ti 
gen.  r'y  statistics.  ♦88 
pass,  and  frt.  haul  and  tratO' 
[I'd,  etc.,  V 
(Sfe  South.) 
Gyration,  radius  q.v.  of,  739 

Hachures,  use,  873 
Hackmen  profit  by  bad  location. 
Hammer  blow,  447  [60.  6a,  68 

Hand-level,  use  of.  838,  847  [*26< 
Hannibal  &  St,  J.  align't  statist, 
Harlan  &  Hoi.  Co.  pass.  car.  *49i 
Haul,   extra,    not   a    burden    on 

[traffic.  61 

pass,  and  freight  C,  C,  C.  & 

[I.,  12  yrs.,  224-5 

U.  S.  and    States,   *97,  ♦us, 

['217  & 
L.  S.  St.  M.  S.  do.,  ♦9a 


Hau-lll 

Haupt,  H.,  on  asst.  engines,  585 

on  inclined  planes,  944 
Head  resistance  table,  522 

eflfect  on  fuel,  530  — 
Headway  of  trains,  det.  and  elev. 

[r'ys,  646 
Heat  from  journal-fric.,y.7'..  314 
Heating  surface,  various  locos., 

„  _,  [*407-io 

Heat-units  and  temperature  dis- 
in  fuels,  *45o  [tinction,*454 
in  steam,  various  press.,    *454 

Heavy  construct'n,  g.v.,  error  in, 

[20  & 

Highways,  errors  resulting  from, 

[835,  850 
examples,  667,  853,  936 
grades  of,  illusions,  844 
old  Mexican  road,  941 
Higley  roller  journals,  923 
Hill,  A.  F..  loco,  test  by,  445 
Hills,  propinq'ty  of,  oc.  illu'n.  846 
Holland,  align't  statist.,  *a6s   [*^^ 
pop'n,  r'ys,  wealth,  etc.,  ♦27, 
Hopper  cars,  dimens.,  etc.,  *486-7 
Horizon,  best  line  lies  beyond,  837 
Horse-cars  benefit   by  bad   loco., 

[60,  62,  6a 
traffic  of  N.  Y.,  ♦714 
per  inhab't,  •714 
Horse-power,  cost  of,  stationary- 
definition,  338,  403  [eng.,  •531 
effective  and  indic'd.464 
increases  as  7'*,  *522 
lbs.  steam  per,  loco..  456  -j- 
stat'n'y  eng.,  *53t 
theoret'l,  all  press.,  *46» 
min.,  fuel  per,  469 
persq.  ft.  grate,  451,  484 
to  utilize  full  adhesion.  ♦45, 
Horse  r'y.  longest  in  world,  ojo 
Houses,  U.  S.,  value,  25 

and  r'y  accidents,  258         [6«4 
Huayacan,  Cuchillode,  spirals  at, 
Hudson,  C.  H.,  loco,  teste  by,  701 
Hudson  river,  fall,  841 
ocular  illus*n  on,  848 
water  of,  purity,  ^378 
Huds.  R.  Rd.,  alignoient  statist., 
level  grades  of.  327  [*259> 

(See  New  York  C.  &  H.  R.) 
Hut.  ocular  illus'n  as  to,  847 
Hydraulic  grade-line  and  sags.  q. 
Hyperbola,  locus  of,  404     [v.,  625 

Ice  and  snow,  cost  due  to,  126 
Idaho  r  area,  popu.,  sidings,  p.  c. 
opg.  exp.,  earnings  per  mile  and 
head,  '90  ;  wealth  per  cap.,  *26 
Illegitimate  r'y  enterprises,  14 
Illinois  :  alignment  statist.,  ^262  ; 
area,  popu.,  sidings,  p.  c.  opg. 
exp.,    earnings    per   mile    and 
bead, *go 
interlocking  law,  814 
water  in,  quality,  *378 
wealth  per  cap.,  26 
Illinois  Cent.,  align't  statist,  *262 
flucts.  in  stock,  '46 
loco,  old,  wt.  in  det'l,  *4i4 
maint.  way  exp.  by  items,  ♦120 
miles  and  earn'gs,  *7i9 
opg.  exp.  and  trains  per  day, 
rates  on,  fall  of,  *726        [*«7* 
train-Id.  growth,  *ioi 
Illusions,  ocular,  q.v.,  84^ 


Imp-Jac 

Impacts,  law  of.  561 
Imperceptible  shp.  q.7>..  445     [785 
Improvement  of  old   lines,   q.v., 
Inception  of  r'y  projects  (ch.  i.),  13 
Inclined  plane,  theory  of.  536 
lifting  car  up  by  vel..  343 
Inclined  planes,  gravity  on,  339 
law  of  motion  on,  339 
passing  summits  by,  689 
pros  and  cons,  686  [*378 

Incrustation,  loco.,  q.v., aval,  daily. 
Indeterminate  problems,  bad  so- 
[lutions  of,  7 
India:  locos., no.  and  work  of,*i59; 
p.  c.   of  operating  exp's,  *iio; 
railway  equipt..  etc.,  ^43  ;  roll- 
ing-stock p)er  mile.  *47 
Indiana :  alignment  statist.  in,*26i 
area,  popu.,  sidings,  p.  c.  opg. 
exp.,    earnings    per   mile   and 
bead, *9o 
interlocking  law,  813 
wealth,  per  cap.,  26  [*26i 

Indian.,  D.  &  S.,  align't  statist.. 
Indicator  diags.,  exs.,  all  cond'ns. 

T   .,•   .,*''f°''yo/' 459.467 +[*476 
Individuals,  each  a  traffic  unit,  715 
Intiernillos.  location  at.  685 
Ingenio  river,  location  in,  675 
Initial  friction,  q.v.,  919  & 
Inspection  of  steel  rails,  q.v.,  neg- 

[lected.  119 
Insurance    cost.     Chicago     r'ds, 
sections,  U.  S.,  *i7o-6  [*i74-6 
trunk  lines,  ♦172-6 
Interchange  of  frt.  cars,  rates  and 
[conditions,  164 
Intercolonial,  rolling-stock  per  m.. 
Interest  charge,  nature  of,  106  [^47 
compound,  tables,  *8o-83 
how  .iffects  location,  17 
on  add'l  locos.,  570,  604 
on  bonds,  p.  c.  of  rev.,  sections 
[U.  S.,  ♦108 
Interlocking,  amt.  used,  England 
and  asst.  eng  ,  601  [&  U.  S.,  809 
easy  curves,  655 
grade-crossings,  790,  802, 
switchbacks,  946  [809 

cabins  for,  size,  809 
cost  of,  810-11 
Inundations  of  r'y  lines,  783 
Invention  and  engineering,  i 
Iowa:  align't  statistics,  ♦262;area, 
population,  etc.,  90 
fall  rivers  in,  841 
growth  r'ys,  popu.,  earnings, 

u     ,[etc.,*77 
r'y  earnings  per  head,  etc.,^77, 

[*9o 

sidings,  p.  c.  opg.  exp.,  etc.,  90 

wealth  per  cap..  ^26 

Iquique  r'y,  Peru,  Fairlieloc.,^4io 

Irrigating  ditches,  oc.  illus'ns  as 

[to,  847 
Italy,  adhesion  in,  assumed.  443 
locos.,  no.  and  work  of,  ♦160 
popu.,  r'ys,  wealth,  etc.,  ^27, 

[*43i  *45 
rolling-Stock,  traffic,  etc.,^43 
p.  c.  opg.  exp..  ♦110 
rects.  per  inh'abt.pass.and  frt., 
Ixtaccihuatl,  mt*n,  927  [♦los 

Jackson,  L.  &  S.,  align't  statistics, 

[♦262 


Jal-Lak 

Jalapa,  highway  via,  928 
horse  r'y  to,  930 
line,  description,  932 

low  grades  needed  for,  670 
map,  928 

Mexican  rep't  on,  930 
profile,  condensed,  698,  701 
zigzag  devel't  on,  678 
Janney  car-coupler,  489 
Jeans.  J.  S.,  table  from,  *i59-6o 
Jervis,  J.  B.,  invented  loco,  truck, 

[421 
Journal,  effect,  size  of,  51^,  012 
M.  C.  B.  st'd,  499 
max.  I'ds  on,  513       [tion,  ^204 
bearing,  cost,   and  deprecia- 
roller,  912,923 
weight  of,  ^163 
box,  defects  of  ord'y,  510  -{■ 

improved,  511 
friction,  509, 913 

as  affected  by  I'd,  503,  611 
expts.  as  to,  913 
app'sfor,  914 
normal  am't,  ^509 
starting,  512  [24* 

'Judgment."  danger  of  trusting, 
Junction  points  for  fr't  cars,  166 
Justifiable  expend,  for  future  $1, 
to  save  $1  per  y'r,  ^83        [*82 
Jura  r'y,  profile,  698 

Kansas:   area.popu.,  sidings,  p.c. 
opg,  exp.,  earnings  per  mile  and 
head,  *9o;  wealth   per  cap.,  ^26 
Kansas  Pac.  loco,  perf'ce,  *439 
Kentucky,  align't    statist.,   ^264; 
area,  popu.,  sidings,  p.  c.  opg. 
exp.,    earnings    per    mile    and 
head,  ^90;  wealth  per  cap,  ^26 
Kentucky  river  bridge,  wt.,  901 
Kindling  fires.  Ph.  &  R.  cost,  *2oo 
Kingwood  tunnel,    temp'y    line, 

[♦700 
Labor,    wages,   q.v.,   Amer.   and 

[Eng.,*4i7 

and  mat  1.  cars,  q.v.,  *i6i-4 

locos.,  y.7/. ,  details,*i33, 

Eng.,  ^133    [*i4S,*i5i 

French.  ^147  [19 

Laborer,  useless  work  no  gain  to, 

Lagging:  loco.,  <7. 7/.,  eflfect  of,  508 

wt.  and  cost,  ^413  -j- 
Lake  Erie  &  W.,  align't  .stat.,^26i 
Lake  Shore  &  M.S. .align't  statist., 
ditching  on,  773  [*26i 

chart  of  financial  record,  33 
exp'ts  on  frt.  speed,  370 
flucts.  in  stock,  *46 
freight  car,  reprs.  on,  162 

renewals  separately,^i6s 
fuel  tests,  529 
loco,  boiler,  life,  *4i9 

water  supply,  +420 
miles  and  earn'gs,  *7i9 
motive-power,  exp.  det'ls,*i47 
radiation  tests,  313 
rates,  through  and  way,  E.  & 
[W.  b'd,  226,  115 
fall  in,  *726 
sidings,  total,  etc.,  ^825 
statistics  frt.  trafl[.,  *98 

pass,  traff.,  ♦gS 
ton-mile  rects..  etc..  ♦iis 
track  Buflfalo  yd  ,  *82i 
train-resist,  tests  of,  518,  909 


Lan-Loc 

Lancashire  &  Y.  loco,  repr.  det'ls. 

Landscape  gardening  and  maint. 

[way,  124 
Landslides,  accidents  from,  *247 
Lap,  def'n  of,  470  [122 

Launhardt,  est.  by,  loc.  rail  wear, 
Latimer  rerailing  guard,  900 
Latitudes  and  departures, 

use  of.  886  [comput'g.  889 

Latrobe,  B.  H.,  cxpts.  on  adh's'n, 

[temp'y  iines  by,  445.  7(x> 

Lava,  basaltic,  character,  684  [443 

river  of,  928-32 
La  Veta  Pass,  *698-9 
Lead,  loco.,  470 

of  freight,  etc.   {See  Haul.) 
Leadville,  high  line  to,  695  4- 
Legal  exp's,  various  rds.  and  sec- 
[tions  U.  S.,  ♦170-6 
Lehigh  &  Susq.  loc.  perform.,  *44o 

sharpest  curve,  ♦325 
Lehigh  Valley  align't  statist.,  ^260 
Consolidation     loc.    invented 
[on.  278,  423 
loc.  performance,  ♦438-40 
Mastodon,  details,  ^410 
Id.  on  drivers  per  sq.  ft. 
[grate,  ^452 
pass,  car,  st'd,  ^491 
rail-sect'n  and  wh'l  tread,  310 
track  Buflfalo  y'd,  ♦82- 
Level,  hand,  use  of.  838.  847 
line,  guessing  at.  838 
party,  organiz'n,  8t>i,867 
slope,  882 
Levelling  on  preliminar's,  861,  865 
Lewisbg&  Tyrone  align't  statist., 

1*260 
Lighters,  no.,  N.Y.  term'ls,  *8i9 
Light  lines  in  difficult  c'try,  20  & 
Light  rails,  q.v.,  and  I't  r'ys,  737 
Light  railways,  737 
and  curvature,  749 
and  dist.  (choosing  route),  722 
and  value  low  grades,  576,  758 

CONCLUSIONS  AS  TO,  761 

expedient  economies,  748 
rel.  value  of  more  traflf.  10,^713 
total  cost,  758  & 
why  do  not  multiply,  737 

Lignite,  H.  U.  in,  ^450  [on.  679-f- 

Lima  &  Oroya  ry.,  developments 
profile,  698-9 

Limiting  curvature,  q.v.,  620 
grades,  q.v.,  536 

Line,  always  easy  to  get  a,  832, 840 
best,  lies  beyond  horizon,  837 
may  survey  a,  but  no^  recon., 
no.  of,  to  survey,  ^.7'., 834  [835 
worst  errors  in  wrong  selec'n, 

[832 

(See  Route,   Location,  Topogra- 
,  phy.) 

Line  cars,  def  n,  i68 

mileage  of,  168 

relative  cost  reprs.,  ^161 
Link,  coupling,  q.v.,  forces  act- 

[ing  at,  303 
Link-motion,  invention,  etc.,  458 
Liverpool,  sidings  at,  827 

station  exp.  at.  828 
Live-stock,  U.  S.  value,  ^25 
Local  freight,  sidings  for,  ^821  + 
Local  rates,  q.7'.,  constant  ratio 
[to  through,  224-6 


mmm 


966 


Loca— Loco 

Local  traffic, i^.7/., true  classifi.,  an 
effect  distance  on,  213 

Locating  engineer,  g.v.,  altitude 

[of  mind,  21,  831  +,  840,  855  & 

end  of,  2  {(q.v.),  684 

Location  and  transition  curves, 
aptitude  for,  and  topog'y,  880 
art  of,  lies  in  choice  of  route, 
av.  practice  in,  4,  583  [840 

bad,  reasons  for,  4  -|- 
care  in,  and  amt.  curv.,  656  & 

CHOICB  OF  ROUTE  WHEN  CLOSE, 

[583 

freer  with  sharp  curves. 

CONDUCT  OF,  831  [656 

correct'g  by  trans'n  curv..  870 
curve  limit  and  topog'y,  655 
difficulty    of  good   prac.    in. 

_  [2  4-,  926 

effect  on  rev.,  48 
errors  in,  &  cont'r  maps.  876 
how  originate,  658 
worst  in  recon'sance,832 

GENERAL    RULES    FOR,  66o,  694 
LINE   ALWAYS   EXISTS,  832,  840 

marvellous  feat  sci.  skill,  qt2 
office  chair  ioc'n,  880  —      [787 
old  lines,  common  errors  in, 
over  prairie  ridge,  66i  4- 
paper,  q.v.,  868  + 
party  for,  867  [328 

possibl«  effect  of  electricity, 
project's  (y.t'.)  and  mapping, 

[886,  890 

RULE        FOR,      IN        MODERATE 

[COUNTRV,  694 

running  in  the,  867  [698 

sharp  curves  give  new  routes. 

Western  States,  errors  in,  6. 

.  [21,  ^263,  330,  588,  660 

Loch  Katrine  water,  purity,  *378 

Locomotive  engine,  399 
adhesion  of,  434 

AMT.   OF,  435  -I- 
computing  from  I'ds,  444 
defic'y,  how  shown,  405 
effec»^  of  changes  in,  *44o 
exp'ts  as  to,  434  -|- 
extreme  resorts  to  incr., 
maximum,  440  [424 

per  sq.  ft.  grate,  *45a 

RATIOS    OF,  437 

Am.  and  for'n,  443 
resistances  which  tax,  49a 
safe  limits  for,  441 
sand,  effect,  437 
slipping,     q.7i.,     drivers, 
flaws,  435  St. 
imperceptible,  445 
speed  does  not  affect,  435 
winter  and  summer,  443 
American,  advantages  of,  422 
decreasing  use,  114 
dimensions,  etc.,  407 
invention  of,  421     [*407-|- 
wt.    various   parts,   •400, 
and  curvature,  f.r-.,  278  & 

stationary  q.71.  engs.,493 
assistant,  q.v.,  585 
boiler-power,  449 

and  tractive  p.,  ♦453 
blast-nozzle,  sizes,  '409 
combust'n  and  evap'n,45o 

max.  rate,  449 
deficiency  in  power,  how 
[shown,  405 


INDEX. 


Locomotive 

Locomotive — Continued. 

Doiler   power,    diagram   of 

dimensions  of  b.,  407-11 

various  parts,  changes, 
efficiency  high,  457  [*409 
energy  stored  in,  *454 
evap'g  boilerful,  time 
[for,  456 
evap  n,  average  rate,  449 
explosions,  *:?47 


JNDEX. 


96; 


Iire-l>ox,  life,  *4i9 
as  aff.  by  water,  *42o 
fractures,  * 
size,  *407- 

grate  area 


420 
410 
and  load    on 


[drivers,  *45a 
H.  P.  per  sq.  ft.  grate,  484 
incrustation,   amt.    daily, 

V.  ■  t*378 
incrusting  solids  in  water, 

[♦378 
lbs.  coal  per  h.  p.,  *46i 
life  of  boiler,  ^ig 
loss  of  heat  in,  a  v.,  *456 
low  water,  gain  by,  455 
pass,     and     fr"t     service 
[same  b.,  403 
p.  c.  efficiency,  457      [402 
power  measured  in  ft.  lbs., 
radiation,  q.v.,  winter  and 
[sum.,  508 
shell,  thickness,  *42o 
steam,    lbs.  per  h.p. 

pressure,  ♦409-10 


av., 

U51 


boiler  and  cffec,  ♦479 
cutting    down,    efi't, 

[405 
higher,  effect,  408,  468 

high,  Ger.  and  Swiss, 

*5»9 
reserve  of,  453-4 

steam-chest     and     b. 

[press.,  473 

tendency  to  incr'se  b.,  408 

tubes,  life  of,  *42o 

no.  and  size,  *409-to 

wt.  and  cost  *4ia-|- 

washing  out,  *42o 

water  supply.quality,  ♦378 

weight  of, ♦407-1 1. ^is-e 

w'ts,  q.v.,   all   parts   and 

[maps,  ♦400,  *4i2  -f- 

to  incr'se  boiler  power 

[id  p.  c,  400 

water  and  steam,  '407- 

1  u         .,  •,     L"'    '♦54 

coal  burned  per  mile,  ^129 

English,  *i3i-2  I 

Penn.  R.  pass.,  ♦134 

compound,  chances,  133 

Consolidation  I.,    q.T>.,    def'n 

[and  origin,  423 

cyl.  q.v.  tract,  power,  553 

change  in,  Penna.  R.,%09 

increased  use  of,  114 

most  used  on  heavy 

[curves,  281 

wts.  of  diff.  sizes,  701,  769 

various  parts,  '400     ['564 

cost  new,  all   types  and  wts.. 

Am.   and   Eng.    per  ton, 

[det'ls,  ^ii 

as  affected    by  wt.,  etc., 

[•4",  ♦564 


Locomotive 

Locomotive — Continued. 

cost,  builders'  approx.  rules, 

details,  150-1-2-4-5 
narrow-gauge,  *564 

disadvantages.  565 
per  ton,  all  types,  ♦564 
cost  of  operating,  121  -f- 
as  aff'd  by  wt.  eng.,  560 
as  pushers,  6:1  -f- 
^cost    of    double    no.   for 
[same  train,  ♦568,  *57i 
double  wt.  for  same  train, 
[*567 

^ain  by  fully  Ioading,*587 
intermitteni  service,  eff  t, 

[603 

mat'l  and  labor.  Am.  and 

[foreign,  ^u  & 

per  year,  *i48  & 

shop  and  gen'l  exp.,  *4ii,. 

[*4i7 
standing  still,  cost,  602 

cylinder  power,  457 

all  cyls.  and  drivers,  •479. 

and  slipping  drivers,  406 

back  pressure,  ami..  472 

compared     with     adhes., 

[diag.,  552 

cut-on,    no    tendency    to 

[early,  ♦467^ 

denciency,    how   shown, 

*  11        •  u  .  f<°5^ 

falls  with  speed,  457 

expansion,  theoret.,  gain 

.     ,  ,  [by,  467 

practical  losses.  470 
indicator  diags.,  *476  -\- 
limits  of,  ex.,  703 
losses  of  eff 'y,  chief,  470 
of  frt.  eng.  and  speed,  474 
often  too  little,  406 
ratio  to  wt.   on    drivers. 

reciproc  g  parts,  loss  by, 

speed,  effect  of  reduc  g, 

varied  easily,  400 
wt.  to  increase  cyl.  p.  lo- 
[p. c,  401 
why  should  be  in  excess, 

cyliDders,  cold  or  hot,  eff't. 

[476- 
clearance  space,  eff't,  472 
common  error  of   design 

[iOi  474 
disadvan.  of  too  large,  40a- 
entrained  water  in,  470 
large     cyls.     disadvanta- 
[geous,  406- 
lead  and  lap.,  def.,  470 
loss  of  press,  in,  *4io 
radiation,    external,   315, 

[377,  471 
internal,  nature,  315,  471 
locos.,  376 

size  of,  why  used  to  de 
[scribe  engines,  40a 
steam  cap'y  of,  *459 
design  of,  402-4- 

fimits  for  same  boiler,  40% 
logical  order,  402 
narrow-gauge.  7^1     [*«4« 
p.  c.  standard,  P.  R.  R.^ 


Locomotive 

Locomotive— C(7«//««(»</. 

dimensions  of  boiler,  ♦407-410 
chimney,  *409-io 
drivers,  French,  535 
frt.,  Gt.  East.  Ry.,  ♦132 
most  powerful  in  world, 

[♦410,  ^421 

pass,  eng ,  477 

Tables    of     all   types, 
[♦407-10,  ^42 1 

various  eng.,  ^279 
earnings  per  year.   Am.  and 
[Eng.,  ♦159 

sections,  U.  S.,  ♦Bg 
Fairlie,  def.  and  use,  424 

in  Mexico,  932 
frame,    wt.   and    cost,    ♦400, 

[*4i->  + 
frt.  Iocs.,  op'g  conditions,  478 
friction  resist.,  q.v.,  of,  530 
fuel  q.v.  consump.  light,  315 
future      improv'ts,     possible 
[efltect,  328 
handling  locos.,  breaking  in 
[two,  359 
cut-off,  usual,  469 
drawing  fires,    fuel    lost, 
first  in  first  out,  141       [199 
heavy  engines  and  break- 
[ages,  360 
running  backward,  950 
starting  of,  how  dune,  797 
switching    Iocs.,    use    as 
[pushers,  79a 
using    heavier   vs.   more, 

u    .    u  .  [560 

height  cent,  of  grav.,  371 
horse-power       in       practice, 

computing  do.,  338 
interest   charge    on,    due    to 
[grades,  570,  604 
hmitations  of,  399  -f- 
and  grades,  327 
and  boiler,  406 
limits  to  work  of,  399 
mileage  of.  Am.  and  Europ'n, 
„  [*i43.  ♦159-60 

as  affected  by  age,  ^418 
C,  B.  &  Q.,  20 years,  157 
exaggerations  in   statist., 
life,  q.v..  ^143        [103,  142 

Pass.  max.  N.  Y.  C,  ^143 
enna.R.R.  pass,  and  fr't. 
[t886,  ♦51-84,  ♦mo,  ♦418 
U.  S.  sections,  ^97 
run  in  general  office,  142 
special  performances.  ^419 
switching,     q.v.,     prop'n 

1/      *  *        «      [mileage,  135 
hfe  of,  ♦143,  ♦418-9.  ^438 

various  parts,  ^419 
machinery,  breakages  of,  ^247 

cost  new,  ^41 2  4- 

essential  elements  of,  457 

link-motion,  458 

repairs,  ^143 

slide-valve,  fric.  of,  532 

valve-gear,  458 

weights  of,  ^400,  ^412  & 
Mastodon  loco.,  423  [553 

cyl.  and  adh.  tract,  power, 

dimensions,  etc.,  ^410 

increased  use  of,  114 
Mogul  loco.,  def'n,  422 

dimensions,  etc.,  ♦408 


Locomotive 

Locomotive— C<;«^z««^^. 

Mogul  loco.,  max.  w't,  769 
motive-power   record,   Penn. 
[R.R.,  1851-84,  ♦mo 
number  of,  various  countries, 

[*i6o 
English,  ^148 
per  mile  all  countries.^43, 
[♦47,  ♦mS,  ♦160 
sections  U.  S.,  ♦Bg 
No.  of  separate  pieces  in,  ♦415 
passenger  l.,coal  consumption 
[light,  132 
grades  affect  little,  479 
need  much  tract  pV,  407 
power  limited   by  boiler, 

performance      of     American 
[Iocs,  (long  table),  ^438 
Mastodon  loco.,  ^410 
rail- wear,  q.v.,  due  to,  122  & 
repairs,  cost  of,  139 

as  affected  by  align't,  ^188 
class  of  engine,  ♦146-8 
curvature,  315 

radius  of,  641 
distance,  201 
grade-crossings,  202 
length  of  trains,  570 
rise  and  fall,  377 
w't  of  engine,  144,  563 
av.  Chicago  r'ds,  ♦174-6 
sections  U.  S.,  ♦170-6 
trunk  lines,  ♦172-6 
cleaning,  147 
details  by  items,  ♦143-9 
deterioration,    causes  for 
[and  rates,  202-3 
distribution  to  causes,^203 

to  loco,  part?,  153 
effect  growth  q.v.   traffic 
[on.  153  & 
English,  ^133 
and  American,  42a 

details,  ^144 
fittings,  ♦mj  [153 

gen'I  exp.  often  notinc'd, 

KSee  Motive  Power.) 
gen.  rep'rs,  freq'cy,  420 
labor  and  mal'al.  Amer. 
[and  foreign,  ♦143-5  & 
Mass.,  etc.,  142 
minor  details  (many),^i4g 
painting,  ^143 
pass,  and  fr't,  ♦148 
past  history  of,  C.  B.  & 

[Q-.  158 

Penna.  R.,  35  y>rs,  140 

p.  c.   m  shop,   P.   R.  R., 

[*i40 

p.  c.  renewals,  ♦146-7,^563 

p.  c.   round-house  rep'rs, 

[♦145-6,  ^149 

per  year  per  engine.  Am. 

[and  Eng.,  ^159 

running  gear,  ^143 

shop,  tools,  and  general 

{q.v.  exp.,  153 

tenders,  q.v..  ♦143-6-7 

trucks,  q.v.,  ^143         [*i29 

trunk-line  exp.,    34    y'rs, 

resistance  of,  av'ge,  ^465,  ^530 

experim'ts,  q.v.,  as  to,  279 

accurate,  diffic't,  533 
coupled     drivers,     extra 
[for,  534-5 


Locomotive 

Locomotive — Continued. 

resistance     of,    in     practice, 

[*463-h 
head,  at  high  speed,  ^522 
error  by  neglecting,  533 
internal,  no    tax  on    ad- 
[hesion,  532 
machY  separately,  534-5 
probable  amt.,  531  4- 
slide-valve  fric,  532 
true  test  for  determining, 
running  gear,  421  [49a 

Am.,    distinctive    peculi- 
[arities,  421-5 
comparative     safety     on 
[curves,  diag.,  433 
coupled    drivers,    extra 

A-  V     ,  '^['■'*^'  434-5 

driving-wheel  base,  rota- 

[tion  of,  427 

foreign,  hard  on  track,  425 

hammer-blow,  447 

H.  P.  transmissible,  452 

journals,  sizes,  ^409 

load   on  driv.    per  sq.  ft. 

...  .     [g'ate,  ♦45? 

slipping  drivers,  285,  406, 

[797 
tires,  cost  q.v.  maint.,  316 

truck,  mechanics  of,  426 

•  u.     ^        L+'  433 

weight  and  cost,  ♦413  -{-, 

♦400 

wheel-base  lengths, 

[♦407-10 

wheel- wear,  C.  &  A.  r'y, 
[♦288 
runs,  tendency  to  incr'se,  169 
starting  q.v.  power  of,  352  & 
slack,  effect  of,  490  [424 

switching,  a.v.,  def.  and  use, 

no  N.  Y.  terminals,  ♦819 

per  cent  of,  sect'ns  U.  S., 
[♦i8i 
tank  Iocs,  as  asst.  engs.,  592 

why  advantag's,  551,  554 
ten-wheel,  def'n,  ^423 

dimensions,  etc.,^4o8 
theoretical  defect,  most  sen- 
three  forces  of,  399      [ous,  329 

deficiency,  how  shown, 

-^  t4oS 

tractive  power,  q.v.,  434 

average  between  stations, 

.532 
compared    with    single 

[tests,  551 
all  cyls.  and  drivers,  ^479 
as  modified  by  speed,  346 

by  type  of  eng.,  280 

causes  of  fluct'ns  in.  ^440 

comparative,  cylinder  and 

[adh.,  55a 

compared     with      boiler 

[power,  452-3 

with  weight,  all  grades, 

[♦688 

deficiency,    how    shown, 

[405 
economy    of      fully    em- 
[ploying,  587 
effect    low   boiler  press., 

[405 
French    practice     as    to, 

head  resistance,  ♦520-21 


968 


IXDEX, 


INDEX. 


969 


Loc— Los 

Locoinoti  \ti— Continued. 

tractive  power,  high  speed, 
horse-power,  *5i9  *i\() 
imperceptible  slip,  445 
increases  faster  than  fuel 
[burned, 133 
loss  at  speed,  nature  of, 

[473 

ON    AI.L   GRADES   IN    DAILY 

[service,  *544  -j- 
fass.    and     freijjht    Iocs., 
[diflf.,  478 
pass.,  needs  much,  407 

P.O.  CHANGE,  FROM  CHANGE 
[in  any    GRADE,  554-7 

p.  c.  wl.  train  to  wt.  eng., 

[all  grades,  669 

ratio  to  total  wt.  loc.,  ♦542 

weight  train,  all  grades, 

[—  *544  4-.  *593 


[ 


f 


speed  reduces,  474 
starting  needs  most,  474 
tank  locos..  551 
testing  by  fiuct'ns  of  vel., 

I-  .     »  ^792 

why  great  in  Am.,  422 

wire-draw'g  reduces,  474 

wt.,   to   increase  lo  p.  c, 

trimmings,  wt.  of,  *4oo      [401 

TVPKs  OF,  defs.,  422 

change  in  most  used.  114 

compar.  cost,  new,  *565 

effect  grades  on,  55';-7 

weight  of,  all  parts  and  m'^t'ls. 

[*4oo,  *4i2  -f,  ^le 

ALL  TYPES.  *407-424,  *279 

as  affected  by  low  grades. 

[566 
by  steel  rails,  561 
by  volume  traffic,  597  & 

boiler,  water  and  steam, 

,   .      .,.  [*^54 

cost  of  doublmg  to  haul 

[same  train.  *567 

details  (full),  *4i2-4-6 

effect  on  cost,  new,  *565 

on  operat'g  exp.,  *56o 

empty    and     in     service, 

[*407-8 
fast  pass.,  wt.,  etc.,  421 
French  practice,  ♦576 
increase  in  recent  years, 
[♦407-10,  *466 
P.  R.  R.  since  1852,  *i4i 
explanation  of.  408 
of  parts,  constancy  in 

[ratio,  *4oo 
on  drivers  compared  with 
[cyl.  p.,  *4o8 
p.  c.  to    train-load,  all 

[grades,  *669,  *688 
p.   c    various   materials, 

[Am.  and  Eng..  ♦416 
ratio  to  trac.  power,  *542 
various  engs.,*279,*407-24 
extra  heavy  eng.,  *42i 
parts  of  eng.,  400 
roads,  ♦438 
Long  chords,  diffs.  length,  det'g. 

Long  tangents,  q.v.,  bad  practice 

[as  to,  324 
Long  Isl.  r'y.  loco,  perf'ce,  ^439 
Loop,  679        {See  Spiral.) 
Loss  and  damage,  cost,  r'ds  and 
[sections,  U.  S.,  ♦170-6 


Los— Mai 

Loss  of  time  by  reduc'g  speed, 

[^.7/.,  *594-s 

Low  grades,  q.v.^  and  asst.  eng., 

London  terminals,  cost,  827     [659 

expenses  at,  827-8 

location  of,  72  [*529 

London,  B.  &  S.  C,  fastest  train, 

kindling  tires,  exp'ce,  *2oo 

locos.,  cost  &  ms.  per  yr.,  ♦159 

tests,  ^462 
traffic  and  fuel  consump,  ♦131 
London,  Chat.  &  D.,  fastest  train, 

[♦529 
London  &  N.  W.,  ara't  sid'gs,  827 


fastest  trains,  *529 


Mai— Mas 

Maintenance  of  ^a\— Continued. 
exps.,  ratio  to  maint.  cars,  etc.! 

[*i3i 
ratios  of  ,to  each  other, 

[♦127-31 

why  constant  pr.  train- 

[mile,  127.  569 

Manchester,  stat  n  exp.  at,  828 

Manhattan     (elev'd,    q.v.)     ry., 

[length,  stops,  etc.,  ♦559 

operating  details,  speed,  etc., 

f*559 
stations  on,  and  power  used, 

[*aoi 


Iocs.,  cost  and  miles  per  yr, 

rep'r  details.  ^145 
interlocking  app's  on,  809 
terminals,  cost,  827 
Louisiana:    area,  pop'n,  sidings, 
p.   c.   op*g   exp.,  earnings  per 
mile  and  head,  *9o;  wealth  per 
cap.,  *26 
Louisville,  fall  at,  841 
Louisville  &  N..  align't  stat,,  ♦264 
fluct.  in  stock,  *46 
maint.  way  exp.  by  items,  *iao 
miles  and  earn'gs,  ^719 
op'g  exp.  and  tr  ns  pr  day,*i72 
train-l'd.  growth,  ♦101 
Louisville,  C.   &    L.,   miles   and 
[earn'gs,  ^719 
Lubricat'n  as  affect'd  by  temp.,506 
bath,  eff'y,  509,  918 
minute  diffs.,  effect,  509 
Luchmanier  pass,  grades  at,  ^700 
Lunch  counters  and  curvat.,  649 
Luxemburg  locos.,  no.  and  work 

[of,  ♦160 

Luxury    in    cars,   why  tends    to 

[incr.,  139,  567 

McAIpine,  C.  L.,  on  sharp  curve. 

[326 

Machinery,  loco.,  q.v.,  cost  new, 

[details,  ♦150-5 

reprs.    p.  c.   due   various 

[causes,  ^203 

minor  detailsof,smaIl, 

shop,  maint.  of.  154  (♦149 

Macon  «&  Br.,  align't  statist.,  ^264 

loco,  perform.,  +4^8   \q.v.,  732 

Mahoning    bch.,  N.  V.  P.,  &  O., 

handling  trains  on.  791 
Making  time  and  curvature,  268  & 
Malicious  obstructions,  derailm'ts 

from,  245 
Maine:  area,  popu..  sidings,  p.  c. 
op'g    ex.,    earnings    per    mile 
and  head,  ^90;  wealth  per  cap., 
*26  [miles,  ♦181 

Maine    Central,  p.  c,   switching- 
Main  (trunk,  ^.7'.),  lines  and  bchs.. 

.^      t707  + 
ex.  of  error  in,  978  & 

Maintenance  of  way,  tiS 

anomalies  in.  127 

as  affected  by  distance,  199 

gauge,  753 

minor  details,  191 

no.  of  trains,  127,  569 

pushing  eng,,  602 

exps.,  details,   U.  S.  sec- 

[tions,  etc.,  ♦128.  ♦170-^ 

general  tendency,  117 

iron  rail  era,  items,  ♦120 

trunk  lines,34  years,^ia9 


.   ^  speed  on  curves,  273 

[*i59  I  Mann  sleeping-cars,  ^491 

Manufacture  of  rails,  121 

of  transportation.  48,  106 
Manufacturing    regions,    burden 
[traffic  into,  618 
heavy  traffic  of,  63 
Mapping  and  project'g  loc'n,  886 
contours  (^.t'.),  pro  and  con 

[874  -f 

GOOD  AND  BAD,  CX,.  888 

large  scales,  best,  884 
loose  sheets  always  best,  886 
Maps,  making  mental,  835,  849 
ex.  of  need  for,  85a 
ocular  illusion,  q.v.^  on,  665 
right  use  of,  836-7 
small  scale,  making,  889 

need  for.  665 
use  in  reconnais.  ex.,  934 
Mari^,  G.,  loco,  tests.  464,  470 
Marine  engines,comp'd,  and  loco., 
coal  per  H.  P..  ^460  [133 

utmost  economy  of,  469 
Marriotte's  law,  467  [♦ada 

Marquette  H.  &  0.,align't  statist., 
Marsh,  Sylvester,  invented  rack 
Marshall  pass.,  ♦egS-g  [r'y,  690 
Marvellous  feat,  sci,  skill.  932 
Maryland:  area,  popu.,  sidings,  p. 
c,  op'g  exp..  earnings  per  mile 
and  head,  ♦90;  wealth  per  cap,, 

[♦26 
Mason  loco..  Am.,  dimens,,  etc., 

[*407 
Id.  on  drivers  persq.  ft. 
[grate,  ^458 
Masonry  and  floods,  781 
cost  of,  752 
dry.  bad, 898 
estimating,  898 
Mexican,  929 

p,  c.  cost  to  total,  ^757,  ^833 
Massachusetts:  align't  statist.,  259; 
area,  popu.,  sidings,  p,  c.  op'g 
exp.,   earnings,    per    mile   and 

[head,  *9o 
classification  of  through  and 
[local  traffic,  211 
cost  per  year  per  eng.  and 
fuel,  cost  of,  136         [car,  ♦148 
interlocking  law.  812 
loco,  reprs.,  cost,  142 
maint,  way  exp.  by  items,  ♦120 
motive-power  exp.,  det'Is,^i47 
ry.  earnings  per  head,  etc.,  ^78 
wealth  per  cap..  26 
Master  Car-B'dersAss'n.  assumed 
[action  on  rail-heads,  307 
Comm,  rep't  on  heavy  eng,, 

[279 
on  interchange  rules,  166 
rule  for  deprec'n  cars,  ♦aos 


Mas-Mid 

Master  Car-B'ders  Ass'n— 0«'</. 
stand'd  axle,  w't  ♦486 
journal.  ^499,  ♦513 
60,000    lb.    box-car,   *ii4, 
[♦490 
Mastodon  loco.,  q.71.,  def.,  423 
introduction  of.  114 
Material,  boring  to  test,  868 
.    cars,  prop'n  to  labor,  ♦161-4 
loco.,  q.v.y  rep'rs,    prop,   of, 

[*'47  + 
prices  of.  Am.  &  Eng.,  ^416 
w't  and  cost  in  locos.,  ^412-6 
Mauch  Chunk,  grav.  r'y  at,  692, 

[945 
Mauritius,  roH'g-stock  per  m.,  *47 

Maximum  and  min,  limits  of  ests., 

[24  & 
Mechanics  of  curve  resist,,  281 
of  train  move't,  331 
tools,  U.  S,  value,  ♦as 
Memphis  &  Ch,  align't  stat.,  ^264 
Mental  perspective,  i 
Merrimack  river,  fall,  841 
Metric  curves,  radii,  ^267 

stationing,  266 
Mexican  Cent.  R'y,  descent  from 
[Tepee,  670  -f- 
into  Ameca  Valley,  682 

ffeneral  route  of.  721 
ong  grade  on,  ^700 
Pacific  b'ch  of,  736,  670 -j- 
Reventon  tunnel,  668 
spirals  on,  678,  682  [721 

Mexican  Nat.  r  y.  gen.  route  of, 
location,  problems  on,  722 
long  grades  on,  ^700 
Mexican  R'y.  curves  on,  326 

error  in  not  going  to  Puebla, 
Fairlie  engines  on,  424        [928 
history  and  descrip'n,  929 
long  grade  of,  ^699 
profile,  698 

i^See  Jalapa  line.)  [65 

Mexican  towns,  ex   of  stations  at, 
Mexico,  Am.  line  to  city  of,  925 
Am.  locos,  in,  422 
plateau  of.  927 

rects.  per  inhab't  pass.  &  frt., 
rolling  slopes  in,  844  [105 

trunk  lines  in,  720 

(See  Jalapa.  etc.) 
triangular  course  traff.,  616 
Michigan,  align't  statistics,  ^262 
area,  pop  n,  sidings,  p.c.  exp., 
[earn'g  per  m.  and  h'd,  ^90 
interlocking  law,  13 
*  rough  country  '  ot,  840 
wealth  per  cap.,  ^26 
Michigan  Air-L,  align't  stat,,  ^262 
Mich.  Cent,  r'd,  chart  of  financial 
fall  of  rates  on,  ^726  [record,  34 
duct's  in  stock,  ^46 
miles  and  earnings,  ^719 
traffic,  local  and  through,  214 
train-load,   fuel     burned, 
growth  of,  ♦100   [♦136 
(See  Canada  Southern.) 
Michigan.  Lake,  water  of,  ^378 
Middle  States:   area,  pop'n,  sid- 
ings,   earnings     per     mile 
and  head,  etc.,  *9i 
bonds  and  stocks  per  m.,  ♦107 
curve  and  grade  statist.,  259 
«arnings  per  mile,  ^107 
distribution  of,  ♦loS 


Mid-Mit 

Middle  States— G? «//««<•</. 

frt.  earn.,  thro'  and  local,  *23i 
gen.  r'y  statist.,  88-90 
growth  r'y  system,  44 
main  results,  oper'n,  ^24 
maint.  way  details,  *i28 
op'g  exp,  and  traffic  details, 

[♦170-6 
pass,  and  fr't  haul  and  train- 
[load,etc,,  ♦g;,  *2i7 
p.c,  op'g  expenses.  91 

pass,  and  frt  traffic,  ♦181 
switching  mileage,  181 
rect's  per  inhab.,  pass  and  fr't, 
rolling-st'k  per  m,,  47    [♦104-5 
switching  mileage,  181 
ton-mile,  rec'is  and  haul,  ♦115 
train-l'd   and    haul,   fr't    and 
[pass,,  ♦97,  +217 
wealth  per  cap.,  26 
Midland  r'y,  fastest  train,  ^529 
locos.,  cost  and  miles  per  y'r, 
reprs.  details,  ♦145      [^159 
motive-power,  exp.,  det'ls, 

cr  ,  .      .  t*'33.  *I47 

traffic  and  fuel  consump.,  ♦131 
Milan  r'y,  profile,  698 
Mileage,  constructive,  218        [103 
loco.,    exaggerations     in, 
rate  for  fr't  cars,  164 
Milwaukee  grain  receipts,  728 
Mineral  traffic,  q.7'.,  and  balance 

[grades,  614 
dead  wt,  of.  610 
changes  in,  609 
Mines,  U,  S.,  value,  ^25 
Mining    regions,   burden     traffic 
[toward,  63,  6x8 
Minnesota:  align't  statist.,  ^263; 
area,  popu.,  sidings,  p.c,   op'g 
exp ,    earnings    per    mile    and 
head,  *9o;  wealth  per  cap.,  ^26 
Minor  details  of  align't.  183 

and  drumming  business, 

[192 

cost  of,  as  aff'd  by  ruling 

[grades,  581 

effect  on  amt,  of  surveys, 

[858 
nature    and    importance, 

[185  + 
possible     variations      in, 
[slight,  189 
relative  imp'ce  ex.,  395 
Mississippi:  area,  popu..  sidings, 
p.c.    op'g    exp.,    earnings    per 
mile  and  head,  ^90;  wealth  per 
cap.,  ^26  [841 

Mississippi  river,  fall,  and  tribs,, 
'points,'  rates  to,  218 
steam-engines  on.  ^460 
water,  purity,  ^378 
Mississippi   valley,  bad  location, 

„, [^.r.,  in,  656  & 

Missouri:     align  t    statist.,    ^264; 

area,  ,popu.,  sidings,  p.c,  op'g 

exp.,    earnings   per.    mile    and 

head,  ^90;  wealth  per  cap.,  26 

Missouri,  K,&  T.  loco,  perfce,^439 

Missouri  Pacific,  miles  and  earn- 

['ogs,  ^719 
Missouri  river,  fall,  841 

•  points,'  rates  to,  218 
Mistakes,  narrow  margin  for,  28 
Mitchell,     A,,    invented    Consol. 
[eng.,  278,  423 


Mix-Neb 

Mixed  trains,  when  used,  95 
Mobile  &  O.,  align't  statist.,  *264 
"  Moderate"  grades,  q.v.,  330 
Modern  r'y  corporation,  the,  28 
Modulus  of  elasticity,  def.,  345 
Mogul   loco.,  q.z'.,   dimens.,   etc., 
rel.  cost  reprs.,  146       [408 
Momentum  and  curve  comp'n,  621 

def'n  as  used,  632 

grades  (virtual,  j^.w.),  def.  and 
[ex.,  344,  701 
Monarch  sleeping  cars,  ^491 
Monopoly  powers   of  r'ys,  effect 

t''^'  32 
Montana:    area,   popu.,    sidings, 

p.  c.   op'g    exp.,    earnings    per 

mile  and  head,  ^90;  wealth  per 

cap..  ^26 

Mont  Cenis  r'y  fric,  grip,  690 

loco,  tests.  464 

profile,  698 

Monte  Carlo  disaster,  252        [753 

Mountainous  regions  and  gauge, 

curve  limit  in,  655 

valleys  q.v.  penetrate 

[into,  586 

Mountains,  slopes  of,  why  eye  ex- 

[aggerates,  845 

propin'q'ty  of,  oc.  illu'n,  846 

Mount  St.  Elias,  ht,,  927 

Mount  Washington  r'y,  first  rack 

[r.,  690 

Moon,  why  large  on  horizon,  845 

Moral  effect  of  curvature,  276 

of  distance,  239 

of  good  maint.  way,  124 

of  large  traffic,  55-7 

Mordecai,  G,,  table  by,  818      [503 

Morin.    A.,   expts.    on    fric,  q.v., 

Morris  &  Essex,  align't  statist., 

[♦260 

Morse,  J.  R,,  table  from  paper, 

L*47 
Mortgage  interest  builds  rds.,  36 
Motion,  accel'd  and  retard.,  laws, 

[331  & 

Motive-power,  cost,  U.S.  r'ds  and 

[sects.,  ♦170-6 

by  items.  ^147 

English,  ^148 

general  exp,  for  (see  Loco.), 

1*147  & 
Mud  and  incrustation,  ^378     [,♦27 
Mulhall.  Diet,  Statis.,  table  from, 
Murders  and  r'y  accidents,  257 
Narrow-gange.  751 
and  cross-ties,  779 
curves  q.v.  on,  326 
curve  resist,  on,  305-6 
in  Colorado.  694 
in  mountainous  regions,  753 
locos.,  comp.  cost,  ♦564-5 

Consolid.  engs.,  281 
origin  of.  424 

useful  effect  on  car  construc- 

[tion,  485 

Nashua  &  Lowell,  p.c.  switching- 

[miles,  ♦181 

Nashville,  Chat,  &  St.  L.,  miles 

and  earnings,  ^719 

'Natural  gift' for  location,  q.v.. 

Nature,  working  with,  589  [22 

Nebraska:  area,  popu.,    sidings, 

p.    c,  op'g   exp..  earnings    per 

mile  and  head,  +90;  wealth  per 

cap.,  ^26 


f 


970 


Nee-New 

Necessary  traffic,  g.v.,  very  little, 

[52 
Nesquehoning     valley,      switch- 

[back, 945 
Netherlands,locos.,  no.  and  work 

[of.  ♦160 
Net  revenue,  g.v.,  sections.  U.  S., 

*92— 4  &, 

Nevada:  area,  popu.,  sidings,  p.  c. 

op'g  exp.,  earnings   per    mile 

and  head,  *9o ;  wealth  per  cap,, 

*26 

Newton,  first  law  of  motion,  341 

New  England  States,  alignment 
[statistics,  *a59 
bonds  and  stock  per  mile,  ♦107 
earnings  per  mile,  *io7 

distribution  of,  *io8 
frt.,  through  and  local,  ♦aii 
general  r'y  statistics.  *88,  *9o 
haul,  train-load,  etc.,  ♦q/ 
growth  r'y  system,  ^44 
main  results  op'n,  *92 
maint.  way  eX)  .,  details,*i28 
op'g  exp.  and  traffic  details, 

[♦170-6 
p.  c.  pass,  and  frt.  traffic.  *i8i 
p.  c.  switching  mileage,  *i8i 
rec'ts  per   inhab.    pass,    and 
[frt  ,*io4-5 
rollmg-stock  per  mile.  47 
ton-mile  rec'ts  and  haul,  *iis 
train-load  and    haul,  frt.  and 
wealth  per  cap.,  26  [pass.,  ♦217 

New  Hampshire,  wealth  per  cap., 

[*26 

New  Jersey:  align't  statist.,  *259  ; 
area,  popu.,  sidings,  p.  c. 
op'g  exp.,  earnings  per  mile 
and  head,  *9o;  wealth  per  cap., 
♦26 

•rough  country  '  of,  840 

New  Mexico:  area,  popu.,  sidings, 

p.  c.    op'g    exp.,  earnings  per 

mile  and  head,  *go\  wealth  per 

cap..  *26  (^08 

New  So.  Wales,  Am.  loco,  in,  422. 

rolling-stock  per  mile,  ^47 
New  York  City,  cost  frt.  cartage, 

t82o 
elevated  g.v.  rys.,  curves  on, 

[645-7 
Gd.  Cent.  Sta.,  cost.  70    [*7i4 
internal  pass,  traffic,  growth, 
points  near,  rates  to,  219 
pop'n.  growth  of,  *7i4 
-Smithville  traffic,  718 
terminal  facilities,  cost,  70,  818 

rates  at,  219 
train  sp>eeds  from,  648-50 
New  York  State,  align't  statistics, 
♦259;  area,  popu.,  sidings,  p.c. 
op'g  exp.,  earnings  per  mile  and 
head,  *9o 
curvature  in,  259 
interlocking  law,  813         [♦120 
maint.   way,    exp.   by  items, 
switching  engines  in,  156 
wealth  per  cap.,  26 
New  York  &  Harlem,  alignment 
[statist.,  *2S9 
N.  Y.  &  New  Eng .    alignment 
[statist.,  ^259 
New  York  Cent.  &  H.  R.,  align't 

[statist.,  *259 


INDEX. 


New  York 

New  York  Cent  &  H.  R.—Cond. 
an  ex.  oi  long  line  prospering, 

[240 
asst.  engs.  on  Hudson  R..  591 
construction  acct.,  items,  *7i 
cars,  box,  wt.  of,  det'ls,  *i63 
distance  and    through  traffic 

[of,  240 
negative  val.  on,  234 
fastest  trains,  *S29 

loss  by  Slops  to,  595 
flucts.  in  stock,  *46 
formation  unforeseen,  707  [724 

HISTORY   AND   SUCCESS   OF,  707, 

level  grades  on,  H.  R.,  327 
Iocs,   cost  and  miles  per  yr.. 
reprs.  by  items,  *i43  [*i59 
p.c.  labor  and  mat  l,*i5a 
maint.    way   and    roll,  stock 
[exp.  comp.  34  yrs.,  ♦129 
miles  and  earnings,  *7i9  [♦172 
op'g  exp.  and  trains  per  day, 
p.  c.  of,  why  high,  no. 
and  rates.  220         [725 
op'g  pushers,  H.  R.  div.,  79a 
pass,  trains,  longest,  596 
rail  section,  307 
rail-wear  on.  pass,  and  frt.,  561 
rates  on.  fall  of,  ^726 

and  Mex.  r'y.  923         [230 
effect  on  p.  c.  op'g  exp., 
sharpest  curve  on,  326 
sidings,  total.  ^825 
Buffalo  y'd,  821 
terminal  exp.,  etc.,  N.  Y.,*8i9 
train-Id.,  frt.  and  pass.,*2i7 

growth  of.  ♦100 
train-mile  cost,  ♦116 
train-resist,  tests,  518 
New  York.  Chic.  &  St.  L., 

sidings,  Buflfalo  yard,  ♦821 
elsewhere.  825 
New  York,  L.  Erie  &  W.,  align't 
[sutist.,  ♦259 
Carr's  Rock  disaster,  255 
connections,    relations    with, 

[221,729 
curve  com  pens  n  on,  621 
distance,  value  of,  to,  221 
dynamom.  tests,  501 
financial  status,  41,  739 
flucts  in  stock,  *46 
freight  time-table  on.  loa 
grades,  balance  of,  618 

60  ft.  and  6*  comb'n,  656 
inundations  on,  783 
location  of  heavy  grades.  585 
locos,  cost  and  miles  per  yr., 
tests  of  (Z.  C).  ♦437  [♦159 
loss  traffic  from  curves,  275 
maint.  way  and  rolling-stock 
[exp.  34  y'rs,  ♦lag 
miles  and  earnings.  *7iq 
op'g  exp.  and  trafhc  detTs,*i7a 

p.  c.  of,  comparison,  no 
pass,  pushers  on,  595 
rates,  fall  of,  ♦726 
rates  on  and  Mex.  r'y,  01% 

and  N.  Y.,  P.  &  O.,  221 
sharp  curves  on,  278.  326 
sidings,  total,  etc..  *825 
term'l  exp.,  etc.,^.  Y.,  'Sig 
tires,  cost  m'nt'g.  316 
ton-mile  rec'ts,  etc.,  *ii5 
track.  Buffalo  y'd.  •821 
train-load,  la,  and  pass.,  *2i7 


INDEX. 


971 


New-Nor 

New  York,  L.  Erie  &  Vf.—Cen'd, 
train-load,  growth  of,  *ioo 
train-mile,  cost,  *ii6 
wheel-wear,  statistics,  •317 
why  has  poor  connect'ns,  730 
New  York,  U.  H.  &  H.,  fastest 
'  [train,  *529 

flucts.  in  stock.  ^46 
locos,  cost  and  duly,  *i59 
sharpest  curve,  *325  [•217 
train-load,  frt.  and  pass  . 
New  York,  Ont.    &    W.,    term'l 
1.T       ,r    .    f«*P»etc.,  N.  Y..  *8i9 
New  York,  Penna.  &  O.,  align't 
[statist.,  *26i 
bad  location  of,  223 
bridge  vibration  tests,  447 
handling  trains  on,  791 
locat'n  at  Springf'd,0.,  56 
Mahoning  B'ch,  732 
op'g  exp.  and   trains  per 
[dav,  *i72 
p.  c.  switching  miles,  •181 
rail-wear  tests  on,  294 
strategic  disadvantage  of,. 
.     ,  [222 

train-load,  frt.  and  pass., 
[•217 
why  a  bad  property.  223 
New  York-Phila.,     etc.,     traffic,. 

XT         1     ,      L*"*^  '?.'.'^'  *39.  709  -I- 
New  Zealand,  rolling-stock    per 

XT-  [m\]c.  *47 

Niagara  cantil.  bridge,  w't,  etc.,. 

».T-  [90^ 

Niagara  river,  discharge,  841 

fall,  841  [695-6- 

Nigger-hill,      develop't     around. 
Non-competitive  traffic  and  good 

[facilities,  58 
and  restaurants,  74 
comparative  rates,  58 
effect  distance  on,  213 
true  classifications  of. 212 
Norfolk  &  Wn.,Consoi.  loco,  tests, 

XT      L  ^  [«t<-'-.  431 

North  British  r'y,  locos.,  cost  and 

XT      L  ^  [miles  per  yr.,  *i59 

North  Carolina:  align't  statists.,^ 
♦263  ;  area,  popu.,  sidings,  p.  c. 
op'g  exp.,  earnings  per  mile  and 
head,*9o;  wealth  per  cap.,  *26 
North  Central  States:  alignment 
statist.,  ^262;  area,  popu.,  earn- 
ings per  mile  and  head,  etc., 
♦91  [*259 

curve  and  grade  statist., 
fall  rivers  in,  841 
freight  earn.,    thro'    and 
[lucal,  *23i 
,en.  r'y  statist..  88,  91 
laul  and  train-1'd,  etc.,  *qT 
no.  pass,  trains,  96 
op'g  exp.  and  traffic  det'ls, 
[*i70-6 
p.  c.  pass,  and  frt.  traffic, 
[♦181 
switching-mileage,  •181 
ton-mile  rec'ts  and  haul, 

[*i«S 

train-load  and   haul,    frt. 

[and  pass.,  *2i7 

North-Eastern  r'y,  Iocds.  cost  and 

[miles  per  y'r,  *i^9 

Northern    Pacitic    r'y,    flucts.  in 

[stock,  '46 


Nor— Ope 

Northern  Pacific  r'y— Continued. 
heavy  cars  on.  485 
loco,  dimens.,  etc.,  553, 407 
tests  on,  552 
-.      ^     Jong  grades,  *7oo 
Northern  r'y  (France),  impercept. 
.    [slip  tests,  445 
Northwestern  gram  receipts,  728 
Northwestern  States:    area,  pop- 
ulation, earnings  per  mile  and 
head,  etc.,  *9i;  general  r'y  stat- 
ist., *88  [*,28 
maint.   way  exp.  details, 
pass,    and   frt.,  haul   and 
[train-load,  etc.,  *97 
{See  Western.) 
Norway,  align't  statist.,  *265 
locos,  no.  and  work  of,  *i6o 

performance  of,  *439 
popu.,   r'ys.  wealth,  etc.,  ♦27, 

Notch,  loco.,  g.v.,  def'n,  797 


0  =  %n  9A  872 
Obelisk,  ex.  of  natural,  684 
Obliquity  of  traction  and    curve 
.  .     [resist.,  301  -f- 

Obstructions,  accidents  from,*247 
Ocular  illusions,  842 
as  to  quantities,  849 
broken  back  curves,  871 
chief  danger  from,  852 
distance  on  maps.  665,  859 
examples  of,  680, 846  & 
grades  in  flat  country,  661 
sharp  ridges,  668 
steep  slopes,  ex.,  684 
Odometer,  use  of,  838 
Office  location,  evils  of,  880  — 
Offsets,  eye  exaggerates,  842  -f 
for  transition    g.v.    curves. 

r.u         ,-  ■  869+.  684 

Ohio:  alignment  statist,  in,  ♦261; 
area,  popu..  sidings,  p.  c.  op'g 
exp.,    earnings    per    mile    and 
head,  *<)o 
interlocking  law,  813 
'  rough  country'  of,  840 
wealth  per  cap.,  26 
Ohio  &  M.,  align't  statist.,  ♦261 -f- 

train-ld..  growth.  ♦loi 
Ohio  river,  &  tribs.,  fall,  841 
Oil  and  waste,  cost,  *i47,  ♦170-9 
Oil  excitement  and  rys.,  30 
Old  Colony,  locos.,  cost  and  miles 
[per  year,  ♦isg 
p.  c.  switching-miles,  ♦181 
washouts  on,  782 
Old  lines  and  oper'g  rules,  791 
improvement  of,  785 

CONXLUSIONS  AS  TO,  8o8 

gaining    double   track, 
[806 
possibilities  as  to,  787 
pushers  on,  788 
sags,  taking  out,  806 
virtual  profile,  798 
usual  errors  in,  787 
origin  of,  789 
Open    road    (the    part    between 
stations),    improving    grades 

on,  ^803 
Operating  ballast  trains.  77^ 
Operating  Expen.ses  (Ch.  v.),  106 
and  bad  bridge  eng.,  3 
as  affected  by  curvature,  313 


Ope— Pap 

Operating  Expenses— Continued. 
as  affected  by  distance,  ♦207-8 
no  trains,  568 
radius  of  curves,  638 
rise  and  fall,  375 
train-Id.,  560 
average  amt.,  108  -+- 

ESTIMA TKn   AVERAGE,  l8o  — 

grand  divisions  in,  117 

great  change  in,  107 

p.  c.  Chicago  roads,  ♦174-6 
English,  ^70,  •188        [♦88 
sees.,  U.  S.,»io8-io,^i7o-6, 
trunk  lines,  ♦172-6 

p.  c.  to  exp.,  no  criterion  of 

[management,  109 

trunk    lines,   g.v.,    cause 

[incr.,  725 

per  mile  road,  English.  ^79 
U.  S.,  ♦170-9,  *99  & 

per  ton-mile,  ♦us  & 

per    train-mile,    English, 

U   „    ^  [*79,*i78 

U.S.,  ♦170-9 
Operating    heavy     grades,    g.v., 

r,  .  ,  [d  iff 'y,  596  + 

Operating  rules  and  ballast  trains, 

[773 
and  impr't  old  lines.  791.  803 
Operation,  lines  in.  See  Old  Lines. 
Optimism  proper  in  loc'n,  832 
Oregon-  area,  popu.,  siding.s,  p.  c. 
op'g  exp  ,  earnings  per  mile  and 
head,  ^90;  wealth  per  cap.,  ^26 
Orizaba,  peak  of.  927 
Oroya  r'y.  developments,  6794- 
sharpest  curve,  ^325 
profile,  698-9 
train,  g.v.,  911 
Oscillatory  train  g.v.  resist,  517, 
Overlaps,  848,  836  [91 1 

ex.  of,  852,  854 
Overloading  cars,  accidents  from, 

[♦246 

Pacific  States:  area,  pop'n,  earn- 
[ings  p.  m.  and  head,  etc.,  ^91 
bonds  and  stock  p.  m.,  ^107 
earnings  per  mile,  ^107 

distribution  of,  ♦loS 
fuel,  cost  of,  136 
frt.  earnings,  thro'  and  local, 
general  r'y  statis.,  88-90   1*231 

growth  r'y  system,  ^44 
aul  and  train  Id.,  etc.,  pass, 
[and  frt..  ^97,  ♦217 
main  results,  op'n.  ^94 
maint.  way  exp.,  details,  ^128 
op'g  exp.  and  traffic  details, 

[♦170-6 
p.  c.  pass,  and  frt.  traffic.  ♦181 

switching  mileage,  ♦181 
rolling  slopes  in,  844 
rolling-stock  per  mile,  ^47 
sidings,  ♦gi 

train-I'd  and  haul,  freight  and 
[pass.,  ^97,  ^217 
ton-mile  rects.  and  haul,  ♦115 
wealth  per  cap.,  ^26 
Painting,  car,  ♦162-4,  ^204 
locos.,  ♦Me,  ♦Mg-SS,  *4i3 
English,  144-6 
Palace-car.  inspection  from,  2 
Pan  Handle,  tunnel  on,  240 

(.S-<'^Pittsb.,C.&St.L.) 
Paper  location,  890 


Pap-Pen 

Paper  location— Continued. 

best  hard  to  secure,  880 
deficiencies  of,  877 
from  office  chair,  878-81 
take  off  by  bearings,  892 
use  of,  868 
Parabola,  cubic,  869 
law  of,  387 
not  suitable  for  r'y  curves,  276 
properties  of,  390 
Parallelogram  of  forces,  302 
Parallel  rules,  best,  887  [♦iss,  ♦4i6. 
Paris  &  Orl.,  cost  locos.,  details, 
per  ton,  details,  ♦411 
repairs,  details,  ♦145-7 
p.  c.  labor  and  mat'ls,^ 

[*i5^ 
wt.  and  cost  in  detail. 

Pans,  Lyons  &  M.  r'y  locos.,  repr., 
[details,  ♦145, 
tests,  464 
Parlor-cars,  dimens.,  etc.,  491 

why  so  freely  used,  567 
Party-wall  laws,  814 
Pass,  lowest  usually  best,  858 

ocular  illusions  as  to,  846  & 
Passaic,  sharp  curve  at,  326 
Passenger  and  freight  locos.,  g.v.^ 
[tire  reprs.,  ♦149, 
cars,  g.v.,  no.  perm.,  world. 

,     •  *   [*'t? 

per  train,  g.v.,  ♦134& 

-mile  rates,   g.v..  Am.   and 

[Eng.,  ♦159, 

revenue,  g.v.,  per  head,  U.  S., 

[sections,  ♦92-4,  103  & 

traffic,  g.7'.,  pushers,  ex.,  607,. 

and  speed,  645  [616 

irregular  eff.  of  grades,577 

LOW  SPEED  REDUCES- 

[grades.  578  -j- 
luxury  in,  why  increas'g,. 

,.  f567& 
no.  01  pass.,  world,  43 
on  branches,  734 
p.  c.  of,  sects.,  U.  S.,  ♦181 
third   class,   likely   to  in- 
[crease,  580 
tram-load,  U.  S.,  sects.,  ^97 
trains  and  grades,  576,  616  — 
gain  on  grades  by  speed, 

[593 
length  for  diff.  speeds,  592 

longest,  592,  596 
manufacture  pass,  trips,  50 
no.  load  and  haul,  U.  S., 
[sects.,  ^97,  ♦lyo-g, 
probable  no.  of,  est'g,  95 
trip,  av.  U.  S.  sections,  ♦97 
Passes,  travel  on,  249 
Payments  per  head  to  r'ys,  U.  S,,. 
"■92-4,  *io3  & 


l*q'. 
for, 


Pedestals,  concrete  lor,  903 

design  and  est'g,  901 
Peekskill,  ocular  illusion  at,  848 
Pegram,  G.  H.,  bridge  formulae,, 
trestle  formula,  901     [766,  903 
Pennsylvania,  align't  statist.,  ♦259. 
area,   pop'n,  sid'gs,    p.   c.  op'g, 
exp.,  earn'gs  p.m.  &  h'd,  ^90 
curves  on  coal  roads,  278 
gravity  r'ys  in,  692 
wealth  per  capita,  ^26 
Penna.  &  N.  Y.  Canal  rd.,  align't 
[statist.,  ♦260 


972 


Pennsylvania 

Penna.  Coal  Co.,  gravity  r'y,  692 

Penna.  Co.,  freight  car,  dimens., 

[etc.,  once  and  now,  *486 

Pennsylvania  Rd.,  align't  statist., 

bal.  of  traffic  on,  *6o9        [*26o 

capital  account,  items,  *-ji 

stock  of  control,  lines,  *7i 
cars,  frt.,  dimens.,  etc.,  once 
[and  now,  *486 
pass,  dimens.,  etc.,  ♦491 
load,  average,  *6io 

changes  in,  485 
movement  of  Id,  *6o9 
condensed  profile,  698 
curvature,  taking  out,  on,  277 
distances.  N.Y.  to  Piitsb.,*6c9 
dynamometer  tests,  501 
expt.  as  to  curve  slipping,  285 
fastest  trains,  *529 
fiucis.  in  stock,  *46 
frt.   move't,   thro,   and  local. 

fuel  burned,  freight,  *i35 
pass.,  134 

good  condition,  value  of,  276 

grades,  balance  of,  618 

location  for  pushers.  585 
Tyr.  &  CI.  branch,  *7oo 

hist,  and  cause  of  success,  725 

inundations  on,  783 

local  traffic,  large  prop'n,  235 

locos.,  breakages  in  starting, 

/-         It  t*4i9 

Consorn,  experience,  *i48 
cost,  new,  details.*  15 1-2-4 

per  ton,  details,  *4it 
fast  pass.,  weight,  etc.,  421 
loads   hauled,   Tyr.   br'h, 
mileage  of,  140  L*44o 


all  ages,  *4i8 
running,  tirst  in  first 
[out,  *i4o,  *4i9 
repairs,  cost  of,  140  & 
per  year  per  eng.,  *i59 
by  divs.,  *i88 
general     repairs    on, 
[frequency,  420 
p.  c.  labor  and  mate- 
Trials,  ♦isz 
■Statists,  loco,  op  n,  185 1-84, 

[*i40 
wt.  and  cost,  det'ls,  *4i2-6 
Consol.  eng.,  *409 
various  parts,  *4oo 
tank,  wi.,  etc.,  421 
wt.  on  drivers  per  sq.  ft. 
[grate,  *452 
maint.  way  exp.  on,   123, 128, 

[130 
and  roll. -stock,  ^4  yrs., 

...  .  1*129-30 

by  Items,  •120 

policy  as  to,  123  & 

miles  and  earnings,  ^719 

motive-power     exp.,    details, 

.     .  [*i47 

statistics,  1851-84,  *i4o 
-op'g  exp.,  and  trains  per  day, 

[*i7a 
p.  c.  of,  why  low,  110,  725 
why  increasing,  725 
planes  on  old  line,  944 

pres't  line  plan'd  for,  944 
pass,  pushers  on,  595 
rail- wear  tests,   119,  295,  320, 

[380,  562 


INDEX. 


Pen-Pit 

Pennsylvania  Vi^.— Continued. 
rates  and  p.  c.  opg.  exp.,  220 & 
fall  in,  726 

ton-mile  rects.,  etc.,  *ii5 
sharpest  curves  on,  *325-6 
term'l  exp.  etc.,  N.  Y.,  *8i9 
tires,  cost  m'nt'g,  316 
track,  best  in  world.  277 -f 
traffic,    disprop'n   E.    &   W., 
[etc.,  *6o9 
tram-Id.,  frt.  and  pass..  *2i7 
growth  of,  100 -f- 
pass.,   no.  cars  and  fuel, 
[*i34.  *595-6 


INDEX. 


train-mile  cost,  •116 
wages  on,  loc.  shops.  *isi 

wheel-record  and  brakes,  377 

why  many  branches,  729 
Peoria  grain  rec'ts,  728 
Per-diem  rate  for  frt.  cars,  165 
Perkiomen  r'y,  align't  statist.,*a6o 
Perote,  Cofre  de,  ht.,  etc.,  927 
Perspective,  mental,  i 
Peruvian  ry"s,  profiles  of,  698-94 
Petersburg,  sharp  curve  at,  326 
Petroleum,  H.  U.  in,  ♦450 
Philadelphia-N.  Y.  traff..  loss  by 

[dist.,  709 

terminals,  loc'n,  etc..  of,  68 

train-speed  to,  648-50 
Phila.      &     Atl.      City,      align't 
r,u-,      »   „  .  [statist.,  *26o 

Pnila.  &  Erie,  align't  statist.,  ♦260 

expts.  as  to  loc.  resist.,  +279 

loco,  performance,  *44o 
rep'rs  by  divs.,  *i88 

trains  and  fuel  consump.,  ♦138 
Phila.  &   Rdg.  coal  car,   heavy, 

„     ,  1*490 

coal  consump.  pass.,  134 
fastest  train,  *529 
fuel  tests,  var.  speeds,  528 
kindling  fires  on.*2oo 
locos.,  cost  new,  *i52 

fast  pass.,  wt.,  etc.,  *42x 
fr't,  heavy.  *42i 
rep'r  details,  *i45 

and  renewals,  *i45 
tests  of  fast,  473 
maint.    way   and     roll. -stock 
,_     .     [exp.,  34yrs.,  *i29 
by  Items,  *i2o 
pushing  serv.,  cost,  601 
Piedmont,  yard  at.,  618 
Piers,  area,  etc.,  N.Y.  term's,  *8i9 

bridge,  estimating,  898 
Pig-iron,  past  prices  of,  763 
Pile-driver  car,  Ga.C,  detis,  *49o 
Piles,  driving  by  vel.  of  car,  ex.. 

Pile  structures,  770  [473 

Piston,  loco.,  q.v.,  loss  energy  by, 

Pittsburg  &  Conn.,  align't  statist., 

„  [*26o 

Pittsburg,  C.   &  St.    L.,  align't 

.    ,  [statist.,  ♦261 

train-Id.  growth,  *ioo 

tunnel  on,  saving  dist..  240 

Pittsburg    &    Ft.    W.,  flucts.    in 

[stock,  *46 
opg.  exp.  and  trains  per  day, 

.  [♦172 

.sharpest  curve,  ♦325 
ton-mile  rates,  etc.,  ♦115 

fall  in,  on.  *726 
train-Id.,  growth,  ♦100 


975 


Pla-Pru 

Planimeter,  use  of,  897 
Plateau  of  Mexico,  descr.,  616 
Platte  Cafion,  697 
Plotting  cross-sections,  868.  897 
mapping,   q.-v.,    proper 
[methods,  886 
Plates.    {See  Engravings.) 
Political  economy  of  cheap  con- 
[struction,  18,  27 
of  distance,  197 
Pony   truck,    g  v.,  mechanics  of, 

[431 


Poor,  H.  v.,  table  by,  *726 

S 


Popocatepetl,  mtn.,  927 


Population,  sections 
growth  of  la..  '77 
Mass.,  *78 
U.  S.  *88-9o 
does  not  help 
large   and   small. 


[*92"- . 
73-81, 


[227 
poor  lines, 
traffic    per 


[head. 


'713 


LAW  OF  ADDITIUM  Ti>  TRAF- 

[PIC,  708 
per  mile  road,  la.,  ♦77 

Mass.,  *78 

sections  U.  S.,  ♦88-90 

world,  ♦43 

law  as  to.  720 
per  sq.  m.  &  m.  r'y,  U.  S.,  ♦SB 
pay'ts  per  head  to  r'ys,  ^92 


.     .  [*»04  & 

r'y  capital  per  head  U.  S..  *fc8 
Portable  engines,  cost  &  eflf 'y,  *53i 
Port  Jervis,  grades  at,  619  [+27,  *4g 
Portugal,  pop'n,  r'ys,  wealth,  etc.. 
Postal-cars,  dimens.,  etc.,  *49i 
Power,  static,  and  dyn.,  292  &. 
Practice    does    not    make     loc'g 

T,        .  [^-'^Ji''",  22  & 

Prairie  ridges,  loc'g  over,  661  -f 
Prairie  States,  bad  loc'n  in,  6,  21  & 
Preliminary  line,  q.v  ,  861-2 

and  contour  maps.  876 
Prepossessions,  abandon'g,  835  & 
Present  worth  of  future  $1.  *82 

of  future  $1  per  year,  *83 
Pressure,  loco.,  q.v.,  steam,  q.v., 
[efTec.  cyl.  in  pract.,  *46i  -f- 
Pnsmoidal  form'a,  use  and  abuse. 

Probabilities,  theory  of,  864,  896 
Profile,   balancing  quantities  of, 

.     ,     .  [89s 

errors  in  laying  grades  on,  329 
estimates  from,  895 
paper  and  actual,  868,  880 
putting  grades  on,  893 
small  scale,  861-2 
need  for,  665 
Profit  from  r'ys,  conditions  for, 

14-16 
Profit  traffic,  importance  of.  62 
Progress  of  r'y  cons.,  q.v..  world, 

.     .y-s.,;44  [V-3 

Projectiles  and  air  resist.,  517 
Projecting    asst.     eng.     grades, 
low,  666        [high,  669 

grade-lines,  675 

location,  q.v.^  890 
Propellers,  no.  N.  Y.  term'ls,  *8x9 
Protractor,  best,  886 
Providence  &Worc'er,  p.c.  switch- 
[ing-mijes,  *i8i 
Provision  cars,  dimens.,  etc.,*487 
Prussia,  cost  r'ys.  etc.,  *45 

loco.  repr.  details,  ♦145 

p.  c.  op  g  exp.,  •110 


Pul-Rai 

Pulley,  transmiss.  of  power  ar'd. 

Pusher  (asst.  q.v.  engine)  grades, 
[projecting,  666 
Pucbla,  error  in  line  to,  928 
Puente  Nacional,  929 
Pulque  district,  Mexico,  928 
Pusterhal  r'y  profile,  698 
Pyramid,  of  traffic,  712,  731 

Quantities,  balance  of.  not  exact, 
estimating  {q.v.).  895  [895 

Quarries,  U.  b.,  value,  *25 
Queensland,  roll'g-st'k  perm.,  *47 
Quincy,  Mass.,  double-truck  car 

[at,  421 


Rack  r'ys,  history,  etc.,  690,  943 

reason  for,  404 
Radiation  and  fr't  speed,  370 
external,  313,  456,471,  508 
boiler   and  cylin.,   comp. 
in  yards,  315    [imp'ce,  471 
winter  and  summer,  508 
internal,  315,  471 
Radius  of  curv.,  q.v.,  cost,  etc., 
designation,  258-66      [635 
gyration  of  car-wheels,  334 
rails,  739 
Radius-bar,  loco.,  def'n,  etc.,  426 
Rail  joints,  accidents  from,  *246 
best  form  of.  123 
wear  of  rail  from,  123 
yielding  at,  561 
Rails,  and  cro.ss-iies,  7754- 
foreign  locos.,  425 
speed,  268, 274 
track  labor,  758 
average  life,  119  [256 

broken,  accidents  from,   246, 
condition  in  winter  and  sum- 
[mer,  315 
cost  of,  best  IS  cheapest,  748 
durability,  *745 
stiffness,  *74j 
strength,  *742 
elastic  reaction  of,  516 
form  of ,307-8,  738 

and  flange  wear,  317,  639 
hard  and  soft,  121 
inspection  of.  121  [*i2o 

iron,  cost  of.  various  roads, 
formerly,  119,  763 
vs.  steel.  110,  268,  561 
light,  and  I't  ry's,  737 
past  prices  of,  763 
renewals  of,  cost,  U.  S.  sec- 
[tions.  etc.,  ♦128,  ♦170-9 
spread,  acc'd'ts  from,  ^246 
steel,  effect  on  op'g  exp.,  ♦130 
revolutionized  mt.  of  way. 
whv  better,  119  [118 

wear  of,  as  affected  by  age  of 
[rails,  296 
curvature.  297-319 

radius  of,  639 
grades,  380 
quality,  320 
rise  and  fall,  379 
sand, 380 
speed.  561 
front  and  back  wheels,  287 
loco,  and  car,  122,  561-2 
nature  of  wear,  308 
of  pa.ss  and  frt.  trains,  562 
on  curves,  q.v.,  293,  319 


Rai— Rec 

Rails — Continued. 

wear,  as  aff.  by  age  and  form. 

CONCLUSJONS,  304         [296 

diff.  European  &  Am. 
[exp..  283 
wt.  of,  and  grading,  749  [744 
comp.  durability,  est'g, 
buying,  strength,  etc.,  739 
choice  of  wt.,  738  [*747 
interest  charge  on,  extra. 


vs.  cross  ties,  776        [13  & 

Railway    projects,   inception    of. 

Railways,  acres  in  crops  per  mile, 

all  legitimate  enterpr.,  14  [*9o 

capital,  p.  c.  to  total,  ^27 

of  world,  ^27 
construction,  est.  of  future,^4i 

past  progress  of,  ^44  -f- 
cost,  *27,  ^43,  *45 

of  world,  progress,  ^42 
value,  ^25,  ♦27.  ^45 
cost  per  head,  world,  ♦27 
total,  world,  *45 
per  mile  English,  *^o 
,      U.S.,  etc,  *25-7,>43-5 
earnings,  q.v.,  per  mile,  ^77, 

[*78«& 
financial  errors  in  projects.  707 
foreclosures,  ^40  [186 

good  lines  for,  popular  error, 
indirect  wealth  from,  ^27 
light,  737 

miles  of.  sections  U.  S.,  ^92-4 
world,  ♦25,27.  ^43-45 
per  head,  world,  ^43 
per  sq.  mile,  ^43 
must  go  to  traffic,  53 
profit  on,  conditions  for,  x6 
Rainfall,  amt.  of,  783 
fluct'ns  in,  783 

and  floods,  784  [759 

Raising  and  surfacing  track,  q.v., 
Rankine,Prof.,  on  steam  exp'n,469 
Rates,  fixing  of.  195  -|-  & 

as  affected  by  diffs.  dist.,  709 
cartage,  820 
distance,  194  -f-,  723  -f- 
strategic      advantages, 
competitive,  212      [218,  723  -|- 

sum  of  two,  218 
division  of,  217 

fractional  per  cents,  227 
E.&W.-boundC.,C.,C.&I., 
L.  S.  &  M.  S.,  226  [225 
how  fixed  on  through  traffic, 
Mex.  r'y  and  N.Y.  C,  932  [217 
on  regular  and  occas'l  traffic, 
{q.v.,  diff.,  235 
per  pass.mile.  Am.  &  Eng., 

[♦^59 

per    ton-mile,    q.v..   Am.    & 
[Eng.  ^159 
recent  fall  of.  726  ± 
through,  division  of,  219 

LAW   AS    TO    DISTANCE   RK- 
[SULTING  FROM,  219 

and  local,  q.v.,  constant 
[ratio  of,  224-6 
why  based  on  distance,  196 
Receipts    per  head    by  sections, 
[♦103-5,  ♦lis  & 
Reconnaissance,  art  of,  831,  21 
conditions  of  success,  22 
maps,  ose  of,  836-7,  934 
rule  for  choosing  grades,  675 
descend 'g  into  valleys,682 


Rec- R  is 

Reconnaissance — Continued. 
to  be  of  line,  not  area,  835 
worst  errors  orig'te  in,  832 

Refrigerator  cars,  dimens.,  etc.,. 

1*487 
Renewals,  p.c.  of,  etc.,  frt.  cars, 

\q.v.,  *\t^Si. 

loco.,  q.v.,  ^145-7  &  [•255 

Rensselaer  &  Sarat.,  align't  stat.. 

Rental,  pd.  by  fixed  charges,  106 

Repose,    grade    q.v.    of,     def'n, 

[341  & 
Rest,  friction  q  v.  of,  920 

Restaurant  and  compet.  traffic,  73 

Retaining  walls,  Colorado,  697 

and  improving  old  lines, 

[8o» 

indic'g  on  profile  934 

Return  grades,  q.v.,  for  Tt  t tains, 

[612 -f 

Return  tracks,  indep't,  693-4 

Reventon  tunnel,  etc.,  668 

Revenue  and   minor  details,  rel. 

[imp'ce,  397 

effect  of  location  on,  48      [*64 

moving    stations   on, 

more  dist.  on,  *229 

from  through  traffic,  q.v.,di- 

[vision  of,  218 

increase  of,  effect  on  profits 

[in& 

more    important    than 

[low  exp..  Ill 

pass,  and  frt.,  sections,  U.  S., 

[etc.,  *92-94 

per  head  by  States,  ♦go.  *io4 

sections,  U.  S.,  etc.,  *89. 

law  as  to,  716-7 

per  mile  road,  sec  s  U.  S.,  ^89 

States,  U.  S.,  *9o 

small  p.c.  decisive  to  proper- 

[ty,  62,  7» 

THEORY  OF   GROWTH  OF,  708 

Revenue  train  mile,  av.  cost,  ♦179. 

difficulty  of  est'g,  103 
Revere  disaster,  254  [*4i4 

Reverse-lever,  loco.,  q.  v.,  wt.,. 
Reynolds,  Lieut.,  ascent  to  Ori- 
r,.  .  [zaba,  927 

Rhigi  r'y  and  Mt.  Wash.,  690 
Rhode  Island:  area,   popu.,  sid- 
ings,  p   c.  opg.  exp.,  earnings 
per  mile  and  head,  ♦go;  wealth 
per  cap.,  ^26 
Rhode  Island  Loco.  Works,  incr. 
o-  u     .,         [wt.  eng.  i5yrs.,  ^466 
Richardson  bal.  slide-valve,  532 
Richelieu  River  disaster,  254 
Richmond    &    Danville,    align't 
„.  [statist.,  *264 

Richmond,  F.&  P., align'tstafist., 

[♦264 
Ricour,  M.,  est.  value  reducing 
[grades,  ^576 
tram-resist,  tests,  527 
Ridge  and  valley  lines,  836  & 

low,  loc'g  over,  ex.,  66i  -{■ 
Ridge  line,  eye  fixes  on,  842  -f- 
Right  of  way,  folly  of  economiz- 

[ing,  16,  53 

cost,  N.Y.C  and  Penna.  rds.. 

Rip-rap,  natural,  850  [^71 

Rise  and  Fall  (Chap.  IX.),  327 

a  minor  detail,  185 

and  ruling  grades,   distinct.^ 

1 327 


^m 


'm9,im'*iwys 


974 


RIs-Rol 

Kise  and  F&U—CoMiiaued. 
as  modi  tied  by  speed,  347 
amount  of,  est'jf,  366,  374 
limits  of  choice  narrow, 

{188 
measured  by  no.  breaks, 

[384 

rys   and    States,    U.    S., 

[•259  -f 

classes  of.  defs.,  330,  374 

cost  of,  375  [injur's,  385 

concentrated  r.  and  f.  less 

CONCHrsiONS,  382-3 

as  aff'd  by  rate  grades,  581 
iron  and  steel  rails,  380 
loco,   reprs.,   small  effect 
[on,  ♦188 
foot    of.  defined,  374 
limits  of  classes,  366,  356 
class  A,  365  -f 
class  B,  363 

class  C,  369   [grade,  375-7 
incl's  whole  rgth 
under     various- 
conditions,  *372  I 
most  imp't  to  frt.,  354  -|- 
relative  importance,  185.  395-}-  I 
sags  and  summits,   different 
[effect,  363* 
speed  in,  #367 
•train-foot '  of,  582 
what  constitutes,  366     [of,  682 
"Rivers,   descending   into   valleys 
est'g  fall  of,  840 
grade-lines  over,  893 
Road  and  equipt.,  cost,  U.  S..*io7 
Road-bed   and   track,   cost,  U.  S. 
[sections,  *i28,  *7i 
cost  as  aff'd  by  rad.  of  curves, 
rise  and  fall,  381    [639 
proper  width  of,  772 
rel.  cost,  833 
Robinson,  S.  W.,  expts.  on  bridge 
[vibration,  44/ 
Rochester  &  Pitts'g,  sidings,  total, 
Buffalo  yd.,  821  [*82s 

Rochester  &  St.  L.,  align't  statist.. 
Rock,  estimating,  897  [*259 

indic'g  on  profile,  934 
testing  for,  893 
Rock  cuts,  needless,  867,  868 
shallow,  881 
on  contour  maps,  877 
Rocky  Mountains  &  rough  coun- 
align't  in,  2,  265  (try,  840 

Rocky  points,  decept.  effect,  836, 
„    ,  [842  +,  848 

Rod,  extended  by  vel.  of  car,  ex., 

[345 
Rogers  Loco.   W'ks,    catalogue, 

[422 
Roller  jour,  bearings,  value,  012, 

Kolling  country,  illusions  as  to, 
r,  „.  locating  in,  661  [849-50 
-Kolhng-friction,    ^.v.,  def'n,  493, 

as    affected     by    coupled 
[wheels,  534-5 
computing  trom   I'ds 

[hauled,  444 
constit.  elements,  505 
effect  like  a  grade,  343 

on  pusher  grades,  597  — 
higher  in  winter,  314 
(Srg  Train  Resistance.) 


INDEX. 


Rol-Sax 

Rolling-load,  diags.  of,  769 

effect  on  wt.  bridges,  767 
Rolling-stock,  485  {See  Car,  Loco.) 
per  mile  U.  S.,  •47 

foreign,  +43 
rel.  cost,  833.  71 
trunk  line,  maint.  exp.  34 
[years,  *i29 
Rome,  W.  &  Ogd.  align't  statist.. 

Roof,  car,  cost,  etc.,  ♦163,  *2o4 
Rough  country  and  grade  con- 
.  [tours,  877 

a  relative  term,  840 
errors  in,  843  &        [849-54 
for  foot-travel,    illusions, 
two  prelims,  in,  865 
Roumania,  locos.,  no.  and  work 

Round-house  reprs.  p.  c,  *  145-6, 

Route,  choice  of,  favored  by  sharp 

[curves,  656 

ONE    GBNRRAL     RULE    FOR, 
[660  & 

easier  with  sharp  curves, 

[698 
to  be  studied  as  a  whole,  665 
Ruling  grades,  q.v.^  and  minor 
.      .  [det'ls,  185 

Running    at  grades,  804  & 
{See  Virtual  Profile.) 
Running-gear,  cars,  rel.  cost  of, 

[*i6i-4 
p.  c.  due  var's  caus.,  *203 
loco.,  q,v.^  cost  new,  details. 


INDEX. 


975 


Sca-Slo 

Scales  of  maps  should  be  large,  884 

small  scales,  use  of,  665  & 
Scenery,  ex.  of  imp't'ce,  678  & 
Schools  and  churches,  U.  S.,value, 
Science  and  Art.  831  [♦25 

Scientific  skill,  marvellous  feat  of^ 

Scott,  Gen.,  route  of,  in  Mex.,  928 

Scrap  credits,  loc.  amt.  of,  *i46  9, 

cars,  details.  *2C4        [♦412 

value  of  rails,  allow'g  for,  122 

Searles,  W.  H.,  train-r,   formula, 

[517 
Section  hands,  limit  to  reduc'n,  199 
Sections,  length  of,  126 

as  affected  by  curvat're,  321 
Selling  price  of  commodities,  how 
Selling  transp'n.  48  -f    [fixed,  196 

and  whims  of  buyer,  52 
Semmering  ry.  profile,  698 
Sharpsville  ry.,  loco,  perf 'ce,  *438 
Shinn.  W.  P..  paper  by,  •7,9 
Shipping,  U.  S.,  value,  *25 


[* 


I 50-1-2-4-5 


repairs,  ♦144-9 
p.  c.  due  various  causes, 

Russia,  locos.,  no.  &  work  of,  *  160 
pop'n,  r'ys,  wealth,  etc.,  •27, 

rolling-stock,  traffic,  etc.',  *43 

Safety,  as  affec.  by  centrif.  force, 

,r>     ^  [etc.,  300 

{See  Curvature,  Grades.) 
Safety-guard  for  bridges,  900 
Sags  and  hydr,  grade-line,  625 
and  summits,  diff.,  367 

vert,  curves  on,  363 
extreme  example  of,  625 
increase  speed.  366-7,  623 
on  grades  and  levels,  366 
safe,  limits  of,  356 
taking  out  on  old  lines,  806 

TO  OBVIATE  ALL  DANGER  FROM, 

why  admissible,  623  [363 

example,  623 

(See  Rise  and  Fall.) 
St.  Gothard  r'y.  location  of,  671 

and  prairie  lines,  est'g  betw'n, 
St.  Louis  grain  rec'ts,  728        [858 

terminals  at,  70 

train  speed  to,  6«;o  [*264 

St.  Louis  &  S.  E.  align't  statist,, 
St.  Louis  &  S.F.,  loco,  perform 'ce, 

[*438 
St.  Paul,  Minn.  &  Man.,  financial 

Q.     A     e*     .  ^.  t^l'S^'y*  *37-38 

band,  effect  on  adhesion,  g.v.,  437 

use  of,  and  rail-wear,  380 

Saving  per  year,  aggregating  $1 

[at  given  dates,  *82 

Saxony,  cost  r'ys,  etc.,  '45 


"  Shoo-fly"  line,  860 
Shop  and  gen'l  charges,  loco.  q.v. 
[maint.,  *i45,  *i54 
English,  133 
Short-haul  traffic,  ^.r.,  and  conve- 
[nient  depots,  57 
Short  line,  moral  effect  of,  239 
trunk  line,  value  of,  728 
law  as  to,  219 
{See  Distance.) 
Side-hills,  illusions  as  to,  850  & 
Side-hill  lines,  culverts  on,  851 

prelim,  ests.  of,  897 
Sidings,  amt.  at  Boston,  *823 
Buffalo,  *82i 
New  York.  *8i9 
and  trunk  lines,  law  as  to,  825 
classes  of,  *82i 
for  pusher  grades,  599 
p.  c.  of,  sections  U.  S.,  *88 
Side-track,  taking,  and  imp't  old 

c-  ,  u.  .  .  [lines,  791 
bignal  cabins,  interlocking,  q.v., 
c,         .  ,,  [sizes,  809 

Silver,  in  world,  etc.,  929 
Silver  Plume,  spiral  at.  680 -f 
Sixth  Ave.  Elev.  ry.  curves,  646 
Skill,  marvellous  feat  of,  932  [359 
Slack  in  couplings,  q.v.^  amt.  of, 
Burlington  tests  of,  490 
effect  of,  359 

import 'ce  of  eliminat'g,  487  & 
Sleeping-cars,  dimens.,  etc.,  ^gi 
English,  ^gi 
whyr  so  freely  used,  567 
sections  in.  ♦491 
Slide-valve,  balanced,  532 
description  of,  457 
friction  of,  532 

life  of,  420  \q.v..  284-6 

Slipping  of  car-wheels  on  curves, 

amt.  due  to  flange  press., 

error  as  to,  287  [294 

vel.  of,  on  curves,  ^289 

of  drivers,  446,  797 

and  skill  of  eng'r,  406 
coeffs.  of  fric,  435 
if  begun,  continues,  285 
must  not  be  too  easy,  406 
no  fault  in  fgt.  eng.,  406    •* 
Slope-level,  use  of,  882         [842  & 
Slopes,  rate  of,  eye  exaggerates, 
smooth,  meaning  of,  843 


Smi-Spa 

Smith,  C.  A  ,  loc.  expts.  by,  445 

tables  from.  468 
Smithville-N.  Y.  traffic,  718,  729 

-Jonesburg,  etc.,  729 
Snow  and  ice,  accid'is  irom,  *247 
cost  due  to,  126 

storms,  as  cause  of  accid't,  255 
Soft-steel   rails,  q.v.^  error  as  to, 

e    -I  ti2i 

Soil,  layer  of,  and  rough  country, 

[840 
South  America,  Am.  Iocs,  in,  422 

rollin<;  slopes  in,  844 
South  Australia,  rolling-stock  per 
.    y,  [mile,  *47 

South  Carolina,  alignm't  statist., 
♦263;  area,  popu.,  sidings,  p.c. 
of  op'g  exp.,  earnings  per  mile 
and  head,  ^90;  wealth  per  cap., 
♦26 
Southern  Pacific,  accident  on,  949 
align't  statist.,  ♦265 
long  grade  on,  *7oo 
miles  and  earnings,  •719 
:Southern    States,  align't  statist., 

[*263 
area,  popu.,  sidings,  p.c,  opg. 
exp.,  earnings  per  mile  and 
head,  etc.,  *9i 
bonds  and  stock  per  mile,*io7 
curvature,  etc.,  in,  263 
earnings  per  mile,  etc.,  *io7-8 
fall  rivers  in,  841 
fr't.  earn.,  thro.  &  local,  *23i 
gen'l  ry.  statistics,  *89-9o 
growth  ry.  system,  *44 
haul    and    train-load,    etc., 

,      ^    [*97i  217 
mam  results  op'n,  *93 

maint.  way  exp.,  details,  *i28 
mineral  devel't,  effect,  616 
opg.  exp.  and  traffic  details, 
[*89-93.  *  1 70-6 
p.    c.   pass,   and   Ir't.    traffic, 

[*i8i 
switching-mileage,  *i8i 
rects.  per  inht.,  pass,  and  fr't, 

[* 104-5 
rolling-stock  per  mile,  *47 
ton-mile  rects.   and  haul,  ♦us 
train-Id.   and   haul,    fr't    and 


[pass  ,  *97.  *2i7 
triangular  course  of  traffic,6i5 
wealth  per  cap.,  *26 
South-western  States:  area,  popu., 
sidings,  earnings  per  mile  and 
bead,  etc.,  *9i 
freight  earnings,  through  and 
[local,  *23i 
general  r'y  statist.,  88 
haul  and    train-Id.,  etc.,  *97, 
main  results  op'n,*93        [*2i7 
maint.  way  exp.,   details,  *r28 
op'g;  exp.  and   traffic   det'ls, 

[♦170-6 
p.  c.  pass,  and  fr't  traffic,  ♦181 

switching-mileage,  ♦181 

rects.  per  inhabt.,  pass,  and 

[fr't,  ♦104-5 

ton-mile  rects.  and  haul,  ♦115 

train-Id.  and  haul,     fr't    and 

-     .  ,        [pass.  ^97,  *ai7 

^pain,  p.  c.  op'g  expenses,  ♦no 

popu.,  r'ys,  wealth,  etc.,  ^27, 

[*43»  *45 
rolling-stock,  traflSc,  etc.,  ^43 


Spa-Sta 

Spalding,  E.   C,  on  car    rep'rs, 

[161 
Specie  U.  S.,  value,  *25 
Speculative  interest,  nature  of,  29 
Speed  and  adhesion,  435 

and  centr'f  force.  ^270 
and  curvature,  268 

diff.  much  or  little,648 
very  sharp,  326 
and  curve  resist,,  305 
and  fr't  loc.  cyls.,  474 
and  heavy  grades,  169 
and  pass,  traffic,  645 
corresp'g  to  time  over  293', 

[♦795 
elevated  r'y  sp.,  648 
effect  on  locos.,  ^476  -^      [579 

TO  REDUCE    PASS.    GRADES, 

to  reduce  grades,  limit, 

[592 
extreme  examp.  of,  625 

fluctuations    of,   in    practice, 

[*46i 
testing  locos,  by,  792 
freight,   and    improving   old 

xt      r  u   *        [lines,  804-7 
English,  ^132 


maximum,  368 

safe  assump'sas  to,  371 

tendency  to  high,  369,  488, 

I.-   ..  [804 

high,  economy  of,  488 

has  caused  large  boilers, 

highest,  Engl.  &  Am.,i529 
tendency  to   use   higher, 
[488,  804 
increased  by  sags,  q.v.,  366-7 
limits  of  objectionable,  *27i-3 
lowest,  at  summits,  353 
loss  of,  from  stop,  274 
on  max.  grades  slow,  622 
pass,  and  fr't  (also  above),  268 
vel. -head  due  to,  ^335 
why  higher  in  Engl'd,  *53o 
Speed-gauge,  injurious  effects  of 

Sphere,    rolling   of,  and    flange- 

c.   ■    ,      ,  [wear,  308 

Spirals,  classes  of,  679 

def.,  and  advantages,  681 

examples  of,  682-4-6 

St.  Gothard  r'y,  671 

series  of.  684 

typical,  679 
Split  stringers,  etc.,  900 
Sprague,  F.  J.,  tests  on  elev.  r'y, 

Springfield,  O.,  loc'n  N.  Y.,  K& 

c     .  [O-  at,  56 

bprings,  car,  compression  of,  272 
by  vel.  of  car,  ex..  345 

loco.  wt.  and  cost,  ♦413  -f 
Stable  equilibrium  on  truck,  282 
Stage-coach  measures    necessary 

[fav.,  52 
Starting,  effect  slack  on,  490 

effect  to  cut  down  trains,  44a 

fric,  q.v.,  journal,  512 

grades  for,  needed,  512 

greatest  trac'n  req'd  for,  474 

locos.,  how  done,  797 

loco,  breakages  from,  ^419 

on  elevated  r'y,  +559 

on  switchback,  947 

pass,  trains,  406 


Sta-Sti 

Starti  ng — Conthi  ued. 

resist,  of,  910. 
{See  Stations,  Stop,  Virtual  Pro. 

file.) 
State  r'ys,  projecting,  20 
Station  (100  ft.),  length  on  slopes, 

Q.  »•  L*34i 

Stationary  engines,  comp.  econo- 

[my  for  planes,  688 

cost  and  eff'y.  ♦531 

loco,  an  equiv't  for,  492 

Stationery  and  printing,  cost,  U. 

[S.  r'ds  and  sects.,  *i7o-9 

Station,  etc., expenses,  abstract  of. 

as  affected  by  dist..  206      [118 

no.  trains,  568 

English,  828 

Stations,  area,  etc.,  N.  Y.,  ♦819 

asst.  engs.  at,  599 

correcting  grades  at,  790.801-3 

cost,  N.  Y.  C.  &  H.  R.,  ^71 

curve  compens'n  at,  633 

diffic'ties  in  moving,  786 

elevated  r'y,  ^559 

effect  on  grade  resist.,  347 

est'd    effect    removing    from 

grades  at,  512  [towns,  ^64 

and  loco,  design,  475 

and  pass,  tr'ns,  491 

growth  of  towns  to,  71 

large,  switch-eng.  as  pushers 

neatness  of,  649  [at,  792 

on  grades,  moving,  803 

on  summits,  and  virt'l  prof., 

[80s,  807 

RULE  FOR   LOCATING,  63,  791  -}- 

virtual  grades  at,  704   791  -j- 
Station  supplies,  cost,   ids.   and 
[sects.,  U.  S.,  ♦170-9 
Stay-bolts,  wt.,  etc.,  in  boilers, 

[*4" 
Steam,    expansive    energy    only 

[used,  457 
lbs.  per  H.  P.,  av.  loc,  451 

theoretical,  ^460  [^454 

wt.  and   heat,  various  press, 
wt.  in  loco.  q.v.  boiler,  ^454 
Steam-boats,  full  stroke  eng.  for, 

o  ^  [*46o 

Steam-chest  and  boiler  press,  473 
Steam-engines,cost  and  eff'cy,^53i 
lead  and  lap,  defin.,470 

Kerfect,  eff'cy  of,  ^460 
liss'pi  river,  ^460  [457 

uses  expansive  energy  only, 
working  full  stroke,  *458 
{See  Stationary,  Loco.) 
Steam-pipe,  loco.,  size,  *409 

wt.  and  cost,  ^412  4- 
Steam-ports,  losses  by,  470 -f- 
Steam-press,  boiler  and  effective. 


English,  ^132 


[*479 


H.  U.  due  to  various,  ^450 
little  effect  on  economy,  473 
theoret.  gain  by  higher,  *468 
Steam-shovel,  working  with,  cost, 

[etc.,  773 
Steel-rail,  q.v.,  per  cent  of.  sec- 
_       ^  [tionsU.  S.,^88 

Stephenson,  G.,  and  link-motion, 

Steubenville,  O.,  tunnel  at,  240 
Stevens,    A.    J.,   inv.    Mastodon 
o  .«  l°c.,  423 

Stiffness,  cost  of  and  wt.   rails, 

[7391  *74i 


wSt 


976 


INDEX. 


INDEX. 


reps. 


203 


Sto-Sur 

Stock  and  bonds  p.  mile,  sections. 

,  .        .  [U.S.,  ♦107 

nuct nations  in  price,  ^e 
nature  of,  29 

per  mile  r'y  and  head,  U.  S., 

watering:,  nature  of,  32      [*88 

Stock  cars,  dimens..  etc.,  *486-7 

Stopping  and  starting,  i^.7/.,acci- 

[dents  from,  *246 

at  grade-crossings,  ^.z/.,  810  & 

loss  by,  810-12 
effcft  on  car  and  eng, 
fuel  burned  for,  200 
Stops,  cost  of,  810 

heavy  trains,  600 
effect  on  grade  resist.,  346 

virtual  profile.  q.7>.,  350-2 
no.  of,  Mich.  C.  R.  R.,  136  & 
on  max.  grades,  effect,  623 
on  pusher  grades,  596 
power  lost  by,  200,  ♦335 
time  lost  by,  201,  274,  595 
Stop-watch  and  loco,  tests,  794 

cost,  etc.,  796 
Storage  sidings,  q.v.,  ♦821 
Stores,  loco.,  7.7'.,  cost,  *i47  & 
Storms  and  structures,  781 

great  ones,  local,  782 
Strategic  advantages,  effect   on 
-,.  ,     ,  [rates,  218,  241  «& 

Streams,  est'g  fall  of,  840 
grade  lines  over,  893 
mental  map  of,  836  «& 
Street  accidents  and  r'y,  257 
Street  r'ys,  cable,  690 
traffic  of,  N.  Y.,  ♦714 

per  inhab't,  ♦714  [*739-42 
strength,  cost  of  and  wt.  rails, 
Stroudley,  Wm.,  loc.  tests  by,  451, 
_  [460 

Success,  conditions  of,  i,  8,  840  — 
Summits,  false,  836 

gravity  r'y  seeks,  692 
high,  ascending  to,  925,  943 
may  cost  little,  590 
often  wise  to  go  to,  590 
lowest  safe  speed  at,  353 
normal  types,  689 
leading,  of  world.  *698"9 

of  Colorado,  696  -}- 
not    always    control  grades, 

[675  - 
not  always  governing  point, 

[670 
passmg.  by  cable  tract'n,  889 

RULE    lOR    PASSING,  66o 

Store  power  in  train,  692 
station,  q.v.^  on,  and  virtual 
[profile,  g  v.,  805,  807 
Sun,  why  larger  on  horizon,  845 
Sundays    disappearing   from  r'y 

[serv.,  97 
tram-work  on,  169 
Superelevation,  298  -f 

common  error  as  to,  301 
effect  of,  271 

on  curve  resist.,  298 
on  position  wheels,  300 
on  safety,  ^00 
lateral  force  from,  298 
on  tang.,  possible  effect,  911 
Surfacing.     {SeeTr^cV.)         [4-5 
Surplus,  fluctuations  in,  etc.,  33- 
Surveys,  care  q.v.   in,  and  amt. 
[curv.,  q.v.,  656* 
compass  lines,  863 


Sur-Tax 

Surveys— Ct>«//««tf</. 
field-work  of,  860 
location  line,  866 
no.  successive  lines,  834,  860 
organization  of  party,  867 
paradox  as  to  time  on,  856 
saving  needless  work,  871-2 
should   start  with  no  curve- 
[limit,  654 
when  to  make,  856 

how  to  determine,  857 
Susquehanna,  grades  at,  619 

river,  fall,  841 
Sweden,  popu.,  r'ys,  wealth,  etc., 

„.  .  f*27.  *43.  *45 

rolling-stock  and  traffic,  *43 
Swing-motion  truck,  q.v.,  def'n, 
objection  to,  428  [426 

Switchbacks,  684,  943 

aut.  switches  for,  946 
best  for  great  inclines,  943 
germ  of  true  plan,  945 
good  loc'n  for,  ex.,  68a 
grades  for,  947 
Peruvian,  685-6,  699 
vs.  spirals,  682-4-6 


977 


Tables— Index  bv  Number: 


Swi-Ten 

Switches,  derailing,  8n 

misplaced,  derail'is  from,  245 
Switching,  accidents  in,  *i46 
slipping  drivers  in,  446,   797 
terminal  charges  for,  156  & 
Switching  engines,  descnp.  and 
as  pushers,  600  [use,  424 

est  d  av.  prop'n  of,  156,  182 
mileage  allowance  fur,  156 
Switchmen,  at  stations,  791 
Switching  mileage,  how  cxagg'd, 

[103 

prop'n  of  English,  135 

sections,  U.  S. 

Switzerland  locos.,  no.  and  work 

high  loc.  press.,  ♦519  lot,  •i6o- 

pop'n,  r'ys,  wealth,  etc.,  *27, 

Syracuse,  B.  &  N.  Y.,  alignment 

[statist.,  *259 

Syracuse,  Gen.,    etc.,    alignment 

.  „       ,  [statist.,  *2sa 

Systfeme  Richenbach,'  690 
Systems  of  rys,  all  lines,  parts  of, 

great,  of  U.  S.,  ♦719 


*Mit  P-  77  *i68t,  P-  539 


tS^f^^  ^""^  '°**"'^  ^^  ^"^^^^"^  ^^  prefixing  a  *  to  the  page  refer- 

Tabor  grade,  +699 
Talcott.  A.  H  ,  &  Mex.  Ry.,929 
Tangent,  breaking  sixty-mile,  663 
desirable  length,  324  [330 

long,  bad  practice  as  to,  324, 
sharp  curves,  q.v.,  lengthen. 
Tank  engines.  424  [641 

as  assist,  eng.,  592 
comparative    power     on 
[grades,  ♦557-8 
why  advantageous,  554 
{Sre  Tender.) 
Taunton  Loco.  W'ks,  increase  wt. 
[engs.,  35  y'rs,  ^ee 
1  axes,  cost  of,  sections  and  r'ds, 
[U.  .S.,  ♦170-9 
as  affected  by  dist.,  206 


Tehachapi  accident.  949 
Tenders  (builders'  rule  for  total 
[weight,  20  lbs.  per  gall,  water.) 
cost  of,  new.  *564-5 

detaiks,  *i5o-i-2-4-s 
and  weights.  •412-4-6 
cost  repr's  of.  det's,  *i43-9 
English,  144-6 
French.  147 

p.  c.  cost  of  eng.  r..  144 
cost  renewals,  146  & 
due  various  causes,  ^203 
for  switching-engs.,  434 
life  of,  ^419 

tires,  cost  of.  •149  [♦407-16 
WTs.  AND  CAp'v,  all  eng., 
whcel-ba.se,  all  eng.,  *^cj  10 


v 


'} 


Tel-Tir 

relegraph.cost  of,  r'ds  and  sect'ns 

[U.  S.,  *i7o.9 

of  U.  S.,  value,  *25  ^    ^ 

offices,     and     improv'g    old 

[lines,  803 

stations  and  asst.  eng.,  601 

Temperature  and  H.  U.,distinc'n, 

and  radiation,  314  L*454 

changes  of,  in  cylinders,  q.v., 

[376 
effect  on  coeff.  fric,  ♦sos 

fuel  consump.,  136-7 
train  resistance,  506 
summer  and  winter,  314 
Temporary  lines,  advantages  of, 

[16,  86,  766 
B.&0.,^7oo 
ex.  of  proper  use,  277,  654 
for  light  r'ys,  750 
sags,  q.v.,  in,  624-5 
examp.,  625-6 
Tennessee:    align't  statist.,  *264; 
area,   popu.,  sidings,  p.  c.  op'g 
exp.,     earnings    per    mile    and 
head,  *9o;  wealth  per  cap.,  *26 
Tennessee  pass.  Col.,  *7oo 
Tepetate.  def'n,  683 
Tepic,  location  at,  675  ■^- 
Terminals  (Chap.  XXVI.),  818 
allowances     on     rates,    q.v., 
and  curvature.  655  [156  & 

expenses,  N.  Y.,  etc.,  ^819 

European,  827 
for  light  r'ys,  749 

{food,  imp'ce  of,  768,  68 
ocat'n    and   cost  of,  various 
[cities,  68-70,  818-27 
must  be  near  largest  cities,  727 
rel.  no.  of.  on  trunk  lines,  729 
Terre  Haute  &  Ind.  loco,  perf'ce. 

[*438 
Terre  H.  &  S.  E.  align't  sut.,  ♦261 
Texas:  area,  pop'n,  sidings,  p.  c. 
opg.  exp.,  earnings  per  mile  and 
head,  *9o-  wealth  per  cap.,  ^26 
Texas  Cent*!,  align't  statist., ^265 
Theis  r'y,  Austria,  est.  for  wtes 

[on,  198 
Thompson,  J.  E.,  on  incl.  planes, 

[944 
Throttle,  loco.,  ^.r.,  effect  of  clos- 

[ing,  473  & 

'Through  '  traff.,  q.v.,  true  clas- 

effect  dist.  on,  215     [sif'n,  211 

rates,  q.v.,    constant  ratio  to 

[local,  224-6 

Thurston,  R.  H.,  fric.  tests  by,  504. 

^.       .  [9184- 

Time  in  seconds  and  speed  trains, 

[*795 
Time,  effect  on  car  and  eng.  reps., 

[♦203 
loss  of  by  reduc'g  sp'd,  595 

est'g  IMPOR-rCE  OF,  649 

on  curves,  ^647  -f- 
round  trip  per  day  limit, 

[649 
of  descent  on  grades,  theory 

[of,  624 
Time-tables,  fr't,   how  arranged. 
Tires,  accidents  from,  *247       [102 
life  of,  420 
maint.  of,  ♦149-I- 
mileage  of,  ♦149-^- 
price.  Am.  and  Eng  ,  +416 
w't  and  cost,  ♦413  ■+■ 

62 


Tod-Tra 

Todhunter's  math'l  series,  331 
Toledo  grain  rec'ts,  728 
Ton  (in  this  vol.  2000  lbs.  or  *  net,' 
[unless  otherwise  stated.) 
Ton-mile,  cost  increasing  grades, 


rates,  q.v, 
E.  & 


,  Am 
W., 


[q.v.,  per,  *574 


&  Eng.,  *i59 
through    and 
[local,  *2i6  & 
through  and  local,  12  y'rs, 

[C,  C,  C.  &  I.,  *224-5 

15  years,  L.  S.  &  M.  S., 

L*226 

rec'ts,  exp.,  etc.,  large  table, 

[*'i5& 
varying  cost  of,  est'g,  198 

Topographer,  frequent  errors  of, 

1       needs  practice,  885  [884 

outfit  of,  882  [867 

Topographical  party,  organiz'n. 
Topography  (mapping),  873 

colored,  873 

CONCLUSION  AS  TO,  88o 

contours,  q.v.,  873 

dangers  ot,  ex.,  881 

double  use  of,  876 

field-sheets  for,  886 

inking  in.  888 

large  scales  best,  884 

plotting,  883 

sh'd  be  taken  in  field,  88a 

taking  topog.,  881 

over  areas.  684  & 
use  and  abuse  of,  873 
"  (physical    geography),   adapt'g 
[low  grades  to,  665 
and  bal.  of  grades,  614 
and  curve  compens'n,  628 
and  transition  curves,  869 
curvature  bunched,  622 
curve  limit  may  be  easy,  655 
effect  insuffic't  study  of,  583 
effect  on  use  of  curves,  635 
fitting  curve  comp'n  to,  »63o 

GENERAL  LAW  AS  TO,  586 

law  of,  as  to  changes  of  level, 
in  easy  country,  660  [+588 
mountain  foot-hills,  937 
no  country  difficult,  832,  840 
often  favors  low  grades.  670 
Peruvian,  679-!- 
rough,  light  lines  in,  832  & 
Tourist    travel,    ex.    of    imp'ce, 
^  [678  & 

Tower,  B.,   fric.  tests  by,  504  -f-. 

Towns,  effect  not  running  to,  on 

[rec'ts,  49 
eifect     of     removing    station 
[from.  64 
growth  of,  to  stations,  ^.7/.,  71 
location  of  stations  at,  *64 
moving  to  r'ys,  66 
often  hard  to  approach,  859 
passing  lines  between  two,  67 
passing,  to  save  dist.,  q.v.,  58 
should  be  entered,  16 

RULE   AS  TO,  63 

Track,  accidents  from,  ^246 

cost  of,  U.   S.   sections.  ♦28,1 
labor,  cost  of.  123  [*  170-6 

relation  to  traffic,  123 
as  aff 'd  by  curvature,  321 
min.  limit  to,  199 
not  exactly  as  dist.,  199 
reduction  difficult,  126 


Traffic 

Track  labor — Continued. 

requirements    for    emer- 

[gencies,  126 

vs.  heavy  rails,  758 

maint'ce,  cost  of,  U.  S.  rds. 

[and  sects.,* 1 20,*  170-6 

as  aff'd  by  no.  of  trains, 

radius  of  curves,  639 
rise  and  fall.  381 
wt.  locos.,  561 
relatively  to  oihtr  items, 

[833 
Trackmen  flatten  P.  C.'s,  275 
Track-walking,  cost,  126 
Traction,  stores  force  in  train,  342 
Traction-increaser,  404 
Tractive  force  and  energy,  con- 
[fusion  as  to,  473 
and  H.  P.,  403 
Trade,  universal  law  of,  55      [733 
Traffic,  additional,  relative  cost, 
anthracite  west,  609 
disproportion  of,  608 

TABLE    OF    GRADES   FOR, 
[612 

daily  fluctuations,  6ii 
effect  on  curve  limits,  652 
effect  to  change  cost 
[transp'n,  198 
into  cities,  heavy,  617 
P.  R.  R.,  35  years,  etc., 
[♦232,  *2l6& 

ratio  of  E.   &  W.   trunk 

[lines,  609 

variable    on    same    road, 

.        .  [609-f 

estimaling,  95-99 

exchanging,   and     narrow-g., 

[753 
export,  grows  relatively  less, 

[615 

GEOMETRIC  EFFECT  OF  INCRHAS- 

[iNG,  708 

getting  all  there  is.  53 
growth  of,  depends  on  facili- 
[ties,  71S 
does  not  help  poor  lines, 

[227 
effect  on  car  rep'rs,  166 
loc.  exp.,  158 
maint.  way,  123-7 
effect  to  reduce  exp.,  114, 

,  ,  ['53 

law  of  growth,  75 

statisiicsof  C.,B.  &  O-.tst 

C,  C.  C.&  I.,  216 

C.&  N.  W.  35 

English,  *79,  *i3i-2 

Iowa,  *77 

L.  S.  &  M.  S.,  *98 

Mass..  78 

New  York  City.  *7i4 

P,   R.    R.,    35    years, 

[*I40,  *23!» 

sections  U.  S.,  *io7-8 

THEORY  OF  GAIN  BV,  708 
TO    BE    CONSIDKRED     ONLY 
FOR   3  TO   5  YEARS,  80.  85 

when  to  choose  line   for, 

[583 
handling  by  trains,  169 

importance  of  increasing,  107 
increases  with  facilities,  76 
interpolating  way,  effect,  ♦/ij 
not  a  monoDoly,  52 


97S 


INDEX. 


INDEX. 


I 


Traf-Train 

Traffic — Continued. 

pass.  p.  c.  local,  through,  etc., 

gain  from  many  trains,  06 

p.   c.  pass,  and   fr't.   sections 

(U.  S..  ♦181 

prop'n  affec'd  by  grades,  576 

regular  and  occas'l  rates,  con- 

[trast,  235 

!        securing,  the  most  imp't  end, 

[193  & 
slight  diffs.,  great  effect  of, 

[62 
through  and  local,  confusion 
[as  to,  211 
triangular  course  of,  608,  615 
true  classification,  212 
trunk  line,  a  v.,  rules  for,  731 
unequal,  balance  grades,  q.v.^ 

[for,  608 
table  of,  *f)ii 
volume  of,  and  cable  trac'n, 

[687 
and  long  inclines,  950 
and  wt.  Iocs.,  567 
estimating  probable,  75 
of  world,  *i6o 
statistics  of,  L.  S.  &  M. 
[S.,  q.v.,  ^99 

n-     a.         ^-  ^-  R-.^-^'-.  etc.,  ^232 
1  ramc-points,  and  branches,  734 
dist.  betvv'n,  eff't  on  earngs, 

CAIN  BY  MORR,  708  [709 

great  and  small,  diff.  in  grth. 

Train  accidents,  q.v.,  causes.  •246 

Train  expenses,  amt  ,  133,  •170-9 

definiiion,  117 

Train-load.  Am.  and  foreign,  575 

and  fuel  consump.,  134 

as  aff'd  by  car-couplings,  566 

disprop.  of  traffic.  100 

grades,  q.v.,  536  & 

av'ge  frt.  and  pass,  .sections, 

[U.  S.,  *2i7,  *97 
and  p.  c.  local,  334 

effect  on  expenses,  560 

fuel  consump.,  •136 

English  coal  trains,  ♦132 

FOR    ALL    GKAOES     AND     LOGS., 

/J  ^      ._.  V  f*543  -1- 

(condensed  table),  593 

frt.,  sections,  U.  S.,  ♦iis  Sl 

growth  of,  ^97,  •q8,  *99.  ♦100. 

f*ioi,  ♦135  & 

pass..  U.  S.  and  States,  *97-8 

does  not  regulate  number 

[trains,  96 

less  with  thin  traffic.  99 

r.    C.    CHANGE   DUK   TO   CHANGK 
[grade,    554-7 

p.  c.  to  Wt.  eng.,  ail  grades, 

.     .  f669 

relative,  on  high  grades,  *669 
why  cut  down  in  winter,  508 
Train-mile,    coal     burned,     135, 

[140  & 
cost,   maint.  way  per,  U.  S. 
[sections,  *i28 
cost  of,  av'ge  u!  S.,  *i79  — 
British,  ^79,  *i78 
trunk  lines,  34  yrs.,  ♦129 
how  made  low,  ♦181 
on   lines  of  diff.   grades, 
tendency  in,  n6  [583 

unimportance  of,  187  j 


979 


Trains 

Train-mile— G>«//««<r</. 

earn'gs  and   exp.,  U.  S.  r'ds 
[and  sees.,  *  170-9,  ♦98 
maint.  way,  constant  per,  127 
ratio  of,  to  eng.  mile,  *i45 
Train  resistance,  492 
air,  £.».,  amt.,  911  & 
as  affected  by  gauge,  753 
temperature,  508  — 
virtual  profile,  q.v.,  346 
axle,  effect  size  of,  513 
freight,  496 

CONCLUSIONS,  502 
main  elements,  pio 
recent  decrease  in,  504,  515 
summer  and  winter,  503-6 
grade  of  repose,  q.v.,  def.,  341 
head  q.zt.  resistance,  522  — 
locomotive,  q.v.,  530  [918 

lubrication,  import,  of,  509  -}-, 
oscillation  and  concuss'n,  911 
passenger,  518  -f- 
starting,   q.v.,  •512,  ♦srg 
subdivisions  of,  493 

table  of  CONCLUijiONS,  *524 

tests  as  to,  •465.  *498  -f ,  •909  & 
velocity  resist.,  493.  517-8 
wheel,  effect  size  of,  513 
Train  rules,  and  imp't  old  lines, 

T         •  w  .    .  [791 

1  rains,  breaking  in  two.  358,  488 
centre  of  gravity  in  sags,^^.?'., 

descending   grades,    vel.    of, 

[♦37a 
fastest,  Engl,  and  Am.,  *529 
handling  heavy,  easier  here- 
[after.  488 
frt.  speeds  to  be  higher, 
[488,804 
safe  assumptions  as  to, 
on  old  lines,  788  [370 

length  of,  and  vertical  curves, 
{q.v.,  364 
and  crossing  stops,  Sia 
and  curve  comp  n,  634 
effect  on  curve  resist.,  301 
shorter  in  winter,  315 
making  up,  effect  on  loc.  and 
[car  rep'rs,  *203 
yard-room  for,  *82i  & 
motion  of,  and   Newton's  ist 

.     .        ,         J 'aw.  342 
and  virtual  profile,  q.v., 

effect  of  speed,  q.v.,  on, 

,  I331 

no.  of,  cost  increasing,  same 

[traffic.  568 

effect  on  rev.,  568      [*574 

for  same  traffic,  all  grades, 

VALtiB     OF     AVOIDING      IN- 

[crkase,  574 

overturning  by  cenirif.  f..  270 

pass.,  effect  grades  on.  577 

growing  wt.  of,  effect,  491 

reason  for,  567 
wt.  of  fast  tr'ns.  530 
per  day,  always  means  each 

K    .K        ^  , [way,  97 

best  basis  for  est  g,  95 
elev.  r'ys,  646 
Philad'a,  69    [♦128,  ♦170-6 
U.  S.  and  States,  etc.,  *97, 
rights  of,  774      [increase,  369 
speed,  q.v.,  of,  frt.,  tends  to 


Tra-Tru 

Trains — Continued. 

wt.  of,  as  affected  by  grade*, 

long  table  of,  *544  [♦688 

,        p.  c.  wt.  eng.,  all  grades. 

Tram  supplies,  cost  of,  rds.  and 

^     .  [sects.  U.  S.,  •170-Q 

Train  wages,  q.v.,  168 

as  affected  by  distance,  206 

length  trains,  568 
cost  of.  Chicago  rds.,  *i74-6 
sections  iT.  S.,  ♦170-6 
trunk  lines,  •172-6 
mode  of  fixing,  205 
Transfer  side  tracks,  q.v.,*^7\  [888 
Transit,  graduating  compass  of, 

vs  compass  lines,  863 
Transition  curves,  869 

examples  of  use,  870  -^-,  684 
projecting,  892 
reasons  for,  275 
Transit  party,  organiz'n,  867 
Transit  work,  860  -+- 

doing,  by  bearings,  888 
Transportation     expenses,    cost, 
[Chicago  rds.,  ♦174-6 
sections  U.  S.,  ♦170-6 
trunk  lines,  ♦lya-e 
manufacture  of,  48 
Trautwine's  pocket-book.  331 
on  kindling  fires,  ♦aoo 
Trestles,  iron,  design  of,  ooo 
ht.,  small  effect  of,  90a 
prelim 'ry  est's  of,  900 
wt.  of,  901 
wood,  cost  of,  and  grading, 

cluster  bent,  900 
design  of,  899,  770 
floor  for,  000 
on  light  rVs,  754 
plan  for.  770 
proper  use  of,  754,  768 
prelim,  est's  of ,  899 
rerailing  guard  for,  900 
Tnapgular  course  of  traffic,  6154. 
.  trips  of  cars,  608      [341.538  + 
Triangle,    right-angled,    solving. 
Tributary  valleys,  q.v.,  good  use 
Trieste  r  y,  prohle,  698      [for,  68a 
Trucks,  accidents  from.  ^246 
Am.  origin  of,  421 
Bissell,  426-30 

frt.    car,  cost  and   deprec'n, 
[items,  ^163,  ♦204 
dimens.  and  wt.,  ^163,  ^486 
loco.,  need  for,  425 

Eony,  426 
anics  of  rolling,  281.  425 
pass,  car,  dimens..  etc.,  491 
position  taken  on  curve.  282 
swing  motion,  objection    to. 

Trunk    lines    and  branch  lines, 
bal.  grades  on.  618  [707 

comparative  earnings.  737 
competitive   and   non-cbmp., 

[718,  723 

CONDITIONS  OF  SUCCESS,  73I 

curves  on,  lost  time  by.  648  & 
fall  of  rates  on.  20  y'rs,  ♦726  ± 
good  condition  pays.  276 
lengths  of.  to  Chicago,  240 
maint.  cars  exp..  34  y'rs.  ♦tag 
maint.  locos,  exp.,  34  y'rs,  ^129 
maint   way  exp.,  34  y'rs,  ♦129 


Tru-Uni 

V.'jnk  \\nc%— Continued.  [^719 
miles  and  earnings.  14  U.  S., 
op'g  exp.    and  traffic  det'ls. 

[•172 
p.  c.  opg.    exp.,  law  as   to, 

[109-10 
effect  rates  on,  320 
sidings,  law  as  to,  825 
termini,  q.v.,  reached  by,  729 

N.  Y.,  etc.,  818 
ton-mile  rec'ts,  etc.,  ♦iis 
traffic,  daily  fluct'ns  in,  6ia 

changes  in, 609 
train-l'd  and  growth,  ♦loo 
train  mile,  cost,  ♦116 
use  too  light  rails,  760       ['204 
Trusses,  fr'i-car,  cost  and  depr'n. 
Tubes,  loco.,  ^.r.,  life  of,  ^420 
Tunnels,  spiral,  671  -f,  679, 684,  700 
unnecessary.  242 
wrong  use  of.  ex.,  667 
Turkey,  pop'n,  r'ys,  wealth,  etc.. 

Tutor,  natural  end  of,  and  culv'ts, 

[781 
Tyrone  &  Clearfield  grades,  ^700 

Uetliberg  r'y,  impercep.  slip  tests, 

Ulster  &  Del.  align 't  statist.,  ^259 
*  Uncle  Dick  '  consol'n  loco.,  w  t, 

[etc.,  421 
Undergrowth,  deceptive  effect  of. 

[836 
from  clearing  up  do..  850 
Undulating  grades,  q.ri.,  &  imp'g 
[old  roads,  799 
curves  Iquiv't  to,  633  — 
eliminated  by  speed,  347 
error  as  to,  329 
putting  into  harness,  692 
Unearned  increment.  32 
Unfamiliar,  eye  deceived  by.  843-f- 
Union  Pacific,  align't  statist., ♦ads 
cost  loco,  rep'rs,  142 
flucts.  in  stock,  ^46 
miles  and  earn'gs,  ^719 
handling  trains  on,  255 
spiral  on,  680  -f- 
Uniied   Kingdom :    progress    r'y 
constr.,*44;  pop'n,  r'ys,  wealth, 
etc..  ^27,  ♦43.  ^45;  rolling-stock, 
traffic,  etc  .  ^43 

{See  Great  Britain.) 
United  R.  R.  N.  J.,  trains  &  fuel 
[consump.,  ^138 
United  States,  cost  r'ys,  etc.,  ^45 
future  r'y  construc'n,  ^41 
growth  of  r'ys,  ♦42-4  [fr't,  ^97 
haul  and  train-l'd.  etc.,  pass.  & 
locos.,  cost  and  miles  per  y'r, 
miles  per  year,  ^97     [^159 
no.  and  work  of,  ^160 
main     results      op'n       r'ys, 

[1871-85.  ^94 
no.  trams  per  day,  etc.,  ^97 
opg.  exp.  and   traffic  details. 

••^♦170-76 
r'y  statists,  by  sects.,  *88  & 
rates,  ^.v.,  of  r'y  divi'ds,  ^41 
ton-miles  per  car.  '97 
train-load,  etc  ,  ^97 
wealth  of.  ^25-78 

by  States.  ^26  [tries,  *27 
comp.  with  other  coun- 
pop'n,  cost  r'ys,  etc.,  ^27 


Unl-VIr 

Unloading  plough,  use  of,  773[59o 
Unnecessary  reouire'ts,  loss  by, 
Utah  :  area,  pop'n,  sidings,  p.  c. 
opg.  exp.,  earnings  per  mile  and 
head,  ♦oo;  wealth  per  cap.,  *26 
Utah  &  No.,  align't  statist.,  ^265 
Uiica  &  B'lk   R.,  align't  statist., 

1*259 
Utica,  Ith.  &  El.,  align't  statist., 

[*2S9 

Vacuum  brakes,  q.v.,  max.  eff'y. 

Valley  lines  and  inundations,  783 
and  overlaps,  848 
descend  into  ag'st  slope,  682 
ex.  of  line  in,  693 
gain  by  following,  586 
nigh-water  in.  850 
Nature  makes  fills,  850 
penetrate  far  into  m'ts,  586 
recon'tring,  errors  in,  844-!- 
rough  foot  travel,  848,  850,  855 
tributary,  use  of,  682 
undergrowth,  etc.,  836 

Valuation  of  States,  total  and  per 

[cap.,  ^26 

Valve-gear,  loco.,  q.v.,  458 

Velocity  acquired  on  grades,  ^372 
and  work,  interconvert  ,  ex., 

composition  of,  ex.,  387 
due  to  any  h't,  ^333 
effect  of,  on  grades,  q.v.,  703 
effect  on  train  q.v.  resist.,  346 
law  of,  and  trains,  331 

Velocity  train  q.v.  resistance,  517 
tests  of,  910 

Velocity-head,  def'n,  333-5 
and  brakes,  q.7'.,  494 
computations  by,  357  ±, 

[519 
due  to  all  speeds,  ♦sss-s 
Vera  Cruz,  Jalapa  q.v.  line  from 

[925 
Vermont:  area,  popu.,  sidings,  p. 
c.  opg.  exp.,  earnings  per  mile 
and^head,  ♦90;  wealth  per  cap., 
♦26 
Vernier,  graduating,  888 
Vertical   curves,  deviation   from 
[intersec.  grades,  ^388 
effect  close  coupler,  365 
need  for,  363 
rationale,  360 
rules  for  projecting,  385 
safe  rule  for,  365 
TO  LAV  OUT,  387 
'  Vertical  plane '  couplers.  489 
Viaduct.  Baranca  Blanca,  678 
estimating,  900 
indicating  on  profile,  934 
two-story.  683-4 
weights  of,  901 
Victoria,  rolling-stock  per  mile, 

[*47 

Vignoles,  C.  B.,  on  minor  details, 

[187 

Virginia:  alignment  statist.,  ♦263; 

area,  popu.,  sidings,  p.  c.  opg. 

exp's,    earnings  per  mile  and 

head,  ^90;  wealth  per  cap.,  ♦ae 

Virginia  &  Truckee,  align't  sta- 

[tist.,  +265 
Virginia    Central,  sharp    temp'y 
[curves,  ♦325 


Vir-Way 

Virtual  profile,  346,  799  [70a 

and  cent.  grav.  of  train, 
and  curve  comp'n,  621  -f- 
as  aff'd  by  length  grade, 

[704 
by  stops,  352 
cautions  as  to,  353 
down  grade,  q.v.,  369 
effect  on  pusher  grades,5o$ 
ex.  of  use,  631,  701 
frt.,  computing,  352     [35,3 
need  not  be  continuous, 
of  long  grade,  355 
of    old     lines,    constr'g, 

....  t794-8 

on  switchbacks,  948 
pass.,  computing,  347  -f 
summit  speeds,  805,  807 
Visible  defects  most  dreaded.  24a 
Von  NSrdling,  W..  est.   of  cost 
[transp'n,  198 
Von  Weber,  on  curve  resist.,  307 

Wabash,  St.  L.  &  P.,    financial 

[status,  41 
miles  and  earning^,  ^719 
Wages,  American,  143,  170-9 
Amer.  and  English,  ♦417 
as  aff'd  by  pusher  engines,  671 

by  rise  and  fall,  381 
engine,  past  tendency  of,  156 
English,  ♦is^ 

shop,  English  and  Amer.,  ♦151 
train,  168,  205 
train  and  telegraph,  803 
Wasen,  spirals  at,  673 
Washing  out  boilers,  q.z'.,  ♦420 
Washington  Terr.:  area,  popu., 
sidings,  p.  c.  opg.   exp.,   earn- 
ings  per  mile    and    head,  *9o; 
wealth  per  cap.,  ^26 
Washouts,  accidents  from,  ♦247 
and  structures,  78a 
and  valley  lines,  783 
derailments  from,  245  [19 

Waste,  avoidance  of,  benefits  all. 
Watchmen,  loco.,  cost  of.  *t47 
Water,  amt.  used  per  mile,  ♦sig  & 
distances  across,  est'g,  845 
entrained,  ^456,  ^470  -f- 
potable.  etc.,  purity,  ^378 
Water-courses,    mental   map   of, 

[836  & 
•  Water-falls '  of  lava,  928 
Water-grate,  wt.,  etc.,  ♦41a 
Watering  stock.  3a 
Water-power.  U.S..  rep't  on,  841 
value  of.  ^25 
in  Mexico,  678 
Water-scoop,  cost  new,  ♦isi 
Water  supply,  loco.,  amt.  used, 156 
cost  of,  147,  170-9 
cost  and  distrib.  of,  156 
in     loco.      q.v.     boilers, 
quality,  ♦378  [♦41S-6 

effect  on  tire-box,  ^420 
Water-tanks,  spacing  of,  156  [893 
Water-ways,     grade-lines     over, 
Way-freight  and  grades,  577 

av.  load,  etc..  wi  [o^  54 
towns,  competing  for  traffic 
traffic,  and  curvature,  242 

EFFECT  ON   REVENUE, 70S 

.    securing  by  distance,  237 

RULE  AS  TO,  238 

ex.  of  error,  928 


gSo 


INDEX. 


Wea-Wes 

Wealth  of  all  nations.  ♦27 
of  U.  S.,  ♦as  ^ 

per  capita,  *a6 
U.  S.  States,  ♦ae 
growth  of,  26-7  [aay 

u°*!  "?t  help  poor  lines. 

w.iSf •■  if*'''  ^-  ^-  ^y  States,  ♦ae 
weDcr,  Von.  maint.  way  tests.  42* 

tram-resist,  formula,  517 
W-est  Alabama,  loco,  perform'ce. 

Western  &  Atl'c,  car  repairs*J5! 
^[full  details,  ♦161-2-3-4 
Western  Pa.,  align't  statist..  •260 
Western    States,    align't    statist 

1*263 


bad  location  in,  6,  21,  330,  sSS^ 
•       .  [660 

bonds  and  stock  per  mile,  'iot 
compar  ve  accidents  in,  252 
curvature  in,  263 
earnings  per  m.,  ♦loy 
disirib'n  of,  ♦108  [♦23, 

freight  earn.,  thro'  and  local, 
grade  and  curve  limits  in,  6, 

„.^A  ■    f^'.'  330,  588,  656 

grade-crossings  in,  809 
growth  r'y  system,  ♦44 
heavy  grades  in,  ♦263 
main  results  op'n,  *93 
rec'ls  per  inhab't,  pass,  and 

rolling  slopes  in,  844 
rolling-stock  per  mile,  47 
tram-load  and  haul,  frt.  and 
[pass.,  *2i7 
growth,  *ioi  ' 

weahh  per  cap.,  26 
West  Md.,  loco  perf'ce.  ^ag 
West  Shore  r'y..   an  example  of 
[wrong:  judgment,  707 
bridges,  specirns  for,  003 

weights  of,  767 
double-track  on,  766 


Wes-Woo 

West  Shore  ry— Continued. 
history  and  cause  failure.  724 
locos,  and  Howard  Fry,  ♦409 
dimens'ns,  etc..  *407-9 
load  on  drivers  per  sq.  ft 

sidin,^s,  total,  *825^'''''*^^^ 
stand  d  box- car,  *486 
»«™'l  exp.,  etc.,  N.  Y.,  •810 
track  Buffalo  yd.,  *82i 
Wetherill,  W.  C.,reporito,94i 
Westinghouse    brake,  q  v.,  max. 

Westinghouse.    G.,     Ixpu^' 1?„5 
Wheat  rate,  effect  long  "^haS' on! 

Wheel-base  and  curve  resist.,  3^° 
oco..  fv.,  all  types,  *407-4,o 
long,  effect  on  wheels,  283 
position   of   trucks,  f.v.,   on 

wu     1  [curves,  q.v.,  282 

Wheel  covers,  loco.,  *4,5        * 
Wheels.    (Ser  Car  Wheels,  etc.) 
Whims,  affecting  traffic,  52-1 

Wh.neryC,  paper  by,  3^6^ 
Whistle,  loco,  cost,  »4i2 
Wilmington     and     No.,    align't 

Mr-  ^     ^  [statist.,  *26o 

Wimmer,  S.,  &  Mex.  r'y.nag 
Winans,    R.    M.,    invented  Am. 

Wind,  accidents  from,  ♦247     * 
and  bridges,  902 

A.r-  ^*J-  °^'  *"**  ^'■ain  tests.  708 
Wire-drawing,  loco.,  q.v.,470-^ 
Wisconsin:  align't  statist.,    *263- 
area,  popu.,  sidings,  p.  c.  op'e 
exp     earnings    per    mile    and 
xxi^^^°'  *9o;  wealth  per  cap.  +26 
Wisconsin  Cent,  train-Id.  growth. 
Wood  as  fuel,  139  [♦,01 

for  kindling.  amt.,*200 
H.  U.  m,  *45o 


Woo— Zam 

Wood,  early  exp'u  ty,  on  adhe- 
Woodbury.  C.  J.  H..fric.^St"s^: 
Wooden  structures,  right  use°*o^ 

Work  and  force,  .338.  4];'' "''''' 
Work  and  vel.,  inierconrert,  ex.. 

how  destroyed,  332  '  ^°^ 

how  expressed,  338 
World,  popu.,  rys,  wealth,  etc., 

[*27,  *43.  *45 


r'y  system  of,  ^a-s 

rel.  traffic  of,  •160 

wealth  of,  *27 

Wurtemberg,  cost  r'ys.etc,  ♦45 

Wyommj::  area,    popu.,  sidings, 

P*  5  i-*^P  F  ^*P '*»'■'*' "Rs  per  mile 
and  head,  *go;  wealth  per  cap., 

Yon  Bait.  &0.,  279  " 

Yards  of  cloth,  selling  less,  49 
Yards,  asst.  engs  q.v.,  at,  599 
classes  of  sidings  for,  ♦821 
greatest  in  world,  822 
N.  Y  terminals,  q.v.,  ♦819 
N.  Y.  7-s.  Buffalo;  823 
often  near  bad  grades,  600 
operaiinjr  of,  810 
slipping  drivers  in.  797 
standing  idle  in.  cost,  6o» 
Yard-work,  effect  on  loc.  and  car 

Youghiogheny  r'y,  loilf^'rf'ce^ 

Zacatecas,  long  grade  at,  ♦700  *^ 
Zangronez,  R.,  4  Jalapa  line,  9,0 
^ero   temperatures    and    dynam, 
1-  .       .  [tests,  50S 

Zigzag  developments,  def.,  678 

example  of,  932 
Zimilihuacan,  barranca  of,  94a 
Zamora,  location  at,  7aa 


ADVERTISEMENTS. 


i< 


AD  VER  TISEMENTS. 


George  Westinghouse,  Jr.,  president. 

C.  H.  Jackson,  vice-president. 

Chas.  R.  Johnson,  signal  enq.  and  gen.  manager. 


Robert  Pitcairn,  treasurer. 
Asaph  T.  Rowan  d,  secretary. 
Henry  Snyder,  gen.  agent. 


SIGp  CO. 


SOLE  MANUFACTURERS  OF  APPROVED 

RAILROAD  SIGNALLING  AND  SWITCHING  APPLIANCES. 

Plans  and  Estimates  and  all  particulars  promptly 
furnished  on  application. 


Spals  for  Switdies,  Grade  Crossioffs,  Joodis  aad  Termioals. 

FEBFECT  ZNTEBLOCEING  AND  AUTOUATIC  BLOCK  SIGNALS. 


OFFICE  AND  WORKS : 

S  "^V I  S  S  "^  .^^  X.  E 


NOTE    CHANGE   OF  ADDRESS. 

"Western  Agent,  H.  H.  McDTJPPEE,  Home  Insurance  B-ailding,  Chicago,  111. 


II 


AD  VER  riSEMENTS. 


THE 


208  South  Fourth  St., 

PHILADELPHIA. 


OFFICES 


J 


2  Wall  St.,  cor.  Broadway, 

NEW  YORK. 


Works   at   STEELTON,  PA. 

MANUFACTURERS  OF 


RAT 


f^i4,    .!;  ^'  "^"^'^  *"''  '■'=''"•  '"  fi'  »»  P='"'">s  of  Rails. 
SIEEL  BLOOMS.  FORGINGS.  and  MERCHANT 

BARS  of  Open  Hearth  or  Bessemer  Steel. 

Capacity  over  400,000  Gross  Tons  of  Steel  per  Annum. 

STEEL    RAIL 
FROGS 

Of  all  the  Standard  Patterns,  with  various  improvements  of  importance 

suited  to  all  conditions  of  service  ' 

SPIIT  SWITCHES 

AND  IMPROVED 


SAFETY  SWITCHES, 

OF  MANY  IMPROVED  PATTERNS. 


SWITCH   STANDS  AND    FIXTURES.    OF  ALL  KINDS. 


This  Company  has  the  createst   capacity  in  the  United  States  for  the  pro- 
duction   of    FROGS     SWTTrwp'c     *,  j    •     •  .  ^ 
nualifv       All         1          ,^^^^^"E^'    &c.,    and    invites    attention    to  prices   and 
quality.     All  work  made  interchangeable,  and  true  to  standards. 


AD  VER  TJSEMENTS. 


lU 


Established  1831. 

m 


Mill 


L 


Annual  Capacity,  600. 


i\ 


m 


ii±  \)  i 


I  lEIS, 


E 


BUENHAM,  PAREY,  WILLIAMS  &  CO., 

T^roprietfyrSf 


Broad  and  Narrow  Gauge  Locomotives, 
Mine  Locomotives, 

Plantation  Locomotives, 

Compressed  Air  Locomotives, 
Logging"  Locomotives, 

Tramway  Motors  and  Steam  Cars. 


ALL  IMPORTANT  PARTS  MADE  TO  STANDARD  GAUGES 

AND   TEMPLATES. 


Me  B^rts  of  different  Enlnes  of  saie  clas^  perfectly  interrli?npalile. 


f, 


AD  VER  TISEMENTS. 


IV 


j.-  •  -  -  -  --wsi \ 


253'--. 


F.  ANDERSON. 


THE    ATCHAFALAYA    BRIOOf. 


C.  C.  BARR^ 


ANDERSON  &  BARR, 

Engineers  and  Contractors. 

Address   S40    Kleventli    Street,   JTerse.r    City^ 


mfiYrir^r^irrfy[i-tTVi'irrf|iir-' 


:^-::^-'l 


:■.'•'/  ".> 


^•.•vV*ivv»>': 


^-HuoaoM  Rivera  tunneu'-.^*"^ 


TUNNELLING  THROUGH  •ILT. 


Pneumatic  Work,  Deep  Foundations,  and  Tunneling  in  Soft  Materials.     Con- 
trol the  Patents  for  the  Automatic  Dredge  and  the  Anderson  System  of  Tunneling. 

The  following  Works,  among  others,  have  been  executed  by  the  present  firm 
of  Anderson  &  Barr,  and  will  show  the  wide  range  of  their  experience. 


Atcha/alaya   Bridge. 

Pneumatic  Cylinders  and  Dredges. 
Little  Rock,  Ark.,  Bridge. 

Pneumatic  Caissons. 

Seekonk  River  Bridge,  Providence,  R.  I. 
Cylinders  sunk  by  Dredges. 

Fourteen-Foot  Light  House,  Delaware  Bay. 
Pneumatic  Caissons,  53  feet  below  water, 
ao  miles  from  nearest  land. 


Chestnut  Street  Bridge,  Philadelphia,  Pa. 

Oblique  Pneumatic  Cylinders. 
Main  Sewers,  Brooklyn,  N.  Y. 

4,000  feet  of  i2-ft.  tunnels  through  sand. 
Ha7vkeii>ury  Bridge,  Australia. 

Open  Caissons,  sunk  170  feet  below  water^ 
by  Dredges. 
Harlem  Riv^r  Bridge,  New  York  City, 

PnetMnatic  Caisson,  54x104  ft. 


AD  VER  TISEMENTS. 


EDGE  MOOR  IRON  CO., 


—DESIGN  AND  MANUFACTURE- 


RAILWAY 


BRIDGES,  VIADUCTS,  AND  ROOFS, 

IN   STEEL   AND    IRON. 


Tension    Members  Forged  without    the  addition    of 
extraneous  Metal,  and  without  Welds,  Piles  or  Buckles. 

Compression    Members   manufactured    by   Processes 
which  insure  an  entire  absence  of  constructional  strains. 


WROUGHT-IRON    TURN-TABLES, 

With  Centres  of  Conical  Steel  Rollers  and  Steel  Plates. 


GALLO^WAY    BOILERS 

Giving  Greatest  Safety,  Economy  and  Durability. 


Main  Office,  Edgemoor,  on  Delaware  River. 

POST-OFFICE,  WILMINGTON,  DEL. 

Philadelphia  Office,  1600  Hamilton  St 

WM.  SELLERS,  Presideni.  GEO.  H.  SELLERS,  Gen.  Supt. 

JOHN  SELLERS,  Jr.,  Vice-Pre»idenf.  WM.  F.  SELLERS,  Secretary. 

WM.  H.  CONNELL,  Treasurer. 


VI 


ADVERTISEMENTS. 


SAMUEL  M.  DODD.  Pretidenf. 
JOHN  B.  GRAY,  Vice-President. 


E.  L.  AOREON,  Sec'y  end  Treei^ 
GEO.  H.  POOR,  8upt. 


American  Brake  Company, 

NEW   YORK    OFFICE,   160   BROADWAY. 

JOHN  B.  GRAY,  Vice-President. 
MANUFACTURERS  OF 

AUTOMATIC    FREIGHT   CAR   BRAKES   AND    STEAM 
DRIVER  AND  TENDER  BRAKES, 

ST.    LOUIS,    MO. 

We  offer  to  Railway  Companies  the  only  Exclusively  Independent  Self-Actin^ 
Freigh  1  ram  Brake  which  has  yet  been  adopted  by  any  Railway  in  the  work? 
•Our   Steam  priver   and    Tender    Brake    is   acknowledged    to   be^the  Che^oest 

RaTroads"^  '''^''^  "^^'^   ^"'^  "°"  '''   "^^-      ^^   ^^  ^^^   by  250  diffeS 


THE      NEW^ 

"IRON  CLAD"  FIBRE  TRACK  WASHERS. 

Perfected  ly  Ten  Years'  Experience. 

Surpassing  all  other  Lock-Nut  devices  in  I>nrabiIUy. 
Eflectivene»8  and  Cheapness.  Strengthened  and 
protected  from  the  weather,  cannot  be  crushed,  or  burst, 
will  not  lose  their  elasticity,  nor  rot.  Adapted  for  both 
plain  and  angle-bars. 

Price,  only  S18.00  per  Thousand. 

They  also  absolutely  protect  the  threads  on 
the  bolts  from  becoming;  chafed,  and  permit 
old  bolts  to  be  utilized  upon  ivhlch  the  threads 
have  become  battered. 

NEW  YORK  OFFICE  : 

ISTo.    15     Dey    Street. 

mmm  fibre  CO,  WjIniiDgtoD,  Dei 


AD  VER  TISEMENTS. 


▼u 


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THE  BEST  AND  MOST  PRACTICAL  WORK  ON  EARTHWORK 

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By  A.  M.  Wellington.  M.  Am.  Soc.  C.  E. 


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Vol.  II.— Plates,     3.50  j 


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Gives  quantities  on  inspection  to  the  nearest  cubic  yard  for  both  regular  and 
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dmsion  Very  simple  in  use.  Contains  a  discussion  on  the  theory  of  he  Pr^ 
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« 


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3a 


GUSTAV    LINDENTHAL, 

CIVIL    ENGINEER, 

Pittsburg,  Pa. 


SPECIALTIES— Diflacult    Foundations,   Long-Span 
Bridges,  and  all  Jron  and  Steel  Constructions. 


LEWIS  M.  HAUPT,  A.  M.,  C.  E., 

Professor  of  Civil  Engineering,  University  of  Pennsylvania,  Philadelphia. 


AUTHOR    OF 

"ENGINEERING,  SPECIFICATIONS  AND  CONTRACTS," 
"THE  TOPOGRAPHER:  HIS  INSTRUMENTS  AND  METHODS," 
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reliable  tests  of  materiak.     Address,  J.  B.  JOHNSON, 

Prof,  Civil  Engineering  and  Director  of  Laboratory. 

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AND  IMPROVEMENT  OF  RAILWAYS. 

Room  97  TRIBUNE  BUILDING,  NEW  YORK  CITY. 


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Business  Manager. 


Engineering  News  is  a  weekly  record  of  all  important  engineering  works 
projected  and  in  progress.  It  discusses  fully  and  carefully  all  problems  con- 
nected with  such  works  as  they  arise.  It  is  especially  full  in  relation  to 
matters  connected  with  Surface,  Cable  and  Elevated  Railways,  Water  Works  and 
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and  is  growing  with  great  rapidity.  Its  proprietors  aim  to  make  it  the  leading 
engineering  journal  of  the  world,  as  the  character  and  extent  of  its  field  de 
mands.  The  cooperation  of  all  engineers  is  asked  to  this  end,  especially  in  the 
following  : 

t^r- INFORMATION  AS  TO  NEW  WORK,  and  technical  descriptions, 
photographs  and  drawings  of  NEW  DESIGNS  of  merit  for  all  engineering 
details,  LARGE  OR  SMALL,  are  always  wanted  for  early  publication. 

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END  OF 

TITLE 


